------------------------------------------------------------------------------------------------------------------------------------------------------
name: STATA_Chapter10b
log: C:\Dropbox\PilesOfVariance\Chapter10b\STATA\STATA_Chapter10b_Output.smcl
log type: smcl
opened on: 30 Jan 2015, 12:19:45
.
. display as result "Chapter 10b: Descriptive Statistics for Time-Varying Variables"
Chapter 10b: Descriptive Statistics for Time-Varying Variables
. summarize symptoms posaff
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
symptoms | 2752 1.660974 1.42964 0 5
posaff | 2747 2.580269 .7319597 0 4
.
. display as result "Ch 10b: Empty Means, Single-Level Model for the Variance for Symptoms"
Ch 10b: Empty Means, Single-Level Model for the Variance for Symptoms
. display as result "Independent Observations"
Independent Observations
. mixed symptoms , ///
> || personid: , noconstant variance mle covariance(unstructured) ///
> || burst: , noconstant covariance(unstructured),
Note: all random-effects equations are empty; model is linear regression
Mixed-effects ML regression Number of obs = 2752
Wald chi2(0) = .
Log likelihood = -4888.0461 Prob > chi2 = .
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1.660974 .0272473 60.96 0.000 1.60757 1.714378
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
var(Residual) | 2.043128 .055079 1.937978 2.153984
------------------------------------------------------------------------------
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -4888.046 2 9780.092 9785.456
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estimates store FitEmpty1S,
.
. display as result "Ch 10b: Empty Means, Two-Level Model for the Variance for Symptoms"
Ch 10b: Empty Means, Two-Level Model for the Variance for Symptoms
. display as result "Sessions Within Burst*Persons"
Sessions Within Burst*Persons
. mixed symptoms , ///
> || personid: , noconstant variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3886.2366
Iteration 1: log likelihood = -3886.2366
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(0) = .
Log likelihood = -3886.2366 Prob > chi2 = .
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1.66991 .057583 29.00 0.000 1.557049 1.78277
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: (empty) |
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | 1.424997 .1010434 1.240101 1.63746
-----------------------------+------------------------------------------------
var(Residual) | .6302559 .0186331 .5947736 .6678549
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 2003.62 Prob >= chibar2 = 0.0000
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3886.237 3 7778.473 7786.52
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat wcorrelation, covariance,
Covariances for personid = 101 burst = 1:
obs | 1 2 3
-------------+------------------------
1 | 2.055
2 | 1.425 2.055
3 | 1.425 1.425 2.055
. estat wcorrelation,
Standard deviations and correlations for personid = 101 burst = 1:
Standard deviations:
obs | 1 2 3
-------------+------------------------
sd | 1.434 1.434 1.434
Correlations:
obs | 1 2 3
-------------+------------------------
1 | 1.000
2 | 0.693 1.000
3 | 0.693 0.693 1.000
. estimates store FitEmpty2S,
.
. display as result "Eq 10b.5: Empty Means, Three-Level Model for the Variance for Symptoms"
Eq 10b.5: Empty Means, Three-Level Model for the Variance for Symptoms
. display as result "Level-1 Sessions Within Level-2 Bursts Within Level-3 Persons"
Level-1 Sessions Within Level-2 Bursts Within Level-3 Persons
. mixed symptoms , ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3762.2643
Iteration 1: log likelihood = -3762.2643
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(0) = .
Log likelihood = -3762.2643 Prob > chi2 = .
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1.704674 .1063595 16.03 0.000 1.496213 1.913135
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.077332 .169218 .7918629 1.465713
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .4255335 .0403582 .3533497 .5124635
-----------------------------+------------------------------------------------
var(Residual) | .6304876 .0186414 .5949896 .6681033
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2251.56 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3762.264 4 7532.529 7543.257
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat icc,
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid | .5049946 .0412796 .4246583 .5850739
burst|personid | .7044617 .0245813 .654126 .7502685
------------------------------------------------------------------------------
. estat wcorrelation, covariance,
Covariances for personid = 101 burst = 1:
obs | 1 2 3
-------------+------------------------
1 | 2.133
2 | 1.503 2.133
3 | 1.503 1.503 2.133
. estat wcorrelation,
Standard deviations and correlations for personid = 101 burst = 1:
Standard deviations:
obs | 1 2 3
-------------+------------------------
sd | 1.461 1.461 1.461
Correlations:
obs | 1 2 3
-------------+------------------------
1 | 1.000
2 | 0.704 1.000
3 | 0.704 0.704 1.000
. estimates store FitEmpty3S,
. lrtest FitEmpty3S FitEmpty2S,
Likelihood-ratio test LR chi2(1) = 247.94
(Assumption: FitEmpty2S nested in FitEmpty3S) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Empty Means, Single-Level Model for the Variance for Positive Affect"
Ch 10b: Empty Means, Single-Level Model for the Variance for Positive Affect
. display as result "Independent Observations"
Independent Observations
. mixed posaff , ///
> || personid: , noconstant variance mle covariance(unstructured) ///
> || burst: , noconstant covariance(unstructured),
Note: all random-effects equations are empty; model is linear regression
Mixed-effects ML regression Number of obs = 2747
Wald chi2(0) = .
Log likelihood = -3040.1781 Prob > chi2 = .
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 2.580269 .013963 184.79 0.000 2.552902 2.607636
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
var(Residual) | .5355699 .0144511 .5079822 .564656
------------------------------------------------------------------------------
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3040.178 2 6084.356 6089.72
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estimates store FitEmpty1P,
.
. display as result "Ch 10b: Empty Means, Two-Level Model for the Variance for Positive Affect"
Ch 10b: Empty Means, Two-Level Model for the Variance for Positive Affect
. display as result "Sessions Within Burst*Persons"
Sessions Within Burst*Persons
. mixed posaff , ///
> || personid: , noconstant variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1987.3615
Iteration 1: log likelihood = -1987.3615
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(0) = .
Log likelihood = -1987.3615 Prob > chi2 = .
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 2.580643 .0296536 87.03 0.000 2.522523 2.638763
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: (empty) |
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3795157 .0267471 .330552 .4357323
-----------------------------+------------------------------------------------
var(Residual) | .1572839 .0046534 .1484227 .1666741
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 2105.63 Prob >= chibar2 = 0.0000
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1987.361 3 3980.723 3988.769
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat wcorrelation, covariance,
Covariances for personid = 101 burst = 1:
obs | 1 2 3
-------------+------------------------
1 | 0.537
2 | 0.380 0.537
3 | 0.380 0.380 0.537
. estat wcorrelation,
Standard deviations and correlations for personid = 101 burst = 1:
Standard deviations:
obs | 1 2 3
-------------+------------------------
sd | 0.733 0.733 0.733
Correlations:
obs | 1 2 3
-------------+------------------------
1 | 1.000
2 | 0.707 1.000
3 | 0.707 0.707 1.000
. estimates store FitEmpty2P,
.
. display as result "Eq 10b.5: Empty Means, Three-Level Model for the Variance for Positive Affect"
Eq 10b.5: Empty Means, Three-Level Model for the Variance for Positive Affect
. display as result "Level-1 Sessions Within Level-2 Bursts Within Level-3 Persons"
Level-1 Sessions Within Level-2 Bursts Within Level-3 Persons
. mixed posaff , ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1788.4815
Iteration 1: log likelihood = -1788.4815
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(0) = .
Log likelihood = -1788.4815 Prob > chi2 = .
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 2.543132 .0562298 45.23 0.000 2.432923 2.65334
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | .3162942 .0466072 .2369536 .4222008
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .0643297 .0068973 .0521372 .0793736
-----------------------------+------------------------------------------------
var(Residual) | .1573514 .0046566 .1484843 .166748
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2503.39 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1788.481 4 3584.963 3595.692
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat icc,
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid | .5879344 .0370292 .5139623 .6581367
burst|personid | .7075119 .0262848 .6534823 .7562593
------------------------------------------------------------------------------
. estat wcorrelation, covariance,
Covariances for personid = 101 burst = 1:
obs | 1 2 3
-------------+------------------------
1 | 0.538
2 | 0.381 0.538
3 | 0.381 0.381 0.538
. estat wcorrelation,
Standard deviations and correlations for personid = 101 burst = 1:
Standard deviations:
obs | 1 2 3
-------------+------------------------
sd | 0.733 0.733 0.733
Correlations:
obs | 1 2 3
-------------+------------------------
1 | 1.000
2 | 0.708 1.000
3 | 0.708 0.708 1.000
. estimates store FitEmpty3P,
. lrtest FitEmpty3P FitEmpty2P,
Likelihood-ratio test LR chi2(1) = 397.76
(Assumption: FitEmpty2P nested in FitEmpty3P) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Eq 10b.6: Saturated Means for Burst by Session"
Eq 10b.6: Saturated Means for Burst by Session
. display as result "Three-Level Model for the Variance for Symptoms"
Three-Level Model for the Variance for Symptoms
. mixed symptoms i.session i.burst i.session#i.burst, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3692.3004
Iteration 1: log likelihood = -3692.3004
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(29) = 144.50
Log likelihood = -3692.3004 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
session |
2 | -.2392776 .10628 -2.25 0.024 -.4475826 -.0309726
3 | -.1194769 .1067581 -1.12 0.263 -.3287189 .089765
4 | -.2734587 .1067867 -2.56 0.010 -.4827568 -.0641606
5 | -.2433253 .1064678 -2.29 0.022 -.4519983 -.0346522
6 | -.2812388 .1071716 -2.62 0.009 -.4912912 -.0711864
|
burst |
2 | .4505038 .1401462 3.21 0.001 .1758223 .7251854
3 | .8033019 .1411198 5.69 0.000 .5267121 1.079892
4 | .4643568 .1444304 3.22 0.001 .1812785 .7474351
5 | .4601041 .1499751 3.07 0.002 .1661582 .7540499
|
session#burst |
2 2 | -.0523891 .154464 -0.34 0.734 -.355133 .2503549
2 3 | -.0405616 .155656 -0.26 0.794 -.3456418 .2645186
2 4 | .0438753 .1586153 0.28 0.782 -.2670051 .3547557
2 5 | -.0204627 .1641928 -0.12 0.901 -.3422746 .3013493
3 2 | -.1824237 .1550723 -1.18 0.239 -.4863598 .1215125
3 3 | -.2678891 .1559832 -1.72 0.086 -.5736106 .0378324
3 4 | -.159026 .1592304 -1.00 0.318 -.4711118 .1530599
3 5 | -.0233802 .1645026 -0.14 0.887 -.3457994 .299039
