------------------------------------------------------------------------------------------------------------------------------------------------------
name: STATA_Chapter6
log: C:\Dropbox\PilesOfVariance\Chapter6\STATA\STATA_Chapter6_Output.smcl
log type: smcl
opened on: 6 Jan 2015, 12:52:22
.
. display as result "Chapter 6 Example: Means by session for RT outcome"
Chapter 6 Example: Means by session for RT outcome
. tabulate session, summarize(rt)
session: | Summary of rt: Response Time in
Occasion | Milliseconds
(1-6) | Mean Std. Dev. Freq.
------------+------------------------------------
1 | 1961.8934 549.53193 101
2 | 1815.1724 509.06784 101
3 | 1750.0346 483.08178 101
4 | 1717.7965 466.41575 101
5 | 1707.1757 460.54053 101
6 | 1672.136 443.54613 101
------------+------------------------------------
Total | 1770.7014 494.08763 606
.
. display as result "Ch 6: 0: Saturated Means, Unstructured Variance Model"
Ch 6: 0: Saturated Means, Unstructured Variance Model
. display as result "TOTAL ANSWER KEY"
TOTAL ANSWER KEY
. mixed rt i.session, ///
> || personid: , noconstant variance reml covariance(unstructured) ///
> residuals(unstructured,t(session)),
Obtaining starting values by EM:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4577.7163 (not concave)
Iteration 1: log restricted-likelihood = -4203.3431
Iteration 2: log restricted-likelihood = -4161.6274 (not concave)
Iteration 3: log restricted-likelihood = -4127.1235
Iteration 4: log restricted-likelihood = -4118.1617
Iteration 5: log restricted-likelihood = -4114.9737
Iteration 6: log restricted-likelihood = -4114.8943
Iteration 7: log restricted-likelihood = -4114.8942
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(5) = 83.60
Log restricted-likelihood = -4114.8942 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
session |
2 | -146.721 29.82087 -4.92 0.000 -205.1688 -88.27315
3 | -211.8587 31.3658 -6.75 0.000 -273.3346 -150.3829
4 | -244.0969 33.64274 -7.26 0.000 -310.0355 -178.1583
5 | -254.7176 35.84557 -7.11 0.000 -324.9737 -184.4616
6 | -289.7574 32.69999 -8.86 0.000 -353.8482 -225.6666
|
_cons | 1961.893 54.68037 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: (empty) |
-----------------------------+------------------------------------------------
Residual: Unstructured |
var(e1) | 301984.3 42695.54 228896.2 398409.8
var(e2) | 259149.5 36634.32 196436.2 341884.5
var(e3) | 233367.6 32989.07 176894.3 307869.9
var(e4) | 217543.3 30752.36 164899 286994.3
var(e5) | 212097.3 29983.2 160769.9 279811.5
var(e6) | 196732.8 27810.84 149124.2 259540.8
cov(e1,e2) | 235658.1 36562.36 163997.1 307319
cov(e1,e3) | 217993.4 34334.82 150698.3 285288.4
cov(e1,e4) | 202606.2 32656.16 138601.3 266611.1
cov(e1,e5) | 192153.1 31760.42 129903.8 254402.4
cov(e1,e6) | 195359.4 31222.49 134164.5 256554.4
cov(e2,e3) | 230216.3 33671.07 164222.2 296210.4
cov(e2,e4) | 213231.3 31897.72 150712.9 275749.6
cov(e2,e5) | 202091.6 30936.96 141456.3 262726.9
cov(e2,e6) | 193267.8 29705.99 135045.2 251490.5
cov(e3,e4) | 205208.6 30461.36 145505.4 264911.8
cov(e3,e5) | 196918.3 29696.25 138714.7 255121.9
cov(e3,e6) | 188604 28530.72 132684.9 244523.2
cov(e4,e5) | 193675.3 28908.89 137014.9 250335.7
cov(e4,e6) | 185320.6 27760.99 130910 239731.1
cov(e5,e6) | 187840 27738.3 133474 242206.1
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(20) = 925.64 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.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4114.894 27 8283.788 8354.397
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat wcorrelation, covariance,
Covariances for personid = 101:
session | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05
2 | 2.4e+05 2.6e+05
3 | 2.2e+05 2.3e+05 2.3e+05
4 | 2.0e+05 2.1e+05 2.1e+05 2.2e+05
5 | 1.9e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05
6 | 2.0e+05 1.9e+05 1.9e+05 1.9e+05 1.9e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
session | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 549.531 509.067 483.081 466.415 460.540 443.546
Correlations:
session | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.842 1.000
3 | 0.821 0.936 1.000
4 | 0.790 0.898 0.911 1.000
5 | 0.759 0.862 0.885 0.902 1.000
6 | 0.802 0.856 0.880 0.896 0.920 1.000
. contrast i.session,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
rt |
session | 5 83.60 0.0000
------------------------------------------------
. margins i.session,
Adjusted predictions Number of obs = 606
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
session |
1 | 1961.893 54.68037 35.88 0.000 1854.722 2069.065
2 | 1815.172 50.65409 35.83 0.000 1715.892 1914.453
3 | 1750.035 48.06839 36.41 0.000 1655.822 1844.247
4 | 1717.796 46.41007 37.01 0.000 1626.834 1808.759
5 | 1707.176 45.82547 37.25 0.000 1617.359 1796.992
6 | 1672.136 44.13445 37.89 0.000 1585.634 1758.638
------------------------------------------------------------------------------
. margins i.session, pwcompare(pveffects)
Pairwise comparisons of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-----------------------------------------------------
| Delta-method Unadjusted
| Contrast Std. Err. z P>|z|
-------------+---------------------------------------
session |
2 vs 1 | -146.721 29.82087 -4.92 0.000
3 vs 1 | -211.8587 31.3658 -6.75 0.000
4 vs 1 | -244.0969 33.64274 -7.26 0.000
5 vs 1 | -254.7176 35.84557 -7.11 0.000
6 vs 1 | -289.7574 32.69999 -8.86 0.000
3 vs 2 | -65.13774 17.82326 -3.65 0.000
4 vs 2 | -97.37592 22.3009 -4.37 0.000
5 vs 2 | -107.9967 25.76813 -4.19 0.000
6 vs 2 | -143.0364 26.20307 -5.46 0.000
4 vs 3 | -32.23819 20.02319 -1.61 0.107
5 vs 3 | -42.85892 22.60911 -1.90 0.058
6 vs 3 | -77.89864 22.8842 -3.40 0.001
5 vs 4 | -10.62073 20.4625 -0.52 0.604
6 vs 4 | -45.66045 20.78531 -2.20 0.028
6 vs 5 | -35.03972 18.11681 -1.93 0.053
-----------------------------------------------------
.
. display as result "Ch 6: 1a: Empty Means, E-Only Variance Model"
Ch 6: 1a: Empty Means, E-Only Variance Model
. mixed rt , ///
> || personid: , noconstant variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Note: all random-effects equations are empty; model is linear regression
Mixed-effects REML regression Number of obs = 606
Wald chi2(0) = .
Log restricted-likelihood = -4614.3025 Prob > chi2 = .
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1770.701 20.07094 88.22 0.000 1731.363 1810.04
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
var(Residual) | 244122.6 14024.48 218126.1 273217.3
------------------------------------------------------------------------------
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4614.303 2 9232.605 9237.835
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat wcorrelation, covariance,
model is linear regression; all observations are independent with standard deviation 494.08763
. estat wcorrelation,
model is linear regression; all observations are independent with standard deviation 494.08763
.
. display as result "Ch 6: 1b: Empty Means, Random Intercept Model"
Ch 6: 1b: Empty Means, Random Intercept Model
. mixed rt , ///
> || personid: , variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4268.4304
Iteration 1: log restricted-likelihood = -4268.4304
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(0) = .
Log restricted-likelihood = -4268.4304 Prob > chi2 = .
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1770.701 45.42063 38.98 0.000 1681.679 1859.724
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 200883 29471.23 150683.2 267806.8
-----------------------------+------------------------------------------------
var(Residual) | 44899.96 2825.63 39689.76 50794.13
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 691.74 Prob >= chibar2 = 0.0000
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4268.43 3 8542.861 8550.706
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat icc,
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid | .8173187 .0239727 .7655942 .8597208
------------------------------------------------------------------------------
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| _cons
-------------+-----------
_cons | 200883
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| _cons
-------------+-----------
_cons | 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.5e+05
2 | 2.0e+05 2.5e+05
3 | 2.0e+05 2.0e+05 2.5e+05
4 | 2.0e+05 2.0e+05 2.0e+05 2.5e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.5e+05
6 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.5e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 495.765 495.765 495.765 495.765 495.765 495.765
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.817 1.000
3 | 0.817 0.817 1.000
4 | 0.817 0.817 0.817 1.000
5 | 0.817 0.817 0.817 0.817 1.000
6 | 0.817 0.817 0.817 0.817 0.817 1.000
.