4 2 | -.0915998 .155092 -0.59 0.555 -.3955744 .2123749
4 3 | -.264445 .1560026 -1.70 0.090 -.5702045 .0413145
4 4 | .1010449 .1589553 0.64 0.525 -.2105017 .4125916
4 5 | .0916405 .1645212 0.56 0.578 -.2308151 .4140961
5 2 | -.0585753 .1548726 -0.38 0.705 -.36212 .2449694
5 3 | -.412858 .1557845 -2.65 0.008 -.71819 -.1075259
5 4 | -.044031 .1587412 -0.28 0.781 -.3551581 .2670961
5 5 | .0744941 .1643144 0.45 0.650 -.2475562 .3965444
6 2 | -.094346 .1553572 -0.61 0.544 -.3988405 .2101485
6 3 | -.4072025 .1562665 -2.61 0.009 -.7134792 -.1009258
6 4 | -.2360026 .1592141 -1.48 0.138 -.5480565 .0760513
6 5 | .0214985 .1647713 0.13 0.896 -.3014472 .3444443
|
_cons | 1.563352 .1394475 11.21 0.000 1.29004 1.836664
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.109327 .1718238 .8188738 1.502804
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3739481 .0360546 .3095578 .4517321
-----------------------------+------------------------------------------------
var(Residual) | .6030572 .0178252 .5691132 .6390258
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2309.11 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3692.3 33 7450.601 7539.111
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. contrast i.session,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
symptoms |
session | 5 76.76 0.0000
------------------------------------------------
. margins i.session,
Predictive margins Number of obs = 2752
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
session |
1 | 1.985311 .1121307 17.71 0.000 1.765539 2.205083
2 | 1.731776 .11213 15.44 0.000 1.512006 1.951547
3 | 1.739471 .1121876 15.51 0.000 1.519588 1.959355
4 | 1.673612 .1121883 14.92 0.000 1.453727 1.893497
5 | 1.650119 .1121586 14.71 0.000 1.430292 1.869946
6 | 1.560679 .1122029 13.91 0.000 1.340766 1.780593
------------------------------------------------------------------------------
. contrast i.burst,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
symptoms |
burst | 4 39.10 0.0000
------------------------------------------------
. margins i.burst,
Predictive margins Number of obs = 2752
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
burst |
1 | 1.370632 .1211829 11.31 0.000 1.133118 1.608146
2 | 1.741385 .1245648 13.98 0.000 1.497243 1.985528
3 | 1.942163 .1252773 15.50 0.000 1.696624 2.187702
4 | 1.786212 .1271938 14.04 0.000 1.536917 2.035508
5 | 1.854672 .1305979 14.20 0.000 1.598705 2.110639
------------------------------------------------------------------------------
. contrast i.session#i.burst,
Contrasts of marginal linear predictions
Margins : asbalanced
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
symptoms |
session#burst | 20 26.44 0.1518
-------------------------------------------------
. margins i.session#i.burst,
Adjusted predictions Number of obs = 2752
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
session#burst |
1 1 | 1.563352 .1394475 11.21 0.000 1.29004 1.836664
1 2 | 2.013856 .1439962 13.99 0.000 1.731628 2.296083
1 3 | 2.366654 .1449415 16.33 0.000 2.082573 2.650734
1 4 | 2.027708 .1481624 13.69 0.000 1.737316 2.318101
1 5 | 2.023456 .1535656 13.18 0.000 1.722473 2.324439
2 1 | 1.324074 .1389888 9.53 0.000 1.051661 1.596487
2 2 | 1.722189 .1439962 11.96 0.000 1.439962 2.004416
2 3 | 2.086814 .1452938 14.36 0.000 1.802044 2.371585
2 4 | 1.832306 .1481624 12.37 0.000 1.541913 2.122699
2 5 | 1.763715 .1535656 11.49 0.000 1.462732 2.064698
3 1 | 1.443875 .1394419 10.35 0.000 1.170574 1.717176
3 2 | 1.711955 .1442963 11.86 0.000 1.429139 1.99477
3 3 | 1.979288 .1452938 13.62 0.000 1.694517 2.264058
3 4 | 1.749206 .1484779 11.78 0.000 1.458194 2.040217
3 5 | 1.880599 .1535656 12.25 0.000 1.579616 2.181582
4 1 | 1.289893 .139446 9.25 0.000 1.016584 1.563202
4 2 | 1.648797 .1442963 11.43 0.000 1.365981 1.931613
4 3 | 1.82875 .1452938 12.59 0.000 1.543979 2.11352
4 4 | 1.855295 .1481624 12.52 0.000 1.564902 2.145688
4 5 | 1.841638 .1535656 11.99 0.000 1.540655 2.142621
5 1 | 1.320026 .1392205 9.48 0.000 1.047159 1.592894
5 2 | 1.711955 .1442963 11.86 0.000 1.429139 1.99477
5 3 | 1.71047 .1452938 11.77 0.000 1.4257 1.995241
5 4 | 1.740352 .1481624 11.75 0.000 1.449959 2.030745
5 5 | 1.854625 .1535656 12.08 0.000 1.553642 2.155608
6 1 | 1.282113 .1396659 9.18 0.000 1.008373 1.555853
6 2 | 1.638271 .1442963 11.35 0.000 1.355455 1.921086
6 3 | 1.678212 .1452938 11.55 0.000 1.393442 1.962983
6 4 | 1.510467 .1481624 10.19 0.000 1.220074 1.80086
6 5 | 1.763715 .1535656 11.49 0.000 1.462732 2.064698
-------------------------------------------------------------------------------
. margins i.session@i.burst,
Contrasts of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
session@burst |
1 | 5 10.79 0.0558
2 | 5 15.14 0.0098
3 | 5 52.39 0.0000
4 | 5 20.88 0.0009
5 | 5 5.86 0.3203
Joint | 25 105.05 0.0000
-------------------------------------------------
. margins i.burst@i.session,
Contrasts of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
burst@session |
1 | 4 33.08 0.0000
2 | 4 30.70 0.0000
3 | 4 16.27 0.0027
4 | 4 22.92 0.0001
5 | 4 16.22 0.0027
6 | 4 13.46 0.0092
Joint | 24 65.68 0.0000
-------------------------------------------------
. estimates store FitSatAllS,
.
. display as result "Eq 10b.7: Piecewise Session Slopes by Observed Burst"
Eq 10b.7: Piecewise Session Slopes by Observed Burst
. display as result "Three-Level Model for the Variance for Symptoms"
Three-Level Model for the Variance for Symptoms
. mixed symptoms c.slope12 c.slope26 i.burst ///
> c.slope12#i.burst c.slope26#i.burst, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3697.037
Iteration 1: log likelihood = -3697.037
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(14) = 134.62
Log likelihood = -3697.037 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
slope12 | -.1903575 .0954842 -1.99 0.046 -.3775031 -.0032119
slope26 | -.020531 .0238719 -0.86 0.390 -.0673191 .026257
|
burst |
2 | .3474688 .1218054 2.85 0.004 .1087346 .586203
3 | .7011409 .1229286 5.70 0.000 .4602052 .9420766
4 | .4955777 .1256592 3.94 0.000 .2492901 .7418653
5 | .4533517 .1305669 3.47 0.001 .1974452 .7092581
|
burst#c.slope12 |
2 | -.1032867 .1386682 -0.74 0.456 -.3750714 .168498
3 | -.1024103 .1396409 -0.73 0.463 -.3761015 .1712808
4 | .0309676 .1423685 0.22 0.828 -.2480695 .3100047
5 | -.0070451 .1473099 -0.05 0.962 -.2957672 .281677
|
burst#c.slope26 |
2 | .0037424 .0347195 0.11 0.914 -.0643067 .0717915
3 | -.0880711 .0349428 -2.52 0.012 -.1565578 -.0195844
4 | -.0447939 .0355927 -1.26 0.208 -.1145542 .0249664
5 | .0179336 .036828 0.49 0.626 -.0542479 .0901152
|
_cons | 1.372849 .1308805 10.49 0.000 1.116328 1.62937
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.109782 .1719018 .8191982 1.50344
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3734815 .0360523 .3091024 .4512694
-----------------------------+------------------------------------------------
var(Residual) | .6055556 .017899 .5714711 .6416731
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2302.67 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3697.037 18 7430.074 7478.352
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. * Session 2 at Burst 1
. lincom _cons*1 + i1.burst
( 1) [symptoms]1b.burst + [symptoms]_cons = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.372849 .1308805 10.49 0.000 1.116328 1.62937
------------------------------------------------------------------------------
. * Session 2 at Burst 2
. lincom _cons*1 + i2.burst
( 1) [symptoms]2.burst + [symptoms]_cons = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.720318 .1351155 12.73 0.000 1.455496 1.985139
------------------------------------------------------------------------------
. * Session 2 at Burst 3
. lincom _cons*1 + i3.burst
( 1) [symptoms]3.burst + [symptoms]_cons = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.07399 .136132 15.24 0.000 1.807176 2.340804
------------------------------------------------------------------------------
. * Session 2 at Burst 4
. lincom _cons*1 + i4.burst
( 1) [symptoms]4.burst + [symptoms]_cons = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.868427 .1386015 13.48 0.000 1.596773 2.140081
------------------------------------------------------------------------------
. * Session 2 at Burst 5
. lincom _cons*1 + i5.burst
( 1) [symptoms]5.burst + [symptoms]_cons = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.826201 .1430637 12.76 0.000 1.545801 2.1066
------------------------------------------------------------------------------
. * Slope12 at Burst 1
. lincom c.slope12*1 + c.slope12#i1.burst
( 1) [symptoms]slope12 + [symptoms]1b.burst#co.slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1903575 .0954842 -1.99 0.046 -.3775031 -.0032119
------------------------------------------------------------------------------
. * Slope12 at Burst 2
. lincom c.slope12*1 + c.slope12#i2.burst
( 1) [symptoms]slope12 + [symptoms]2.burst#c.slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2936442 .1005567 -2.92 0.003 -.4907316 -.0965567
------------------------------------------------------------------------------
. * Slope12 at Burst 3
. lincom c.slope12*1 + c.slope12#i3.burst
( 1) [symptoms]slope12 + [symptoms]3.burst#c.slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2927678 .1018943 -2.87 0.004 -.492477 -.0930587
------------------------------------------------------------------------------
. * Slope12 at Burst 4
. lincom c.slope12*1 + c.slope12#i4.burst
( 1) [symptoms]slope12 + [symptoms]4.burst#c.slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1593899 .1056009 -1.51 0.131 -.3663639 .0475842
------------------------------------------------------------------------------
. * Slope12 at Burst 5
. lincom c.slope12*1 + c.slope12#i5.burst
( 1) [symptoms]slope12 + [symptoms]5.burst#c.slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1974026 .1121739 -1.76 0.078 -.4172593 .0224541
------------------------------------------------------------------------------
. * Slope26 at Burst 1
. lincom c.slope26*1 + c.slope26#i1.burst
( 1) [symptoms]slope26 + [symptoms]1b.burst#co.slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.020531 .0238719 -0.86 0.390 -.0673191 .026257
------------------------------------------------------------------------------
. * Slope26 at Burst 2
. lincom c.slope26*1 + c.slope26#i2.burst
( 1) [symptoms]slope26 + [symptoms]2.burst#c.slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0167886 .0252107 -0.67 0.505 -.0662008 .0326235
------------------------------------------------------------------------------
. * Slope26 at Burst 3
. lincom c.slope26*1 + c.slope26#i3.burst
( 1) [symptoms]slope26 + [symptoms]3.burst#c.slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1086022 .0255173 -4.26 0.000 -.1586152 -.0585891
------------------------------------------------------------------------------
. * Slope26 at Burst 4
. lincom c.slope26*1 + c.slope26#i4.burst
( 1) [symptoms]slope26 + [symptoms]4.burst#c.slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0653249 .0264002 -2.47 0.013 -.1170685 -.0135814
------------------------------------------------------------------------------
. * Slope26 at Burst 5
. lincom c.slope26*1 + c.slope26#i5.burst
( 1) [symptoms]slope26 + [symptoms]5.burst#c.slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0025974 .0280435 -0.09 0.926 -.0575616 .0523668
------------------------------------------------------------------------------
. estimates store FitPiecebyBurstMeansS,
.