. display as result "Ch 6: 2a: Fixed Linear Time, Random Intercept Model"
Ch 6: 2a: Fixed Linear Time, Random Intercept Model
. mixed rt c.time1, ///
> || personid: , variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4207.344
Iteration 1: log restricted-likelihood = -4207.344
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(1) = 131.82
Log restricted-likelihood = -4207.344 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time1 | -51.57185 4.491815 -11.48 0.000 -60.37565 -42.76806
_cons | 1899.631 46.7882 40.60 0.000 1807.928 1991.334
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 202422.7 29469.85 152172.6 269266.3
-----------------------------+------------------------------------------------
var(Residual) | 35661.79 2246.481 31519.73 40348.16
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 787.61 Prob >= chibar2 = 0.0000
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4207.344 4 8422.688 8433.149
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| _cons
-------------+-----------
_cons | 202422.7
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| _cons
-------------+-----------
_cons | 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.4e+05
2 | 2.0e+05 2.4e+05
3 | 2.0e+05 2.0e+05 2.4e+05
4 | 2.0e+05 2.0e+05 2.0e+05 2.4e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
6 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 487.939 487.939 487.939 487.939 487.939 487.939
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.850 1.000
3 | 0.850 0.850 1.000
4 | 0.850 0.850 0.850 1.000
5 | 0.850 0.850 0.850 0.850 1.000
6 | 0.850 0.850 0.850 0.850 0.850 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1899.631 46.7882 40.60 0.000 1807.928 1991.334
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1
( 1) [rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1848.059 45.91765 40.25 0.000 1758.062 1938.056
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2
( 1) 2*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1796.487 45.47612 39.50 0.000 1707.356 1885.619
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3
( 1) 3*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1744.916 45.47612 38.37 0.000 1655.784 1834.047
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4
( 1) 4*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1693.344 45.91765 36.88 0.000 1603.347 1783.341
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5
( 1) 5*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1641.772 46.7882 35.09 0.000 1550.069 1733.475
------------------------------------------------------------------------------
. estimates store FitFixLin,
.
. display as result "Ch 6: 2b: Random Linear Time Model"
Ch 6: 2b: Random Linear Time Model
. mixed rt c.time1, ///
> || personid: time1, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4186.0513
Iteration 1: log restricted-likelihood = -4186.0512
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(1) = 70.17
Log restricted-likelihood = -4186.0512 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time1 | -51.57185 6.156722 -8.38 0.000 -63.63881 -39.5049
_cons | 1899.631 51.4998 36.89 0.000 1798.693 2000.569
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 2233.833 552.9239 1375.178 3628.626
var(_cons) | 253258 37897.26 188881.9 339575.3
cov(time1,_cons) | -12700.79 3621.977 -19799.74 -5601.848
-----------------------------+------------------------------------------------
var(Residual) | 27905.42 1963.419 24310.74 32031.62
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 830.20 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4186.051 6 8384.102 8399.793
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 2233.833
_cons | -12700.79 253258
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 1
_cons | -.5339786 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.8e+05 2.4e+05 2.3e+05 2.2e+05 2.0e+05 1.9e+05
2 | 2.4e+05 2.6e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
3 | 2.3e+05 2.2e+05 2.4e+05 2.0e+05 1.9e+05 1.9e+05
4 | 2.2e+05 2.1e+05 2.0e+05 2.3e+05 1.9e+05 1.9e+05
5 | 2.0e+05 2.0e+05 1.9e+05 1.9e+05 2.2e+05 1.8e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.1e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 530.248 507.933 489.179 474.408 464.003 458.259
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.893 1.000
3 | 0.878 0.884 1.000
4 | 0.855 0.868 0.875 1.000
5 | 0.823 0.843 0.859 0.868 1.000
6 | 0.781 0.809 0.833 0.852 0.864 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1899.631 51.4998 36.89 0.000 1798.693 2000.569
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1
( 1) [rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1848.059 48.57668 38.04 0.000 1752.851 1943.268
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2
( 1) 2*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1796.487 46.2922 38.81 0.000 1705.756 1887.218
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3
( 1) 3*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1744.916 44.7443 39.00 0.000 1657.218 1832.613
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4
( 1) 4*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1693.344 44.01077 38.48 0.000 1607.084 1779.603
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5
( 1) 5*[rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1641.772 44.13223 37.20 0.000 1555.274 1728.269
------------------------------------------------------------------------------
. estimates store FitRandLin,
. lrtest FitRandLin FitFixLin,
Likelihood-ratio test LR chi2(2) = 42.59
(Assumption: FitFixLin nested in FitRandLin) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: 3a: Fixed Quadratic, Random Linear Time Model"
Ch 6: 3a: Fixed Quadratic, Random Linear Time Model
. mixed rt c.time1 c.time1#c.time1, ///
> || personid: time1, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4170.7387
Iteration 1: log restricted-likelihood = -4170.7386
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 97.86
Log restricted-likelihood = -4170.7386 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
time1 | -120.8999 14.54147 -8.31 0.000 -149.4007 -92.39917
|
c.time1#c.time1 | 13.86561 2.634761 5.26 0.000 8.701578 19.02965
|
_cons | 1945.85 52.2433 37.25 0.000 1843.455 2048.245
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 2332.667 551.5799 1467.501 3707.891
var(_cons) | 254164 37895.62 189758.3 340429.7
cov(time1,_cons) | -12947.88 3620.697 -20044.31 -5851.442
-----------------------------+------------------------------------------------
var(Residual) | 26175.83 1844.008 22800.05 30051.42
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 851.78 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4170.739 7 8355.477 8373.783
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 2332.667
_cons | -12947.88 254164
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 1
_cons | -.5317594 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.8e+05 2.4e+05 2.3e+05 2.2e+05 2.0e+05 1.9e+05
2 | 2.4e+05 2.6e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
3 | 2.3e+05 2.2e+05 2.4e+05 2.0e+05 2.0e+05 1.9e+05
4 | 2.2e+05 2.1e+05 2.0e+05 2.2e+05 1.9e+05 1.9e+05
5 | 2.0e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05 1.8e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.1e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 529.471 506.731 487.728 472.913 462.687 457.360
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.899 1.000
3 | 0.884 0.890 1.000
4 | 0.860 0.874 0.882 1.000
5 | 0.826 0.848 0.865 0.875 1.000
6 | 0.782 0.812 0.838 0.858 0.871 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0 + c.time1#c.time1*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1945.85 52.2433 37.25 0.000 1843.455 2048.245
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1 + c.time1#c.time1*1
( 1) [rt]time1 + [rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1838.815 48.60842 37.83 0.000 1743.545 1934.086
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2 + c.time1#c.time1*4
( 1) 2*[rt]time1 + 4*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1759.512 46.82235 37.58 0.000 1667.742 1851.283
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3 + c.time1#c.time1*9
( 1) 3*[rt]time1 + 9*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1707.941 45.29258 37.71 0.000 1619.169 1796.712
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4 + c.time1#c.time1*16
( 1) 4*[rt]time1 + 16*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1684.1 44.04581 38.24 0.000 1597.772 1770.428
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5 + c.time1#c.time1*25
( 1) 5*[rt]time1 + 25*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1687.991 44.99763 37.51 0.000 1599.797 1776.184
------------------------------------------------------------------------------
. * Linear Slope at Session=1 Time=0
. lincom c.time1*1 + c.time1#c.time1*0
( 1) [rt]time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -120.8999 14.54147 -8.31 0.000 -149.4007 -92.39917
------------------------------------------------------------------------------
. * Linear Slope at Session=2 Time=1
. lincom c.time1*1 + c.time1#c.time1*2
( 1) [rt]time1 + 2*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -93.1687 10.01913 -9.30 0.000 -112.8058 -73.53157
------------------------------------------------------------------------------
. * Linear Slope at Session=3 Time=2
. lincom c.time1*1 + c.time1#c.time1*4
( 1) [rt]time1 + 4*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -65.43747 6.696805 -9.77 0.000 -78.56296 -52.31197
------------------------------------------------------------------------------
. * Linear Slope at Session=4 Time=3
. lincom c.time1*1 + c.time1#c.time1*6
( 1) [rt]time1 + 6*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -37.70624 6.696805 -5.63 0.000 -50.83174 -24.58074
------------------------------------------------------------------------------
. * Linear Slope at Session=5 Time=4
. lincom c.time1*1 + c.time1#c.time1*8
( 1) [rt]time1 + 8*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -9.975015 10.01913 -1.00 0.319 -29.61214 9.662113
------------------------------------------------------------------------------
. * Linear Slope at Session=6 Time=5
. lincom c.time1*1 + c.time1#c.time1*10
( 1) [rt]time1 + 10*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 17.75621 14.54147 1.22 0.222 -10.74454 46.25697
------------------------------------------------------------------------------
. estimates store FitFixQuad,
.