. display as result "Eq 10b.8: Piecewise Session Slopes by Quadratic Burst"
Eq 10b.8: Piecewise Session Slopes by Quadratic Burst
. display as result "Three-Level Model for the Variance for Symptoms"
Three-Level Model for the Variance for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope12#c.burst1 c.slope26#c.burst1 ///
> c.slope12#c.burst1#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3702.5302
Iteration 1: log likelihood = -3702.5302
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(8) = 122.88
Log likelihood = -3702.5302 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .4928563 .0988198 4.99 0.000 .299173 .6865395
|
c.burst1#c.burst1 | -.0970135 .0243349 -3.99 0.000 -.144709 -.049318
|
slope12 | -.2096013 .0906799 -2.31 0.021 -.3873307 -.0318719
slope26 | -.0058096 .0226752 -0.26 0.798 -.0502522 .038633
|
c.slope12#c.burst1 | -.0701371 .1119713 -0.63 0.531 -.2895968 .1493226
|
c.slope26#c.burst1 | -.0712009 .0280099 -2.54 0.011 -.1260993 -.0163024
|
c.slope12#c.burst1#c.burst1 | .0206203 .0275953 0.75 0.455 -.0334656 .0747061
|
c.slope26#c.burst1#c.burst1 | .0174983 .006904 2.53 0.011 .0039667 .03103
|
_cons | 1.36775 .1284077 10.65 0.000 1.116075 1.619424
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.106977 .1716897 .8168064 1.500231
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3791913 .0365095 .3139803 .457946
-----------------------------+------------------------------------------------
var(Residual) | .6073158 .0179517 .5731309 .6435397
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2300.32 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3702.53 12 7429.06 7461.246
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. * Slope12 at Burst 1
. lincom c.slope12*1 + c.slope12#c.burst1*0 + c.slope12#c.burst1#c.burst1*0
( 1) [symptoms]slope12 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2096013 .0906799 -2.31 0.021 -.3873307 -.0318719
------------------------------------------------------------------------------
. * Slope12 at Burst 2
. lincom c.slope12*1 + c.slope12#c.burst1*1 + c.slope12#c.burst1#c.burst1*1
( 1) [symptoms]slope12 + [symptoms]c.slope12#c.burst1 + [symptoms]c.slope12#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2591182 .0617355 -4.20 0.000 -.3801175 -.1381188
------------------------------------------------------------------------------
. * Slope12 at Burst 3
. lincom c.slope12*1 + c.slope12#c.burst1*2 + c.slope12#c.burst1#c.burst1*4
( 1) [symptoms]slope12 + 2*[symptoms]c.slope12#c.burst1 + 4*[symptoms]c.slope12#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2673945 .0715055 -3.74 0.000 -.4075428 -.1272462
------------------------------------------------------------------------------
. * Slope12 at Burst 4
. lincom c.slope12*1 + c.slope12#c.burst1*3 + c.slope12#c.burst1#c.burst1*9
( 1) [symptoms]slope12 + 3*[symptoms]c.slope12#c.burst1 + 9*[symptoms]c.slope12#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2344303 .0639159 -3.67 0.000 -.359703 -.1091575
------------------------------------------------------------------------------
. * Slope12 at Burst 5
. lincom c.slope12*1 + c.slope12#c.burst1*4 + c.slope12#c.burst1#c.burst1*16
( 1) [symptoms]slope12 + 4*[symptoms]c.slope12#c.burst1 + 16*[symptoms]c.slope12#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1602255 .1046946 -1.53 0.126 -.3654232 .0449722
------------------------------------------------------------------------------
. * Slope26 at Burst 1
. lincom c.slope26*1 + c.slope26#c.burst1*0 + c.slope26#c.burst1#c.burst1*0
( 1) [symptoms]slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0058096 .0226752 -0.26 0.798 -.0502522 .038633
------------------------------------------------------------------------------
. * Slope26 at Burst 2
. lincom c.slope26*1 + c.slope26#c.burst1*1 + c.slope26#c.burst1#c.burst1*1
( 1) [symptoms]slope26 + [symptoms]c.slope26#c.burst1 + [symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0595122 .0154592 -3.85 0.000 -.0898117 -.0292127
------------------------------------------------------------------------------
. * Slope26 at Burst 3
. lincom c.slope26*1 + c.slope26#c.burst1*2 + c.slope26#c.burst1#c.burst1*4
( 1) [symptoms]slope26 + 2*[symptoms]c.slope26#c.burst1 + 4*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.078218 .0179044 -4.37 0.000 -.1133099 -.0431261
------------------------------------------------------------------------------
. * Slope26 at Burst 4
. lincom c.slope26*1 + c.slope26#c.burst1*3 + c.slope26#c.burst1#c.burst1*9
( 1) [symptoms]slope26 + 3*[symptoms]c.slope26#c.burst1 + 9*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0619272 .0159908 -3.87 0.000 -.0932685 -.0305859
------------------------------------------------------------------------------
. * Slope26 at Burst 5
. lincom c.slope26*1 + c.slope26#c.burst1*4 + c.slope26#c.burst1#c.burst1*16
( 1) [symptoms]slope26 + 4*[symptoms]c.slope26#c.burst1 + 16*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0106397 .026176 -0.41 0.684 -.0619438 .0406644
------------------------------------------------------------------------------
. estimates store FitPiecebyQuadBurstS,
. lrtest FitPiecebyBurstMeansS FitPiecebyQuadBurstS,
Likelihood-ratio test LR chi2(6) = 10.99
(Assumption: FitPiecebyQu~S nested in FitPiecebyBu~S) Prob > chi2 = 0.0888
.
. display as result "Eq 10b.9: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Eq 10b.9: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Three-Level Model for the Variance for Symptoms"
Three-Level Model for the Variance for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3702.8547
Iteration 1: log likelihood = -3702.8547
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 122.21
Log likelihood = -3702.8547 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5192184 .0894733 5.80 0.000 .343854 .6945828
|
c.burst1#c.burst1 | -.1047624 .0220219 -4.76 0.000 -.1479245 -.0616003
|
slope12 | -.2280933 .0460023 -4.96 0.000 -.3182562 -.1379305
slope26 | -.00351 .0204896 -0.17 0.864 -.043669 .0366489
|
c.slope26#c.burst1 | -.079968 .0242784 -3.29 0.001 -.1275528 -.0323833
|
c.slope26#c.burst1#c.burst1 | .0200767 .0059822 3.36 0.001 .0083517 .0318016
|
_cons | 1.360861 .1250753 10.88 0.000 1.115718 1.606004
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.107072 .1717053 .8168751 1.500362
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3792306 .0365165 .3140077 .4580009
-----------------------------+------------------------------------------------
var(Residual) | .6074726 .0179565 .5732785 .6437061
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2299.95 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3702.855 10 7425.709 7452.531
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. * Slope26 at Burst 1
. lincom c.slope26*1 + c.slope26#c.burst1*0 + c.slope26#c.burst1#c.burst1*0
( 1) [symptoms]slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.00351 .0204896 -0.17 0.864 -.043669 .0366489
------------------------------------------------------------------------------
. * Slope26 at Burst 2
. lincom c.slope26*1 + c.slope26#c.burst1*1 + c.slope26#c.burst1#c.burst1*1
( 1) [symptoms]slope26 + [symptoms]c.slope26#c.burst1 + [symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0634014 .0145768 -4.35 0.000 -.0919714 -.0348314
------------------------------------------------------------------------------
. * Slope26 at Burst 3
. lincom c.slope26*1 + c.slope26#c.burst1*2 + c.slope26#c.burst1#c.burst1*4
( 1) [symptoms]slope26 + 2*[symptoms]c.slope26#c.burst1 + 4*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0831395 .0165427 -5.03 0.000 -.1155625 -.0507164
------------------------------------------------------------------------------
. * Slope26 at Burst 4
. lincom c.slope26*1 + c.slope26#c.burst1*3 + c.slope26#c.burst1#c.burst1*9
( 1) [symptoms]slope26 + 3*[symptoms]c.slope26#c.burst1 + 9*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0627242 .0149999 -4.18 0.000 -.0921236 -.0333249
------------------------------------------------------------------------------
. * Slope26 at Burst 5
. lincom c.slope26*1 + c.slope26#c.burst1*4 + c.slope26#c.burst1#c.burst1*16
( 1) [symptoms]slope26 + 4*[symptoms]c.slope26#c.burst1 + 16*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0021557 .0233887 -0.09 0.927 -.0479967 .0436853
------------------------------------------------------------------------------
. estimates store FitPieceQuadBurst26S,
. lrtest FitPiecebyBurstMeansS FitPieceQuadBurst26S,
Likelihood-ratio test LR chi2(8) = 11.64
(Assumption: FitPieceQu~26S nested in FitPiecebyBu~S) Prob > chi2 = 0.1682
. lrtest FitSatAllS FitPieceQuadBurst26S,
Likelihood-ratio test LR chi2(23) = 21.11
(Assumption: FitPieceQu~26S nested in FitSatAllS) Prob > chi2 = 0.5745
.
. display as result "Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Linear Burst Slope across Persons for Symptoms"
Add Random Linear Burst Slope across Persons for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1, variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3699.5353
Iteration 1: log likelihood = -3699.4476
Iteration 2: log likelihood = -3699.4471
Iteration 3: log likelihood = -3699.4471
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 120.82
Log likelihood = -3699.4471 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5182214 .0881245 5.88 0.000 .3455005 .6909423
|
c.burst1#c.burst1 | -.1033469 .0215518 -4.80 0.000 -.1455877 -.0611061
|
slope12 | -.2278842 .0460016 -4.95 0.000 -.3180455 -.1377228
slope26 | -.0037004 .020489 -0.18 0.857 -.0438581 .0364574
|
c.slope26#c.burst1 | -.0798012 .0242778 -3.29 0.001 -.1273849 -.0322176
|
c.slope26#c.burst1#c.burst1 | .0200441 .0059821 3.35 0.001 .0083194 .0317687
|
_cons | 1.359967 .1175118 11.57 0.000 1.129648 1.590286
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0124957 .0102588 .0025 .0624579
var(_cons) | .9360185 .1728257 .6518073 1.344156
cov(burst1,_cons) | .044102 .0322018 -.0190123 .1072163
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3490797 .0399419 .2789521 .4368372
-----------------------------+------------------------------------------------
var(Residual) | .6074532 .0179559 .5732603 .6436856
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(4) = 2306.77 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3699.447 12 7422.894 7455.08
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0124957
_cons | .044102 .9360185
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | .4077897 1
. estimates store FitRandBurstLin3S,
. lrtest FitRandBurstLin3S FitPieceQuadBurst26S,
Likelihood-ratio test LR chi2(2) = 6.82
(Assumption: FitPieceQu~26S nested in FitRandBurs~3S) Prob > chi2 = 0.0331
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Quadratic Burst Slope across Persons for Symptoms"
Add Random Quadratic Burst Slope across Persons for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1 burst1sq, variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3698.6421 (not concave)
Iteration 1: log likelihood = -3698.5451 (not concave)
Iteration 2: log likelihood = -3698.2889 (not concave)
Iteration 3: log likelihood = -3698.1659
Iteration 4: log likelihood = -3698.0564 (backed up)
Iteration 5: log likelihood = -3698.0018
Iteration 6: log likelihood = -3698.0017
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 118.95
Log likelihood = -3698.0017 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5269017 .091979 5.73 0.000 .3466261 .7071773
|
c.burst1#c.burst1 | -.106011 .0224261 -4.73 0.000 -.1499654 -.0620566
|
slope12 | -.2275968 .0459993 -4.95 0.000 -.3177538 -.1374398
slope26 | -.0037946 .0204879 -0.19 0.853 -.0439501 .0363609
|
c.slope26#c.burst1 | -.079671 .0242765 -3.28 0.001 -.127252 -.0320899
|
c.slope26#c.burst1#c.burst1 | .0200137 .0059818 3.35 0.001 .0082896 .0317378
|
_cons | 1.359554 .1139834 11.93 0.000 1.136151 1.582957
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .1104859 .1175527 .0137297 .8891022
var(burst1sq) | .005474 .0069282 .0004581 .0654077
var(_cons) | .8703938 .1776125 .5834715 1.29841
cov(burst1,burst1sq) | -.0229248 .0278112 -.0774338 .0315843
cov(burst1,_cons) | .1214871 .1050662 -.0844388 .327413
cov(burst1sq,_cons) | -.0230128 .025123 -.072253 .0262274
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .3238874 .0462246 .2448569 .428426
-----------------------------+------------------------------------------------
var(Residual) | .6073896 .0179532 .5732017 .6436165
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(7) = 2309.66 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3698.002 15 7426.003 7466.235
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 burst1sq _cons
-------------+---------------------------------
burst1 | .1104859
burst1sq | -.0229248 .005474
_cons | .1214871 -.0230128 .8703938