. display as result "Ch 6: 3b: Random Quadratic Time Model"
Ch 6: 3b: Random Quadratic Time Model
. mixed rt c.time1 c.time1#c.time1, ///
> || personid: time1 time1sq, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4153.7932
Iteration 1: log restricted-likelihood = -4151.7999
Iteration 2: log restricted-likelihood = -4151.3732
Iteration 3: log restricted-likelihood = -4151.3728
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 71.74
Log restricted-likelihood = -4151.3728 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
time1 | -120.8999 20.04752 -6.03 0.000 -160.1923 -81.6075
|
c.time1#c.time1 | 13.86561 3.41541 4.06 0.000 7.171534 20.55969
|
_cons | 1945.85 53.84993 36.13 0.000 1840.306 2051.394
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 25839.79 5864.685 16561.42 40316.29
var(time1sq) | 634.4659 172.375 372.5198 1080.605
var(_cons) | 276207.8 41445.59 205831.2 370647.1
cov(time1,time1sq) | -3903.291 982.6248 -5829.2 -1977.381
cov(time1,_cons) | -35734.05 11947.96 -59151.62 -12316.48
cov(time1sq,_cons) | 3901.974 1950.304 79.44722 7724.5
-----------------------------+------------------------------------------------
var(Residual) | 20298.19 1649.117 17310.19 23801.96
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 890.51 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4151.373 10 8322.746 8348.897
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time1 time1sq _cons
-------------+---------------------------------
time1 | 25839.79
time1sq | -3903.291 634.4659
_cons | -35734.05 3901.974 276207.8
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time1 time1sq _cons
-------------+---------------------------------
time1 | 1
time1sq | -.9640116 1
_cons | -.4229799 .2947557 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05 2.4e+05 2.2e+05 2.0e+05 2.0e+05 2.0e+05
2 | 2.4e+05 2.5e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
3 | 2.2e+05 2.2e+05 2.4e+05 2.1e+05 2.0e+05 1.9e+05
4 | 2.0e+05 2.1e+05 2.1e+05 2.3e+05 2.0e+05 1.8e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.1e+05 1.8e+05
6 | 2.0e+05 1.9e+05 1.9e+05 1.8e+05 1.8e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 544.524 501.507 485.637 474.878 460.147 448.305
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.895 1.000
3 | 0.833 0.900 1.000
4 | 0.789 0.876 0.906 1.000
5 | 0.781 0.864 0.894 0.902 1.000
6 | 0.799 0.851 0.863 0.869 0.885 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0 + c.time1#c.time1*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1945.85 53.84993 36.13 0.000 1840.306 2051.394
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1 + c.time1#c.time1*1
( 1) [rt]time1 + [rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1838.815 48.48658 37.92 0.000 1743.784 1933.847
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2 + c.time1#c.time1*4
( 1) 2*[rt]time1 + 4*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1759.512 46.99744 37.44 0.000 1667.399 1851.626
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3 + c.time1#c.time1*9
( 1) 3*[rt]time1 + 9*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1707.941 45.89598 37.21 0.000 1617.986 1797.895
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4 + c.time1#c.time1*16
( 1) 4*[rt]time1 + 16*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1684.1 44.23964 38.07 0.000 1597.392 1770.808
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5 + c.time1#c.time1*25
( 1) 5*[rt]time1 + 25*[rt]c.time1#c.time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1687.991 44.20394 38.19 0.000 1601.352 1774.629
------------------------------------------------------------------------------
. * Linear Slope at Session=1 Time=0
. lincom c.time1*1 + c.time1#c.time1*0
( 1) [rt]time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -120.8999 20.04752 -6.03 0.000 -160.1923 -81.6075
------------------------------------------------------------------------------
. * Linear Slope at Session=2 Time=1
. lincom c.time1*1 + c.time1#c.time1*2
( 1) [rt]time1 + 2*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -93.1687 13.64968 -6.83 0.000 -119.9216 -66.4158
------------------------------------------------------------------------------
. * Linear Slope at Session=3 Time=2
. lincom c.time1*1 + c.time1#c.time1*4
( 1) [rt]time1 + 4*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -65.43747 8.002796 -8.18 0.000 -81.12266 -49.75228
------------------------------------------------------------------------------
. * Linear Slope at Session=4 Time=3
. lincom c.time1*1 + c.time1#c.time1*6
( 1) [rt]time1 + 6*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -37.70624 5.92417 -6.36 0.000 -49.3174 -26.09508
------------------------------------------------------------------------------
. * Linear Slope at Session=5 Time=4
. lincom c.time1*1 + c.time1#c.time1*8