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 burst1sq _cons
-------------+---------------------------------
burst1 | 1
burst1sq | -.9321747 1
_cons | .3917588 -.3333933 1
. estimates store FitRandBurstQuad3S,
. lrtest FitRandBurstQuad3S FitRandBurstLin3S,
Likelihood-ratio test LR chi2(3) = 2.89
(Assumption: FitRandBurs~3S nested in FitRandBurs~3S) Prob > chi2 = 0.4088
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Linear Slope12 Across Bursts for Symptoms"
Add Random Linear Slope12 Across Bursts for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1, variance mle covariance(unstructured) ///
> || burst: slope12, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3690.1654
Iteration 1: log likelihood = -3689.7255
Iteration 2: log likelihood = -3689.7235
Iteration 3: log likelihood = -3689.7235
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 108.77
Log likelihood = -3689.7235 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5161885 .0874173 5.90 0.000 .3448537 .6875234
|
c.burst1#c.burst1 | -.102869 .0213798 -4.81 0.000 -.1447727 -.0609654
|
slope12 | -.2282787 .0501206 -4.55 0.000 -.3265133 -.1300441
slope26 | -.0041686 .0202552 -0.21 0.837 -.043868 .0355308
|
c.slope26#c.burst1 | -.0780539 .0242595 -3.22 0.001 -.1256016 -.0305062
|
c.slope26#c.burst1#c.burst1 | .0195277 .005978 3.27 0.001 .007811 .0312445
|
_cons | 1.360315 .1173719 11.59 0.000 1.130271 1.59036
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0120151 .0102013 .0022752 .0634502
var(_cons) | .939182 .1731805 .6543234 1.348053
cov(burst1,_cons) | .0436477 .0321411 -.0193477 .1066431
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .2482196 .0653033 .1482165 .415696
var(_cons) | .3721178 .0426019 .2973244 .4657258
cov(slope12,_cons) | .0684791 .0372976 -.0046228 .141581
-----------------------------+------------------------------------------------
var(Residual) | .5661321 .0187067 .5306296 .6040098
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 2326.22 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3689.724 14 7407.447 7444.997
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0120151
_cons | .0436477 .939182
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | .4108875 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | .2482196
_cons | .0684791 .3721178
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | 1
_cons | .22532 1
. estimates store FitRandSlope12at2S,
. lrtest FitRandSlope12at2S FitRandBurstLin3S,
Likelihood-ratio test LR chi2(2) = 19.45
(Assumption: FitRandBurs~3S nested in FitRandSlop~2S) Prob > chi2 = 0.0001
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Linear Slope12 Across Persons for Symptoms"
Add Random Linear Slope12 Across Persons for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1 slope12, variance mle covariance(unstructured) ///
> || burst: slope12, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3688.5088
Iteration 1: log likelihood = -3687.0505
Iteration 2: log likelihood = -3686.9825
Iteration 3: log likelihood = -3686.9732
Iteration 4: log likelihood = -3686.9725
Iteration 5: log likelihood = -3686.9725
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 111.64
Log likelihood = -3686.9725 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5149366 .0871241 5.91 0.000 .3441765 .6856968
|
c.burst1#c.burst1 | -.1024276 .0212925 -4.81 0.000 -.1441601 -.060695
|
slope12 | -.2284078 .0537517 -4.25 0.000 -.3337591 -.1230565
slope26 | -.0044558 .0201869 -0.22 0.825 -.0440215 .0351099
|
c.slope26#c.burst1 | -.0779484 .0241365 -3.23 0.001 -.1252551 -.0306416
|
c.slope26#c.burst1#c.burst1 | .0195428 .0059476 3.29 0.001 .0078857 .0311999
|
_cons | 1.361381 .1165319 11.68 0.000 1.132983 1.589779
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0125428 . . .
var(slope12) | .0490724 . . .
var(_cons) | .920561 . . .
cov(burst1,slope12) | .0194093 . . .
cov(burst1,_cons) | .0469846 . . .
cov(slope12,_cons) | -.0463498 . . .
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .198475 . . .
var(_cons) | .3708477 . . .
cov(slope12,_cons) | .0634174 . . .
-----------------------------+------------------------------------------------
var(Residual) | .5661444 . . .
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(9) = 2331.72 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3686.972 7 7387.945 7406.72
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | .0125428
slope12 | .0194093 .0490724
_cons | .0469846 -.0463498 .920561
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | 1
slope12 | .7823386 1
_cons | .4372534 -.2180735 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | .198475
_cons | .0634174 .3708477
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | 1
_cons | .2337534 1
. estimates store FitRandSlope12at23S,
. lrtest FitRandSlope12at23S FitRandSlope12at2S, force
Likelihood-ratio test LR chi2(7) = -5.50
(Assumption: FitRandSlo~23S nested in FitRandSlop~2S) Prob > chi2 = 1.0000
.
. display as result "Eq 10b.10: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Eq 10b.10: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Linear Slope26 Across Bursts for Symptoms"
Add Random Linear Slope26 Across Bursts for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1, variance mle covariance(unstructured) ///
> || burst: slope12 slope26, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3679.983
Iteration 1: log likelihood = -3677.3207
Iteration 2: log likelihood = -3677.2405
Iteration 3: log likelihood = -3677.2402
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 96.58
Log likelihood = -3677.2402 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5190886 .0944081 5.50 0.000 .334052 .7041251
|
c.burst1#c.burst1 | -.1036762 .023117 -4.48 0.000 -.1489847 -.0583677
|
slope12 | -.226874 .0480213 -4.72 0.000 -.3209941 -.132754
slope26 | -.0048296 .022309 -0.22 0.829 -.0485544 .0388952
|
c.slope26#c.burst1 | -.0778458 .027002 -2.88 0.004 -.1307688 -.0249229
|
c.slope26#c.burst1#c.burst1 | .0194929 .0066559 2.93 0.003 .0064476 .0325381
|
_cons | 1.359586 .1210293 11.23 0.000 1.122373 1.596799
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0123132 .0100391 .002491 .0608651
var(_cons) | .938353 .172137 .6549631 1.34436
cov(burst1,_cons) | .0431171 .0317323 -.0190771 .1053114
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .20098 .0772613 .0946088 .4269472
var(slope26) | .0119842 .0047983 .0054676 .0262675
var(_cons) | .512536 .0658087 .3985029 .6591999
cov(slope12,slope26) | .0089391 .0137867 -.0180824 .0359605
cov(slope12,_cons) | .0993057 .0529121 -.0044002 .2030116
cov(slope26,_cons) | -.0459361 .0144282 -.0742148 -.0176573
-----------------------------+------------------------------------------------
var(Residual) | .5362453 .0204725 .4975844 .5779101
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(9) = 2351.18 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3677.24 17 7388.48 7434.077
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0123132
_cons | .0431171 .938353
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | .4011268 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | .20098
slope26 | .0089391 .0119842
_cons | .0993057 -.0459361 .512536
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | .1821424 1
_cons | .3094108 -.5861217 1
. * Slope26 at Burst 1
. lincom c.slope26*1 + c.slope26#c.burst1*0 + c.slope26#c.burst1#c.burst1*0
( 1) [symptoms]slope26 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0048296 .022309 -0.22 0.829 -.0485544 .0388952
------------------------------------------------------------------------------
. * Slope26 at Burst 2
. lincom c.slope26*1 + c.slope26#c.burst1*1 + c.slope26#c.burst1#c.burst1*1
( 1) [symptoms]slope26 + [symptoms]c.slope26#c.burst1 + [symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0631826 .0155575 -4.06 0.000 -.0936746 -.0326905
------------------------------------------------------------------------------
. * Slope26 at Burst 3
. lincom c.slope26*1 + c.slope26#c.burst1*2 + c.slope26#c.burst1#c.burst1*4
( 1) [symptoms]slope26 + 2*[symptoms]c.slope26#c.burst1 + 4*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0825498 .0178286 -4.63 0.000 -.1174933 -.0476064
------------------------------------------------------------------------------
. * Slope26 at Burst 4
. lincom c.slope26*1 + c.slope26#c.burst1*3 + c.slope26#c.burst1#c.burst1*9
( 1) [symptoms]slope26 + 3*[symptoms]c.slope26#c.burst1 + 9*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0629314 .0160508 -3.92 0.000 -.0943905 -.0314723
------------------------------------------------------------------------------
. * Slope26 at Burst 5
. lincom c.slope26*1 + c.slope26#c.burst1*4 + c.slope26#c.burst1#c.burst1*16
( 1) [symptoms]slope26 + 4*[symptoms]c.slope26#c.burst1 + 16*[symptoms]c.slope26#c.burst1#c.burst1 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0043272 .0256325 -0.17 0.866 -.0545659 .0459116
------------------------------------------------------------------------------
. estimates store FitRandSlope26at2S,
. lrtest FitRandSlope26at2S FitRandSlope12at2S,
Likelihood-ratio test LR chi2(3) = 24.97
(Assumption: FitRandSlop~2S nested in FitRandSlop~2S) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
. predict PredUncS, xb,
. margins, at (c.slope12=-1 c.slope26=0 c.burst1=(0(1)4)) vsquish,
Adjusted predictions Number of obs = 2752
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 0
slope12 = -1
slope26 = 0
2._at : burst1 = 1
slope12 = -1
slope26 = 0
3._at : burst1 = 2
slope12 = -1
slope26 = 0
4._at : burst1 = 3
slope12 = -1
slope26 = 0
5._at : burst1 = 4
slope12 = -1
slope26 = 0
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 1.58646 .1230454 12.89 0.000 1.345295 1.827624
2 | 2.001872 .1149095 17.42 0.000 1.776654 2.227091
3 | 2.209932 .124346 17.77 0.000 1.966219 2.453646
4 | 2.21064 .1277847 17.30 0.000 1.960186 2.461093
5 | 2.003995 .1518102 13.20 0.000 1.706452 2.301537
------------------------------------------------------------------------------
. margins, at (c.slope12=0 c.slope26=(0(1)4) c.burst1=(0(1)4)) vsquish,
Adjusted predictions Number of obs = 2752
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 0
slope12 = 0
slope26 = 0
2._at : burst1 = 0
slope12 = 0
slope26 = 1
3._at : burst1 = 0
slope12 = 0
slope26 = 2
4._at : burst1 = 0
slope12 = 0
slope26 = 3
5._at : burst1 = 0
slope12 = 0
slope26 = 4
6._at : burst1 = 1
slope12 = 0
slope26 = 0
7._at : burst1 = 1
slope12 = 0
slope26 = 1
8._at : burst1 = 1
slope12 = 0
slope26 = 2
9._at : burst1 = 1
slope12 = 0
slope26 = 3
10._at : burst1 = 1
slope12 = 0
slope26 = 4
11._at : burst1 = 2
slope12 = 0
slope26 = 0
12._at : burst1 = 2
slope12 = 0
slope26 = 1
13._at : burst1 = 2
slope12 = 0
slope26 = 2
14._at : burst1 = 2
slope12 = 0
slope26 = 3
15._at : burst1 = 2
slope12 = 0
slope26 = 4
16._at : burst1 = 3
slope12 = 0
slope26 = 0
17._at : burst1 = 3
slope12 = 0
slope26 = 1
18._at : burst1 = 3
slope12 = 0
slope26 = 2
19._at : burst1 = 3
slope12 = 0
slope26 = 3
20._at : burst1 = 3
slope12 = 0
slope26 = 4
21._at : burst1 = 4
slope12 = 0
slope26 = 0
22._at : burst1 = 4
slope12 = 0
slope26 = 1
23._at : burst1 = 4
slope12 = 0
slope26 = 2
24._at : burst1 = 4
slope12 = 0
slope26 = 3
25._at : burst1 = 4
slope12 = 0
slope26 = 4
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 1.359586 .1210293 11.23 0.000 1.122373 1.596799
2 | 1.354756 .1142729 11.86 0.000 1.130785 1.578727
3 | 1.349927 .1116418 12.09 0.000 1.131113 1.56874
4 | 1.345097 .1134234 11.86 0.000 1.122791 1.567403
5 | 1.340267 .1194204 11.22 0.000 1.106208 1.574327
6 | 1.774998 .1128553 15.73 0.000 1.553806 1.99619
7 | 1.711816 .1091593 15.68 0.000 1.497867 1.925764
8 | 1.648633 .1076071 15.32 0.000 1.437727 1.859539
9 | 1.58545 .1082907 14.64 0.000 1.373205 1.797696
10 | 1.522268 .1111689 13.69 0.000 1.304381 1.740155
11 | 1.983058 .1225 16.19 0.000 1.742963 2.223154
12 | 1.900508 .1181252 16.09 0.000 1.668987 2.132029
13 | 1.817958 .1163468 15.63 0.000 1.589923 2.045994
14 | 1.735409 .1172831 14.80 0.000 1.505538 1.965279
15 | 1.652859 .120871 13.67 0.000 1.415956 1.889762
16 | 1.983766 .12599 15.75 0.000 1.73683 2.230701
17 | 1.920834 .1224784 15.68 0.000 1.680781 2.160888
18 | 1.857903 .1210113 15.35 0.000 1.620725 2.095081
19 | 1.794971 .1216624 14.75 0.000 1.556517 2.033425
20 | 1.73204 .1243987 13.92 0.000 1.488223 1.975857
21 | 1.777121 .1502634 11.83 0.000 1.48261 2.071631
22 | 1.772794 .1431498 12.38 0.000 1.492225 2.053362
23 | 1.768466 .1404233 12.59 0.000 1.493242 2.043691
24 | 1.764139 .1423362 12.39 0.000 1.485165 2.043113
25 | 1.759812 .1487095 11.83 0.000 1.468347 2.051277
------------------------------------------------------------------------------
. corr symptoms PredUncS
(obs=2752)
| symptoms PredUncS
-------------+------------------
symptoms | 1.0000
PredUncS | 0.1583 1.0000
.