( 1) [rt]time1 + 8*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -9.975015 9.973315 -1.00 0.317 -29.52235 9.572324
------------------------------------------------------------------------------
. * Linear Slope at Session=6 Time=5
. lincom c.time1*1 + c.time1#c.time1*10
( 1) [rt]time1 + 10*[rt]c.time1#c.time1 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 17.75621 16.03616 1.11 0.268 -13.67408 49.18651
------------------------------------------------------------------------------
. estimates store FitRandQuad,
. lrtest FitRandQuad FitFixQuad,
Likelihood-ratio test LR chi2(3) = 38.73
(Assumption: FitFixQuad nested in FitRandQuad) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: 3b: Random Quadratic Time Model (0=Session 6)"
Ch 6: 3b: Random Quadratic Time Model (0=Session 6)
. mixed rt c.time6 c.time6#c.time6, ///
> || personid: time6 time6sq, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4153.4279
Iteration 1: log restricted-likelihood = -4151.4942
Iteration 2: log restricted-likelihood = -4151.3729
Iteration 3: log restricted-likelihood = -4151.3728
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 71.74
Log restricted-likelihood = -4151.3728 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
time6 | 17.75621 16.03619 1.11 0.268 -13.67415 49.18657
|
c.time6#c.time6 | 13.86561 3.415417 4.06 0.000 7.17152 20.55971
|
_cons | 1687.991 44.20384 38.19 0.000 1601.353 1774.628
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time6) | 11220.67 3863.737 5713.673 22035.48
var(time6sq) | 634.4708 172.3738 372.5257 1080.605
var(_cons) | 180678.4 27942.63 133433.4 244651.5
cov(time6,time6sq) | 2441.391 788.0532 896.8351 3985.947
cov(time6,_cons) | -1645.855 7298.43 -15950.52 12658.8
cov(time6sq,_cons) | 247.1107 1545.719 -2782.443 3276.664
-----------------------------+------------------------------------------------
var(Residual) | 20298.18 1649.115 17310.19 23801.95
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 890.51 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4151.373 10 8322.746 8348.897
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time6 time6sq _cons
-------------+---------------------------------
time6 | 11220.67
time6sq | 2441.391 634.4708
_cons | -1645.855 247.1107 180678.4
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time6 time6sq _cons
-------------+---------------------------------
time6 | 1
time6sq | .915002 1
_cons | -.0365535 .0230798 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05 2.4e+05 2.2e+05 2.0e+05 2.0e+05 2.0e+05
2 | 2.4e+05 2.5e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
3 | 2.2e+05 2.2e+05 2.4e+05 2.1e+05 2.0e+05 1.9e+05
4 | 2.0e+05 2.1e+05 2.1e+05 2.3e+05 2.0e+05 1.8e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.1e+05 1.8e+05
6 | 2.0e+05 1.9e+05 1.9e+05 1.8e+05 1.8e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 544.522 501.506 485.637 474.878 460.147 448.304
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.895 1.000
3 | 0.833 0.900 1.000
4 | 0.789 0.876 0.906 1.000
5 | 0.781 0.864 0.894 0.902 1.000
6 | 0.799 0.851 0.863 0.869 0.885 1.000
. * Intercept at Session=1 Time=-5
. lincom _cons*1 + c.time6*-5 + c.time6#c.time6*25
( 1) - 5*[rt]time6 + 25*[rt]c.time6#c.time6 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1945.85 53.84975 36.13 0.000 1840.306 2051.393
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=-4
. lincom _cons*1 + c.time6*-4 + c.time6#c.time6*16
( 1) - 4*[rt]time6 + 16*[rt]c.time6#c.time6 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1838.815 48.48645 37.92 0.000 1743.784 1933.847
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=-3
. lincom _cons*1 + c.time6*-3 + c.time6#c.time6*9
( 1) - 3*[rt]time6 + 9*[rt]c.time6#c.time6 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1759.512 46.99736 37.44 0.000 1667.399 1851.626
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=-2
. lincom _cons*1 + c.time6*-2 + c.time6#c.time6*4
( 1) - 2*[rt]time6 + 4*[rt]c.time6#c.time6 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1707.941 45.89593 37.21 0.000 1617.986 1797.895
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=-1
. lincom _cons*1 + c.time6*-1 + c.time6#c.time6*1
( 1) - [rt]time6 + [rt]c.time6#c.time6 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1684.1 44.23958 38.07 0.000 1597.392 1770.808
------------------------------------------------------------------------------
. * Intercept at Session=6 Time= 0
. lincom _cons*1 + c.time6*0 + c.time6#c.time6*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1687.991 44.20384 38.19 0.000 1601.353 1774.628
------------------------------------------------------------------------------
. * Linear Slope at Session=1 Time=-5
. lincom c.time6*1 + c.time6#c.time6*-10
( 1) [rt]time6 - 10*[rt]c.time6#c.time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -120.8999 20.04756 -6.03 0.000 -160.1924 -81.60743
------------------------------------------------------------------------------
. * Linear Slope at Session=2 Time=-4
. lincom c.time6*1 + c.time6#c.time6*-8
( 1) [rt]time6 - 8*[rt]c.time6#c.time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -93.1687 13.6497 -6.83 0.000 -119.9216 -66.41577
------------------------------------------------------------------------------
. * Linear Slope at Session=3 Time=-3
. lincom c.time6*1 + c.time6#c.time6*-6
( 1) [rt]time6 - 6*[rt]c.time6#c.time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -65.43747 8.002802 -8.18 0.000 -81.12267 -49.75226
------------------------------------------------------------------------------
. * Linear Slope at Session=4 Time=-2
. lincom c.time6*1 + c.time6#c.time6*-4
( 1) [rt]time6 - 4*[rt]c.time6#c.time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -37.70624 5.924171 -6.36 0.000 -49.3174 -26.09508
------------------------------------------------------------------------------
. * Linear Slope at Session=5 Time=-1
. lincom c.time6*1 + c.time6#c.time6*-2
( 1) [rt]time6 - 2*[rt]c.time6#c.time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -9.975015 9.973331 -1.00 0.317 -29.52239 9.572356
------------------------------------------------------------------------------
. * Linear Slope at Session=6 Time= 0
. lincom c.time6*1 + c.time6#c.time6*0
( 1) [rt]time6 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 17.75621 16.03619 1.11 0.268 -13.67415 49.18657
------------------------------------------------------------------------------
.
. display as result "Ch 6: 4a: Fixed Slope12, Fixed Slope26, Random Intercept Model"
Ch 6: 4a: Fixed Slope12, Fixed Slope26, Random Intercept Model
. mixed rt c.slope12 c.slope26, ///
> || personid: , variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4191.3436
Iteration 1: log restricted-likelihood = -4191.3436
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 161.98
Log restricted-likelihood = -4191.3436 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
slope12 | -163.644 23.24149 -7.04 0.000 -209.1965 -118.0915
slope26 | -32.89317 5.810373 -5.66 0.000 -44.28129 -21.50504
_cons | 1961.893 48.4187 40.52 0.000 1866.994 2056.792
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 202683.4 29469.65 152424.8 269513.6
-----------------------------+------------------------------------------------
var(Residual) | 34098.04 2150.109 30133.91 38583.65
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 805.80 Prob >= chibar2 = 0.0000
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4191.344 5 8392.687 8405.763
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| _cons
-------------+-----------
_cons | 202683.4
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| _cons
-------------+-----------
_cons | 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.4e+05
2 | 2.0e+05 2.4e+05
3 | 2.0e+05 2.0e+05 2.4e+05
4 | 2.0e+05 2.0e+05 2.0e+05 2.4e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
6 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 486.602 486.602 486.602 486.602 486.602 486.602
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.856 1.000
3 | 0.856 0.856 1.000
4 | 0.856 0.856 0.856 1.000
5 | 0.856 0.856 0.856 0.856 1.000
6 | 0.856 0.856 0.856 0.856 0.856 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.slope12*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 48.4187 40.52 0.000 1866.994 2056.792
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.slope12*1 + c.slope26*0
( 1) [rt]slope12 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 47.00349 38.26 0.000 1706.124 1890.375
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.slope12*1 + c.slope26*1
( 1) [rt]slope12 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 45.91347 38.45 0.000 1675.367 1855.345
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.slope12*1 + c.slope26*2
( 1) [rt]slope12 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 45.54434 38.04 0.000 1643.198 1821.728
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.slope12*1 + c.slope26*3
( 1) [rt]slope12 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 45.91347 37.02 0.000 1609.581 1789.559
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.slope12*1 + c.slope26*4
( 1) [rt]slope12 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 47.00349 35.46 0.000 1574.552 1758.802
------------------------------------------------------------------------------
. * Difference between slope12 and slope26
. lincom c.slope12*-1 + c.slope26*1
( 1) - [rt]slope12 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 130.7508 26.62648 4.91 0.000 78.56389 182.9378
------------------------------------------------------------------------------
. estimates store FitFix12Fix26,
.