. display as result "Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)"
Ch 10b: Piecewise Session Slopes (Slope26 by Quadratic Burst Only)
. display as result "Add Random Linear Slope26 Across Persons for Symptoms"
Add Random Linear Slope26 Across Persons for Symptoms
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1 slope26, variance mle covariance(unstructured) ///
> || burst: slope12 slope26, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3680.0144
Iteration 1: log likelihood = -3676.4099
Iteration 2: log likelihood = -3676.3035
Iteration 3: log likelihood = -3676.303
Iteration 4: log likelihood = -3676.303
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.5 30
burst | 462 1 6.0 6
-----------------------------------------------------------
Wald chi2(6) = 99.45
Log likelihood = -3676.303 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5182707 .0936172 5.54 0.000 .3347843 .7017571
|
c.burst1#c.burst1 | -.1033755 .0229132 -4.51 0.000 -.1482847 -.0584664
|
slope12 | -.2270469 .048026 -4.73 0.000 -.3211762 -.1329177
slope26 | -.004931 .0223514 -0.22 0.825 -.0487389 .0388769
|
c.slope26#c.burst1 | -.0779094 .0266366 -2.92 0.003 -.1301161 -.0257026
|
c.slope26#c.burst1#c.burst1 | .0195081 .0065659 2.97 0.003 .0066392 .0323771
|
_cons | 1.359681 .1223793 11.11 0.000 1.119822 1.59954
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0122386 .0100362 .002453 .06106
var(slope26) | .0016078 .0021105 .0001227 .0210672
var(_cons) | .9829422 .185155 .6794988 1.421894
cov(burst1,slope26) | .0027703 .002983 -.0030762 .0086169
cov(burst1,_cons) | .0381618 .0327078 -.0259444 .1022679
cov(slope26,_cons) | -.0134628 .0147446 -.0423616 .015436
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .2010762 .0772909 .0946609 .4271206
var(slope26) | .0106164 .0050532 .0041766 .0269856
var(_cons) | .5059069 .0656506 .392294 .6524233
cov(slope12,slope26) | .0074706 .013868 -.0197102 .0346515
cov(slope12,_cons) | .1053492 .0532018 .0010757 .2096228
cov(slope26,_cons) | -.0424978 .0146379 -.0711876 -.0138081
-----------------------------+------------------------------------------------
var(Residual) | .536319 .0204778 .4976482 .5779948
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(12) = 2353.06 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3676.303 20 7392.606 7446.249
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope26 _cons
-------------+---------------------------------
burst1 | .0122386
slope26 | .0027703 .0016078
_cons | .0381618 -.0134628 .9829422
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope26 _cons
-------------+---------------------------------
burst1 | 1
slope26 | .6245299 1
_cons | .3479354 -.3386557 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | .2010762
slope26 | .0074706 .0106164
_cons | .1053492 -.0424978 .5059069
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | .1616923 1
_cons | .3303054 -.5798866 1
. estimates store FitRandSlope26at23S,
. lrtest FitRandSlope26at23S FitRandSlope26at2S,
Likelihood-ratio test LR chi2(3) = 1.87
(Assumption: FitRandSlop~2S nested in FitRandSlo~23S) Prob > chi2 = 0.5989
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Final Unconditional Model for Symptoms"
Ch 10b: Final Unconditional Model for Symptoms
. display as result "Remove Level-2 Random Effects Variances and Covariances"
Remove Level-2 Random Effects Variances and Covariances
. mixed symptoms c.burst1 c.burst1#c.burst1 c.slope12 c.slope26 ///
> c.slope26#c.burst1 c.slope26#c.burst1#c.burst1, ///
> || personid: burst1, variance mle covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -3884.2212
Iteration 1: log likelihood = -3884.2212
Computing standard errors:
Mixed-effects ML regression Number of obs = 2752
Group variable: personid Number of groups = 108
Obs per group: min = 4
avg = 25.5
max = 30
Wald chi2(6) = 130.15
Log likelihood = -3884.2212 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
burst1 | .5220526 .0677584 7.70 0.000 .3892485 .6548567
|
c.burst1#c.burst1 | -.1028784 .0157865 -6.52 0.000 -.1338194 -.0719373
|
slope12 | -.2293217 .0531987 -4.31 0.000 -.3335891 -.1250542
slope26 | -.0053104 .0236943 -0.22 0.823 -.0517505 .0411296
|
c.slope26#c.burst1 | -.0789205 .0280769 -2.81 0.005 -.1339503 -.0238907
|
c.slope26#c.burst1#c.burst1 | .0199375 .0069183 2.88 0.004 .0063779 .0334971
|
_cons | 1.362601 .1171124 11.63 0.000 1.133065 1.592137
---------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0551579 .0112188 .0370236 .0821747
var(_cons) | 1.160262 .1721284 .8675166 1.551795
cov(burst1,_cons) | -.0210214 .0326716 -.0850565 .0430137
-----------------------------+------------------------------------------------
var(Residual) | .8129323 .0228633 .7693338 .8590016
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1937.22 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -3884.221 11 7790.442 7819.946
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0551579
_cons | -.0210214 1.160262
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | -.083096 1
. estimates store FitNo2S,
. lrtest FitRandSlope26at2S FitNo2S,
Likelihood-ratio test LR chi2(6) = 413.96
(Assumption: FitNo2S nested in FitRandSlop~2S) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Eq 10b.6: Saturated Means for Burst by Session"
Eq 10b.6: Saturated Means for Burst by Session
. display as result "Three-Level Model for the Variance for Positive Affect"
Three-Level Model for the Variance for Positive Affect
. mixed posaff i.session i.burst i.session#i.burst, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1742.7414
Iteration 1: log likelihood = -1742.7414
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(29) = 93.95
Log likelihood = -1742.7414 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
session |
2 | -.1646552 .0537188 -3.07 0.002 -.2699422 -.0593682
3 | -.2882953 .0539617 -5.34 0.000 -.3940582 -.1825324
4 | -.1864175 .0541293 -3.44 0.001 -.292509 -.080326
5 | -.2396754 .0538176 -4.45 0.000 -.3451559 -.1341949
6 | -.130029 .0543155 -2.39 0.017 -.2364854 -.0235725
|
burst |
2 | -.0831215 .0650971 -1.28 0.202 -.2107096 .0444666
3 | -.3306387 .0655381 -5.04 0.000 -.4590911 -.2021864
4 | -.3275894 .0670465 -4.89 0.000 -.4589982 -.1961807
5 | -.408072 .0695754 -5.87 0.000 -.5444373 -.2717067
|
session#burst |
2 2 | .0188219 .0779666 0.24 0.809 -.1339899 .1716336
2 3 | .1298707 .0785547 1.65 0.098 -.0240936 .2838351
2 4 | .1048851 .0800569 1.31 0.190 -.0520236 .2617938
2 5 | .16985 .0828655 2.05 0.040 .0074365 .3322635
3 2 | .1411002 .0782728 1.80 0.071 -.0123116 .294512
3 3 | .262113 .0787212 3.33 0.001 .1078223 .4164037
3 4 | .2569171 .0803662 3.20 0.001 .0994023 .4144319
3 5 | .3142694 .0830232 3.79 0.000 .151547 .4769917
4 2 | .0750118 .0783884 0.96 0.339 -.0786266 .2286503
4 3 | .2204502 .0788361 2.80 0.005 .0659344 .374966
4 4 | .2231991 .0803329 2.78 0.005 .0657495 .3806488
4 5 | .2435604 .0831322 2.93 0.003 .0806242 .4064965
5 2 | .0777434 .0781735 0.99 0.320 -.0754738 .2309606
5 3 | .3139876 .0787524 3.99 0.000 .1596358 .4683395
5 4 | .2557673 .0801232 3.19 0.001 .0987287 .412806
5 5 | .3461689 .0829296 4.17 0.000 .1836299 .5087079
6 2 | .0523075 .0785172 0.67 0.505 -.1015834 .2061984
6 3 | .209223 .0789641 2.65 0.008 .0544561 .3639899
6 4 | .1208336 .0804585 1.50 0.133 -.0368623 .2785294
6 5 | .175488 .0834331 2.10 0.035 .0119622 .3390138
|
_cons | 2.801692 .0707759 39.59 0.000 2.662974 2.94041
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | .3258367 .0477945 .2444239 .4343665
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .0567707 .006275 .0457128 .0705034
-----------------------------+------------------------------------------------
var(Residual) | .1532679 .0045349 .1446324 .1624189
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2552.57 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1742.741 33 3551.483 3639.993
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. contrast i.session,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
posaff |
session | 5 19.00 0.0019
------------------------------------------------
. margins i.session,
Predictive margins Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
session |
1 | 2.586608 .0592399 43.66 0.000 2.4705 2.702716
2 | 2.500649 .0592328 42.22 0.000 2.384555 2.616743
3 | 2.482404 .0592596 41.89 0.000 2.366258 2.598551
4 | 2.543796 .059275 42.92 0.000 2.427619 2.659973
5 | 2.533504 .0592529 42.76 0.000 2.417371 2.649638
6 | 2.562338 .0592847 43.22 0.000 2.446142 2.678534
------------------------------------------------------------------------------
. contrast i.burst,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
posaff |
burst | 4 33.82 0.0000
------------------------------------------------
. margins i.burst,
Predictive margins Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
burst |
1 | 2.633587 .0615269 42.80 0.000 2.512997 2.754178
2 | 2.611203 .0627243 41.63 0.000 2.488266 2.734141
3 | 2.492029 .0629856 39.57 0.000 2.36858 2.615479
4 | 2.466131 .0636433 38.75 0.000 2.341392 2.59087
5 | 2.433605 .0648439 37.53 0.000 2.306513 2.560696
------------------------------------------------------------------------------
. contrast i.session#i.burst,
Contrasts of marginal linear predictions
Margins : asbalanced
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
posaff |
session#burst | 20 38.12 0.0086
-------------------------------------------------
. margins i.session#i.burst,
Adjusted predictions Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
session#burst |
1 1 | 2.801692 .0707759 39.59 0.000 2.662974 2.94041
1 2 | 2.718571 .0725332 37.48 0.000 2.576408 2.860733
1 3 | 2.471053 .0729272 33.88 0.000 2.328119 2.613988
1 4 | 2.474103 .0742826 33.31 0.000 2.328512 2.619694
1 5 | 2.39362 .0765679 31.26 0.000 2.24355 2.543691
2 1 | 2.637037 .0704401 37.44 0.000 2.498977 2.775097
2 2 | 2.572737 .0725332 35.47 0.000 2.430575 2.7149
2 3 | 2.436269 .0730923 33.33 0.000 2.293011 2.579527
2 4 | 2.414333 .0742826 32.50 0.000 2.268742 2.559924
2 5 | 2.398815 .0765679 31.33 0.000 2.248745 2.548885
3 1 | 2.513397 .0706623 35.57 0.000 2.374901 2.651892
3 2 | 2.571376 .0726778 35.38 0.000 2.42893 2.713822
3 3 | 2.444871 .0730923 33.45 0.000 2.301613 2.58813
3 4 | 2.442725 .0744403 32.81 0.000 2.296824 2.588625
3 5 | 2.419594 .0765679 31.60 0.000 2.269524 2.569665
4 1 | 2.615275 .0707824 36.95 0.000 2.476544 2.754006
4 2 | 2.607165 .0726778 35.87 0.000 2.464719 2.749611
4 3 | 2.505086 .0730923 34.27 0.000 2.361828 2.648345
4 4 | 2.510884 .0742826 33.80 0.000 2.365293 2.656476
4 5 | 2.450763 .0765679 32.01 0.000 2.300693 2.600833
5 1 | 2.562017 .0705529 36.31 0.000 2.423736 2.700298
5 2 | 2.556639 .0726778 35.18 0.000 2.414193 2.699085
5 3 | 2.545366 .0732323 34.76 0.000 2.401833 2.688898
5 4 | 2.490195 .0742826 33.52 0.000 2.344604 2.635786
5 5 | 2.500114 .0765679 32.65 0.000 2.350043 2.650184
6 1 | 2.671663 .0708913 37.69 0.000 2.532719 2.810608
6 2 | 2.640849 .0726778 36.34 0.000 2.498403 2.783295
6 3 | 2.550248 .0730923 34.89 0.000 2.406989 2.693506
6 4 | 2.464907 .0742826 33.18 0.000 2.319316 2.610499
6 5 | 2.439079 .0767632 31.77 0.000 2.288626 2.589532
-------------------------------------------------------------------------------
. margins i.session@i.burst,
Contrasts of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
session@burst |
1 | 5 34.08 0.0000
2 | 5 11.52 0.0419
3 | 5 7.37 0.1946
4 | 5 3.33 0.6489
5 | 5 3.89 0.5646
Joint | 25 60.20 0.0001
-------------------------------------------------
. margins i.burst@i.session,
Contrasts of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-------------------------------------------------
| df chi2 P>chi2
--------------+----------------------------------
burst@session |
1 | 4 54.63 0.0000
2 | 4 20.12 0.0005
3 | 4 6.66 0.1550
4 | 4 8.47 0.0759
5 | 4 1.86 0.7612
6 | 4 17.80 0.0014
Joint | 24 71.98 0.0000
-------------------------------------------------
. estimates store FitSatAllP,
.
. display as result "Eq 10b.7: Piecewise Session Slopes by Observed Burst"
Eq 10b.7: Piecewise Session Slopes by Observed Burst
. display as result "Three-Level Model for the Variance for Positive Affect"
Three-Level Model for the Variance for Positive Affect
. mixed posaff c.slope12 c.slope26 i.burst ///
> c.slope12#i.burst c.slope26#i.burst, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1750.7182
Iteration 1: log likelihood = -1750.7182
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(14) = 77.64
Log likelihood = -1750.7182 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
slope12 | -.2245959 .0483801 -4.64 0.000 -.3194192 -.1297726
slope26 | .011249 .0120779 0.93 0.352 -.0124233 .0349212
|
burst |
2 | -.011982 .0548121 -0.22 0.827 -.1194117 .0954477
3 | -.1468239 .0553261 -2.65 0.008 -.2552611 -.0383866
4 | -.1425882 .0565245 -2.52 0.012 -.2533742 -.0318021
5 | -.1681563 .0587066 -2.86 0.004 -.283219 -.0530936
|
burst#c.slope12 |
2 | .0715265 .0701297 1.02 0.308 -.0659252 .2089781
3 | .184226 .0706054 2.61 0.009 .045842 .3226101
4 | .1854155 .0719935 2.58 0.010 .0443108 .3265202
5 | .2403342 .0744929 3.23 0.001 .0943308 .3863376
|
burst#c.slope26 |
2 | .0008844 .0175455 0.05 0.960 -.0335041 .0352729
3 | .021576 .017665 1.22 0.222 -.0130467 .0561987
4 | .0036036 .0179869 0.20 0.841 -.03165 .0388572
5 | .0049608 .0186422 0.27 0.790 -.0315773 .0414989
|
_cons | 2.577305 .0663925 38.82 0.000 2.447178 2.707432
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | .3259172 .0478093 .2444799 .4344815
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .0565401 .0062715 .0454925 .0702706
-----------------------------+------------------------------------------------
var(Residual) | .1543539 .004567 .1456574 .1635696
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2540.87 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1750.718 18 3537.436 3585.715
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. * Session 2 at Burst 1
. lincom _cons*1 + i1.burst
( 1) [posaff]1b.burst + [posaff]_cons = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.577305 .0663925 38.82 0.000 2.447178 2.707432
------------------------------------------------------------------------------
. * Session 2 at Burst 2
. lincom _cons*1 + i2.burst
( 1) [posaff]2.burst + [posaff]_cons = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.565323 .0680606 37.69 0.000 2.431927 2.698719
------------------------------------------------------------------------------
. * Session 2 at Burst 3
. lincom _cons*1 + i3.burst
( 1) [posaff]3.burst + [posaff]_cons = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.430481 .068473 35.50 0.000 2.296277 2.564686
------------------------------------------------------------------------------
. * Session 2 at Burst 4
. lincom _cons*1 + i4.burst
( 1) [posaff]4.burst + [posaff]_cons = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.434717 .0694442 35.06 0.000 2.298609 2.570825
------------------------------------------------------------------------------
. * Session 2 at Burst 5
. lincom _cons*1 + i5.burst
( 1) [posaff]5.burst + [posaff]_cons = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.409149 .0712306 33.82 0.000 2.269539 2.548758
------------------------------------------------------------------------------
. * Slope12 at Burst 1
. lincom c.slope12*1 + c.slope12#i1.burst
( 1) [posaff]slope12 + [posaff]1b.burst#co.slope12 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2245959 .0483801 -4.64 0.000 -.3194192 -.1297726
------------------------------------------------------------------------------
. * Slope12 at Burst 2
. lincom c.slope12*1 + c.slope12#i2.burst
( 1) [posaff]slope12 + [posaff]2.burst#c.slope12 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.1530694 .0507668 -3.02 0.003 -.2525705 -.0535684
------------------------------------------------------------------------------
. * Slope12 at Burst 3
. lincom c.slope12*1 + c.slope12#i3.burst
( 1) [posaff]slope12 + [posaff]3.burst#c.slope12 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0403699 .0514251 -0.79 0.432 -.1411611 .0604214
------------------------------------------------------------------------------
. * Slope12 at Burst 4
. lincom c.slope12*1 + c.slope12#i4.burst
( 1) [posaff]slope12 + [posaff]4.burst#c.slope12 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0391804 .0533145 -0.73 0.462 -.1436749 .0653141
------------------------------------------------------------------------------
. * Slope12 at Burst 5
. lincom c.slope12*1 + c.slope12#i5.burst
( 1) [posaff]slope12 + [posaff]5.burst#c.slope12 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .0157383 .0566441 0.28 0.781 -.0952821 .1267586
------------------------------------------------------------------------------
. * Slope26 at Burst 1
. lincom c.slope26*1 + c.slope26#i1.burst
( 1) [posaff]slope26 + [posaff]1b.burst#co.slope26 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .011249 .0120779 0.93 0.352 -.0124233 .0349212
------------------------------------------------------------------------------
. * Slope26 at Burst 2
. lincom c.slope26*1 + c.slope26#i2.burst
( 1) [posaff]slope26 + [posaff]2.burst#c.slope26 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .0121333 .0127266 0.95 0.340 -.0128104 .0370771
------------------------------------------------------------------------------
. * Slope26 at Burst 3
. lincom c.slope26*1 + c.slope26#i3.burst
( 1) [posaff]slope26 + [posaff]3.burst#c.slope26 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .032825 .0128909 2.55 0.011 .0075592 .0580907
------------------------------------------------------------------------------
. * Slope26 at Burst 4
. lincom c.slope26*1 + c.slope26#i4.burst
( 1) [posaff]slope26 + [posaff]4.burst#c.slope26 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .0148526 .0133286 1.11 0.265 -.0112711 .0409762
------------------------------------------------------------------------------
. * Slope26 at Burst 5
. lincom c.slope26*1 + c.slope26#i5.burst
( 1) [posaff]slope26 + [posaff]5.burst#c.slope26 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .0162098 .0142006 1.14 0.254 -.0116229 .0440425
------------------------------------------------------------------------------
. estimates store FitPiecebyBurstMeansP,
. lrtest FitSatAllP FitPiecebyBurstMeansP,
Likelihood-ratio test LR chi2(15) = 15.95
(Assumption: FitPiecebyBu~P nested in FitSatAllP) Prob > chi2 = 0.3851
.
. display as result "Eq 10b.11and12: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Eq 10b.11and12: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Three-Level Model for the Variance for Positive Affect"
Three-Level Model for the Variance for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: , variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1753.325
Iteration 1: log likelihood = -1753.325
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 72.27
Log likelihood = -1753.325 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0451263 .0100681 -4.48 0.000 -.0648593 -.0253932
slope12 | -.0119746 .0291711 -0.41 0.681 -.0691488 .0451997
|
c.slope12#c.b1or2 | -.1926462 .040259 -4.79 0.000 -.2715524 -.1137399
|
slope26 | .0173261 .0058144 2.98 0.003 .00593 .0287222
_cons | 2.573432 .0606517 42.43 0.000 2.454557 2.692307
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | .3261875 .0478305 .2447099 .4347936
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .0566794 .0062859 .0456062 .0704411
-----------------------------+------------------------------------------------
var(Residual) | .1546451 .0045757 .145932 .1638784
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2540.43 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1753.325 8 3522.65 3544.107
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. lincom c.slope12*1 + c.slope12#c.b1or2*1 // Slope12 at Burst 1 or 2
( 1) [posaff]slope12 + [posaff]c.slope12#c.b1or2 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2046207 .0324168 -6.31 0.000 -.2681564 -.141085
------------------------------------------------------------------------------
. estimates store FitPieceBurst1or2P,
. lrtest FitPiecebyBurstMeansP FitPieceBurst1or2P,
Likelihood-ratio test LR chi2(10) = 5.21
(Assumption: FitPieceBur~2P nested in FitPiecebyBu~P) Prob > chi2 = 0.8765
. lrtest FitSatAllP FitPieceBurst1or2P,
Likelihood-ratio test LR chi2(25) = 21.17
(Assumption: FitPieceBur~2P nested in FitSatAllP) Prob > chi2 = 0.6833
.
. display as result "Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Random Linear Burst across Persons for Positive Affect"
Add Random Linear Burst across Persons for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1, variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1741.6336
Iteration 1: log likelihood = -1741.5542
Iteration 2: log likelihood = -1741.5541
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 62.08
Log likelihood = -1741.5541 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0466484 .0127068 -3.67 0.000 -.0715532 -.0217435
slope12 | -.0114019 .0291498 -0.39 0.696 -.0685344 .0457305
|
c.slope12#c.b1or2 | -.1940458 .0401782 -4.83 0.000 -.2727936 -.1152979
|
slope26 | .0173501 .0058145 2.98 0.003 .0059538 .0287464
_cons | 2.574073 .0590674 43.58 0.000 2.458303 2.689843
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0075015 .002198 .0042242 .0133215
var(_cons) | .3171065 .0492531 .2338816 .4299462
cov(burst1,_cons) | -.0030382 .0079038 -.0185293 .0124529
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .038483 .0056786 .028818 .0513894
-----------------------------+------------------------------------------------
var(Residual) | .1546556 .0045762 .1459416 .1638899
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(4) = 2563.98 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1741.554 10 3503.108 3529.93
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0075015
_cons | -.0030382 .3171065
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | -.0622928 1
. estimates store FitRandBurstLin3P,
. lrtest FitRandBurstLin3P FitPieceBurst1or2P,
Likelihood-ratio test LR chi2(2) = 23.54
(Assumption: FitPieceBur~2P nested in FitRandBurs~3P) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Fixed and Random Quadratic Burst across Persons for Positive Affect"
Add Fixed and Random Quadratic Burst across Persons for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26 ///
> c.burst1#c.burst1, ///
> || personid: burst1 burst1sq, variance mle covariance(unstructured) ///
> || burst: , covariance(unstructured),
Note: single-variable random-effects specification in burst equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1740.8307
Iteration 1: log likelihood = -1738.6478
Iteration 2: log likelihood = -1738.6248
Iteration 3: log likelihood = -1738.6248
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(5) = 61.49
Log likelihood = -1738.6248 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0592724 .034344 -1.73 0.084 -.1265854 .0080406
slope12 | -.0115499 .0291629 -0.40 0.692 -.0687082 .0456084
|
c.slope12#c.b1or2 | -.1939415 .0402168 -4.82 0.000 -.272765 -.1151181
|
slope26 | .0173518 .0058147 2.98 0.003 .0059553 .0287483
|
c.burst1#c.burst1 | .0034946 .0078757 0.44 0.657 -.0119416 .0189307
|
_cons | 2.578144 .0594371 43.38 0.000 2.46165 2.694639
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0377655 .017755 .0150284 .0949025
var(burst1sq) | .0013213 .0009302 .0003325 .0052513
var(_cons) | .3107503 .0499008 .2268424 .4256953
cov(burst1,burst1sq) | -.0063745 .0039267 -.0140706 .0013217
cov(burst1,_cons) | .001891 .0222695 -.0417564 .0455384
cov(burst1sq,_cons) | -.0023346 .0050295 -.0121922 .007523
-----------------------------+------------------------------------------------
burst: Identity |
var(_cons) | .0320881 .0062047 .0219661 .0468744
-----------------------------+------------------------------------------------
var(Residual) | .1546624 .0045764 .145948 .1638972
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(7) = 2569.66 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1738.625 14 3505.25 3542.799
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 burst1sq _cons
-------------+---------------------------------
burst1 | .0377655
burst1sq | -.0063745 .0013213
_cons | .001891 -.0023346 .3107503
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 burst1sq _cons
-------------+---------------------------------
burst1 | 1
burst1sq | -.9023887 1
_cons | .0174558 -.1152118 1
. estimates store FitRandBurstQuad3P,
. lrtest FitRandBurstQuad3P FitRandBurstLin3P,
Likelihood-ratio test LR chi2(4) = 5.86
(Assumption: FitRandBurs~3P nested in FitRandBurs~3P) Prob > chi2 = 0.2100
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Random Linear Slope12 across Bursts for Positive Affect"
Add Random Linear Slope12 across Bursts for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1, variance mle covariance(unstructured) ///
> || burst: slope12, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1732.4468
Iteration 1: log likelihood = -1731.998
Iteration 2: log likelihood = -1731.9973
Iteration 3: log likelihood = -1731.9973
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 55.86
Log likelihood = -1731.9973 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0464781 .0127425 -3.65 0.000 -.0714529 -.0215033
slope12 | -.0105262 .0321616 -0.33 0.743 -.0735618 .0525094
|
c.slope12#c.b1or2 | -.1957484 .045241 -4.33 0.000 -.2844192 -.1070777
|
slope26 | .0172927 .0056116 3.08 0.002 .006294 .0282913
_cons | 2.573746 .0590767 43.57 0.000 2.457957 2.689534
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0074955 .0021969 .0042201 .0133131
var(_cons) | .3176082 .0495009 .2340062 .4310781
cov(burst1,_cons) | -.0030325 .0079121 -.0185401 .012475
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .063641 .0166456 .0381154 .1062608
var(_cons) | .0418009 .0063762 .0309988 .0563671
cov(slope12,_cons) | .0100355 .0082626 -.0061588 .0262298
-----------------------------+------------------------------------------------
var(Residual) | .1440331 .0047658 .1349887 .1536835
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 2583.09 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1731.997 12 3487.995 3520.18
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | .0074955
_cons | -.0030325 .3176082
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 _cons
-------------+----------------------
burst1 | 1
_cons | -.062153 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | .063641
_cons | .0100355 .0418009
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | 1
_cons | .1945714 1
. estimates store FitRandSlope12at2P,
. lrtest FitRandSlope12at2P FitRandBurstLin3P,
Likelihood-ratio test LR chi2(2) = 19.11
(Assumption: FitRandBurs~3P nested in FitRandSlop~2P) Prob > chi2 = 0.0001
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Random Linear Slope12 across Persons for Positive Affect"
Add Random Linear Slope12 across Persons for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1 slope12, variance mle covariance(unstructured) ///
> || burst: slope12, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1720.1036
Iteration 1: log likelihood = -1718.4318
Iteration 2: log likelihood = -1718.4185
Iteration 3: log likelihood = -1718.4185
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 55.40
Log likelihood = -1718.4185 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0458576 .0126849 -3.62 0.000 -.0707196 -.0209955
slope12 | -.0175468 .0355707 -0.49 0.622 -.0872641 .0521705
|
c.slope12#c.b1or2 | -.1952573 .0421846 -4.63 0.000 -.2779375 -.112577
|
slope26 | .0172575 .0056115 3.08 0.002 .0062592 .0282558
_cons | 2.572517 .0604893 42.53 0.000 2.45396 2.691074
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0075149 .0022016 .004232 .0133444
var(slope12) | .0355946 .0118085 .018578 .0681978
var(_cons) | .3370042 .0521226 .2488769 .4563374
cov(burst1,slope12) | .0016119 .0034793 -.0052075 .0084312
cov(burst1,_cons) | -.0032454 .0081031 -.0191273 .0126364
cov(slope12,_cons) | .059022 .0187265 .0223188 .0957251
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .0281096 .016177 .0090989 .0868395
var(_cons) | .0395538 .0060423 .0293195 .0533604
cov(slope12,_cons) | .0002913 .0071279 -.0136791 .0142618
-----------------------------+------------------------------------------------
var(Residual) | .1440272 .0047656 .1349833 .1536771
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(9) = 2610.25 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1718.419 15 3466.837 3507.069
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | .0075149
slope12 | .0016119 .0355946
_cons | -.0032454 .059022 .3370042
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | 1
slope12 | .0985541 1
_cons | -.0644902 .5388943 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | .0281096
_cons | .0002913 .0395538
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 _cons
-------------+----------------------
slope12 | 1
_cons | .0087376 1
. estimates store FitRandSlope12at23P,
. lrtest FitRandSlope12at23P FitRandSlope12at2P, force
Likelihood-ratio test LR chi2(3) = 27.16
(Assumption: FitRandSlop~2P nested in FitRandSlo~23P) Prob > chi2 = 0.0000
.
. display as result "Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Ch 10b: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Random Linear Slope26 across Bursts for Positive Affect"
Add Random Linear Slope26 across Bursts for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1 slope12, variance mle covariance(unstructured) ///
> || burst: slope12 slope26, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1716.1042
Iteration 1: log likelihood = -1712.9724
Iteration 2: log likelihood = -1712.9215
Iteration 3: log likelihood = -1712.9214
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 54.87
Log likelihood = -1712.9214 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0454578 .0125592 -3.62 0.000 -.0700735 -.0208422
slope12 | -.0186313 .0350211 -0.53 0.595 -.0872714 .0500089
|
c.slope12#c.b1or2 | -.192637 .0421474 -4.57 0.000 -.2752444 -.1100297
|
slope26 | .0171986 .0059992 2.87 0.004 .0054404 .0289569
_cons | 2.571882 .0610517 42.13 0.000 2.452222 2.691541
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0072541 .0021556 .0040518 .0129874
var(slope12) | .0333611 .0116208 .0168553 .0660303
var(_cons) | .3400255 .0525445 .2511738 .4603081
cov(burst1,slope12) | .0012682 .0033967 -.0053892 .0079257
cov(burst1,_cons) | -.0031354 .0080271 -.0188683 .0125975
cov(slope12,_cons) | .0576154 .0185722 .0212146 .0940161
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .0317297 .0199663 .0092435 .1089168
var(slope26) | .0027606 .0012144 .0011656 .006538
var(_cons) | .0629268 .0121192 .043142 .0917848
cov(slope12,slope26) | -.0013289 .003605 -.0083946 .0057368
cov(slope12,_cons) | .0097419 .0116005 -.0129947 .0324785
cov(slope26,_cons) | -.0082264 .0032799 -.014655 -.0017979
-----------------------------+------------------------------------------------
var(Residual) | .1371476 .0052431 .1272469 .1478186
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(12) = 2621.24 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1712.921 18 3461.843 3510.121
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | .0072541
slope12 | .0012682 .0333611
_cons | -.0031354 .0576154 .3400255
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope12 _cons
-------------+---------------------------------
burst1 | 1
slope12 | .0815233 1
_cons | -.0631312 .540957 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | .0317297
slope26 | -.0013289 .0027606
_cons | .0097419 -.0082264 .0629268
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | -.1419886 1
_cons | .2180181 -.6241541 1
. estimates store FitRandSlope26at2P,
. lrtest FitRandSlope26at2P FitRandSlope12at23P,
Likelihood-ratio test LR chi2(3) = 10.99
(Assumption: FitRandSlo~23P nested in FitRandSlop~2P) Prob > chi2 = 0.0118
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Eq 10b.13: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2"
Eq 10b.13: Piecewise Session Slopes, Linear Burst, Slope12 by Burst1or2
. display as result "Add Random Linear Slope26 across Persons for Positive Affect"
Add Random Linear Slope26 across Persons for Positive Affect
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1 slope12 slope26, variance mle covariance(unstructured) ///
> || burst: slope12 slope26, covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1710.8396
Iteration 1: log likelihood = -1706.4108
Iteration 2: log likelihood = -1706.2931
Iteration 3: log likelihood = -1706.291
Iteration 4: log likelihood = -1706.291
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
-----------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
personid | 108 4 25.4 30
burst | 462 1 5.9 6
-----------------------------------------------------------
Wald chi2(4) = 57.67
Log likelihood = -1706.291 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0451101 .01253 -3.60 0.000 -.0696685 -.0205518
slope12 | -.0158038 .0334038 -0.47 0.636 -.081274 .0496664
|
c.slope12#c.b1or2 | -.1940035 .0421584 -4.60 0.000 -.2766324 -.1113745
|
slope26 | .0160071 .0067886 2.36 0.018 .0027016 .0293125
_cons | 2.573924 .0584683 44.02 0.000 2.459328 2.68852
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0071941 .0021487 .0040063 .0129184
var(slope12) | .0214065 .0120304 .0071149 .064405
var(slope26) | .0013223 .0007078 .0004631 .0037752
var(_cons) | .3069705 .0504973 .2223679 .4237612
cov(burst1,slope12) | -.0000682 .0034065 -.0067447 .0066083
cov(burst1,slope26) | .000639 .0008402 -.0010076 .0022857
cov(burst1,_cons) | -.0048056 .007899 -.0202874 .0106762
cov(slope12,slope26) | .0020752 .0021443 -.0021274 .0062779
cov(slope12,_cons) | .0369675 .018135 .0014235 .0725116
cov(slope26,_cons) | .0062512 .0042516 -.0020817 .0145842
-----------------------------+------------------------------------------------
burst: Unstructured |
var(slope12) | .0353523 .0210495 .0110051 .1135641
var(slope26) | .0014414 .0012585 .0002604 .0079791
var(_cons) | .0605116 .0122123 .0407428 .0898725
cov(slope12,slope26) | -.0010621 .0037995 -.008509 .0063848
cov(slope12,_cons) | .0109375 .0122531 -.0130781 .0349531
cov(slope26,_cons) | -.006213 .0033236 -.012727 .0003011
-----------------------------+------------------------------------------------
var(Residual) | .1371382 .0052425 .1272387 .147808
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(16) = 2634.50 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1706.291 22 3456.582 3515.589
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope12 slope26 _cons
-------------+--------------------------------------------
burst1 | .0071941
slope12 | -.0000682 .0214065
slope26 | .000639 .0020752 .0013223
_cons | -.0048056 .0369675 .0062512 .3069705
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope12 slope26 _cons
-------------+--------------------------------------------
burst1 | 1
slope12 | -.0054953 1
slope26 | .2071902 .3900563 1
_cons | -.1022608 .4560364 .3102773 1
. estat recovariance, relevel(burst),
Random-effects covariance matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | .0353523
slope26 | -.0010621 .0014414
_cons | .0109375 -.006213 .0605116
. estat recovariance, relevel(burst) correlation,
Random-effects correlation matrix for level burst
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | -.1487911 1
_cons | .2364779 -.6652489 1
. lincom c.slope12*1 + c.slope12#c.b1or2*1 // Slope12 at Burst 1 or 2
( 1) [posaff]slope12 + [posaff]c.slope12#c.b1or2 = 0
------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.2098073 .0362321 -5.79 0.000 -.2808209 -.1387937
------------------------------------------------------------------------------
. estimates store FitRandSlope26at23P,
. lrtest FitRandSlope26at23P FitRandSlope26at2P,
Likelihood-ratio test LR chi2(4) = 13.26
(Assumption: FitRandSlop~2P nested in FitRandSlo~23P) Prob > chi2 = 0.0101
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
. predict PredUncP, xb,
. margins, at (c.slope12=-1 c.slope26=0 c.b1or2=1 c.burst1=(0(1)1)) vsquish,
Adjusted predictions Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 0
slope12 = -1
b1or2 = 1
slope26 = 0
2._at : burst1 = 1
slope12 = -1
b1or2 = 1
slope26 = 0
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 2.783731 .0588962 47.27 0.000 2.668297 2.899166
2 | 2.738621 .057845 47.34 0.000 2.625247 2.851995
------------------------------------------------------------------------------
. margins, at (c.slope12=-1 c.slope26=0 c.b1or2=0 c.burst1=(2(1)4)) vsquish,
Adjusted predictions Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 2
slope12 = -1
b1or2 = 0
slope26 = 0
2._at : burst1 = 3
slope12 = -1
b1or2 = 0
slope26 = 0
3._at : burst1 = 4
slope12 = -1
b1or2 = 0
slope26 = 0
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 2.499508 .0574972 43.47 0.000 2.386815 2.6122
2 | 2.454397 .0603448 40.67 0.000 2.336124 2.572671
3 | 2.409287 .0655062 36.78 0.000 2.280897 2.537677
------------------------------------------------------------------------------
. margins, at (c.slope12=0 c.slope26=(0(1)4) c.b1or2=1 c.burst1=(0(1)1)) vsquish,
Adjusted predictions Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 0
slope12 = 0
b1or2 = 1
slope26 = 0
2._at : burst1 = 0
slope12 = 0
b1or2 = 1
slope26 = 1
3._at : burst1 = 0
slope12 = 0
b1or2 = 1
slope26 = 2
4._at : burst1 = 0
slope12 = 0
b1or2 = 1
slope26 = 3
5._at : burst1 = 0
slope12 = 0
b1or2 = 1
slope26 = 4
6._at : burst1 = 1
slope12 = 0
b1or2 = 1
slope26 = 0
7._at : burst1 = 1
slope12 = 0
b1or2 = 1
slope26 = 1
8._at : burst1 = 1
slope12 = 0
b1or2 = 1
slope26 = 2
9._at : burst1 = 1
slope12 = 0
b1or2 = 1
slope26 = 3
10._at : burst1 = 1
slope12 = 0
b1or2 = 1
slope26 = 4
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 2.573924 .0584683 44.02 0.000 2.459328 2.68852
2 | 2.589931 .0585831 44.21 0.000 2.47511 2.704752
3 | 2.605938 .0594776 43.81 0.000 2.489364 2.722512
4 | 2.621945 .0611177 42.90 0.000 2.502157 2.741734
5 | 2.637952 .0634454 41.58 0.000 2.513602 2.762303
6 | 2.528814 .056597 44.68 0.000 2.417886 2.639742
7 | 2.544821 .056833 44.78 0.000 2.43343 2.656212
8 | 2.560828 .05787 44.25 0.000 2.447405 2.674251
9 | 2.576835 .0596662 43.19 0.000 2.459892 2.693779
10 | 2.592842 .0621558 41.72 0.000 2.471019 2.714665
------------------------------------------------------------------------------
. margins, at (c.slope12=0 c.slope26=(0(1)4) c.b1or2=0 c.burst1=(2(1)4)) vsquish,
Adjusted predictions Number of obs = 2747
Expression : Linear prediction, fixed portion, predict()
1._at : burst1 = 2
slope12 = 0
b1or2 = 0
slope26 = 0
2._at : burst1 = 2
slope12 = 0
b1or2 = 0
slope26 = 1
3._at : burst1 = 2
slope12 = 0
b1or2 = 0
slope26 = 2
4._at : burst1 = 2
slope12 = 0
b1or2 = 0
slope26 = 3
5._at : burst1 = 2
slope12 = 0
b1or2 = 0
slope26 = 4
6._at : burst1 = 3
slope12 = 0
b1or2 = 0
slope26 = 0
7._at : burst1 = 3
slope12 = 0
b1or2 = 0
slope26 = 1
8._at : burst1 = 3
slope12 = 0
b1or2 = 0
slope26 = 2
9._at : burst1 = 3
slope12 = 0
b1or2 = 0
slope26 = 3
10._at : burst1 = 3
slope12 = 0
b1or2 = 0
slope26 = 4
11._at : burst1 = 4
slope12 = 0
b1or2 = 0
slope26 = 0
12._at : burst1 = 4
slope12 = 0
b1or2 = 0
slope26 = 1
13._at : burst1 = 4
slope12 = 0
b1or2 = 0
slope26 = 2
14._at : burst1 = 4
slope12 = 0
b1or2 = 0
slope26 = 3
15._at : burst1 = 4
slope12 = 0
b1or2 = 0
slope26 = 4
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 2.483704 .0574621 43.22 0.000 2.37108 2.596327
2 | 2.499711 .0578101 43.24 0.000 2.386405 2.613017
3 | 2.515718 .0589431 42.68 0.000 2.400192 2.631244
4 | 2.531725 .0608173 41.63 0.000 2.412525 2.650925
5 | 2.547732 .0633669 40.21 0.000 2.423535 2.671929
6 | 2.438594 .0609473 40.01 0.000 2.319139 2.558048
7 | 2.454601 .0613842 39.99 0.000 2.33429 2.574912
8 | 2.470608 .0625591 39.49 0.000 2.347994 2.593221
9 | 2.486615 .0644316 38.59 0.000 2.360331 2.612898
10 | 2.502622 .0669432 37.38 0.000 2.371416 2.633828
11 | 2.393483 .0666427 35.92 0.000 2.262866 2.524101
12 | 2.409491 .0671419 35.89 0.000 2.277895 2.541086
13 | 2.425498 .0683154 35.50 0.000 2.291602 2.559393
14 | 2.441505 .0701293 34.81 0.000 2.304054 2.578956
15 | 2.457512 .0725356 33.88 0.000 2.315345 2.599679
------------------------------------------------------------------------------
. corr posaff PredUncP
(obs=2747)
| posaff PredUncP
-------------+------------------
posaff | 1.0000
PredUncP | 0.1090 1.0000
.
. display as result "Ch 10b: Final Unconditional Model for Positive Affect"
Ch 10b: Final Unconditional Model for Positive Affect
. display as result "Removing Level-2 Random Effects Variances and Covariances"
Removing Level-2 Random Effects Variances and Covariances
. mixed posaff c.burst1 c.slope12 c.slope12#c.b1or2 c.slope26, ///
> || personid: burst1 slope12 slope26, variance mle covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1783.0551
Iteration 1: log likelihood = -1782.2876
Iteration 2: log likelihood = -1782.2401
Iteration 3: log likelihood = -1782.2365
Iteration 4: log likelihood = -1782.2364
Computing standard errors:
Mixed-effects ML regression Number of obs = 2747
Group variable: personid Number of groups = 108
Obs per group: min = 4
avg = 25.4
max = 30
Wald chi2(4) = 62.96
Log likelihood = -1782.2364 Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------
posaff | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
burst1 | -.0469074 .0125342 -3.74 0.000 -.071474 -.0223408
slope12 | -.0117781 .0332119 -0.35 0.723 -.0768722 .0533159
|
c.slope12#c.b1or2 | -.2037908 .0419766 -4.85 0.000 -.2860634 -.1215181
|
slope26 | .016143 .0068026 2.37 0.018 .0028101 .029476
_cons | 2.572251 .0584622 44.00 0.000 2.457668 2.686835
-----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(burst1) | .0112076 .0021025 .0077595 .0161879
var(slope12) | .0163753 .0110789 .0043481 .0616708
var(slope26) | .0008998 .0006663 .0002108 .0038414
var(_cons) | .3305789 .0502067 .2454703 .4451962
cov(burst1,slope12) | -.0000394 .0033902 -.006684 .0066052
cov(burst1,slope26) | .0006353 .0008382 -.0010075 .0022781
cov(burst1,_cons) | -.0113276 .0078818 -.0267756 .0041205
cov(slope12,slope26) | .0034552 .0019577 -.0003819 .0072923
cov(slope12,_cons) | .0357959 .0179491 .0006163 .0709755
cov(slope26,_cons) | .0062738 .0042158 -.001989 .0145366
-----------------------------+------------------------------------------------
var(Residual) | .1714907 .0050148 .1619382 .1816067
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(10) = 2482.61 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(108),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 108 . -1782.236 16 3596.473 3639.387
-----------------------------------------------------------------------------
Note: N=108 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| burst1 slope12 slope26 _cons
-------------+--------------------------------------------
burst1 | .0112076
slope12 | -.0000394 .0163753
slope26 | .0006353 .0034552 .0008998
_cons | -.0113276 .0357959 .0062738 .3305789
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| burst1 slope12 slope26 _cons
-------------+--------------------------------------------
burst1 | 1
slope12 | -.0029084 1
slope26 | .2000619 .9001093 1
_cons | -.1860983 .4865194 .363755 1
. estimates store FitNo2P,
. lrtest FitRandSlope26at23P FitNo2P,
Likelihood-ratio test LR chi2(6) = 151.89
(Assumption: FitNo2P nested in FitRandSlo~23P) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. ****** END CHAPTER 10b MODELS ******
.
. * Close log
. log close STATA_Chapter10b
name: STATA_Chapter10b
log: C:\Dropbox\PilesOfVariance\Chapter10b\STATA\STATA_Chapter10b_Output.smcl
log type: smcl
closed on: 30 Jan 2015, 12:23:46
------------------------------------------------------------------------------------------------------------------------------------------------------