. display as result "Ch 6: 4b: Random Slope12, Fixed Slope26 Model"
Ch 6: 4b: Random Slope12, Fixed Slope26 Model
. mixed rt c.slope12 c.slope26, ///
> || personid: slope12, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4159.8067
Iteration 1: log restricted-likelihood = -4159.8066
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 104.99
Log restricted-likelihood = -4159.8066 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
slope12 | -163.644 31.24619 -5.24 0.000 -224.8854 -102.4026
slope26 | -32.89317 4.891648 -6.72 0.000 -42.48062 -23.30571
_cons | 1961.893 54.6805 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(slope12) | 59940.74 12743.1 39514.9 90925
var(_cons) | 277818.2 42741.21 205497.6 375590.5
cov(slope12,_cons) | -69063.12 18931.72 -106168.6 -31957.64
-----------------------------+------------------------------------------------
var(Residual) | 24167.5 1702.528 21050.73 27745.74
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 868.87 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4159.807 7 8333.613 8351.919
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| slope12 _cons
-------------+----------------------
slope12 | 59940.74
_cons | -69063.12 277818.2
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| slope12 _cons
-------------+----------------------
slope12 | 1
_cons | -.5351861 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05
2 | 2.1e+05 2.2e+05
3 | 2.1e+05 2.0e+05 2.2e+05
4 | 2.1e+05 2.0e+05 2.0e+05 2.2e+05
5 | 2.1e+05 2.0e+05 2.0e+05 2.0e+05 2.2e+05
6 | 2.1e+05 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.2e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 549.532 473.075 473.075 473.075 473.075 473.075
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.803 1.000
3 | 0.803 0.892 1.000
4 | 0.803 0.892 0.892 1.000
5 | 0.803 0.892 0.892 0.892 1.000
6 | 0.803 0.892 0.892 0.892 0.892 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.slope12*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 54.6805 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.slope12*1 + c.slope26*0
( 1) [rt]slope12 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 46.04488 39.05 0.000 1708.003 1888.496
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.slope12*1 + c.slope26*1
( 1) [rt]slope12 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 45.25866 39.01 0.000 1676.651 1854.062
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.slope12*1 + c.slope26*2
( 1) [rt]slope12 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 44.99353 38.50 0.000 1644.277 1820.649
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.slope12*1 + c.slope26*3
( 1) [rt]slope12 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 45.25866 37.55 0.000 1610.865 1788.275
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.slope12*1 + c.slope26*4
( 1) [rt]slope12 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 46.04488 36.20 0.000 1576.43 1756.923
------------------------------------------------------------------------------
. * Difference between slope12 and slope26
. lincom c.slope12*-1 + c.slope26*1
( 1) - [rt]slope12 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 130.7508 33.10537 3.95 0.000 65.8655 195.6361
------------------------------------------------------------------------------
. estimates store FitRand12Fix26,
. lrtest FitRand12Fix26 FitFix12Fix26,
Likelihood-ratio test LR chi2(2) = 63.07
(Assumption: FitFix12Fix26 nested in FitRand12Fix26) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: 4c: Random Slope12, Random Slope26 Model"
Ch 6: 4c: Random Slope12, Random Slope26 Model
. mixed rt c.slope12 c.slope26, ///
> || personid: slope12 slope26, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4137.6957
Iteration 1: log restricted-likelihood = -4137.6872
Iteration 2: log restricted-likelihood = -4137.6872
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 73.15
Log restricted-likelihood = -4137.6872 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
slope12 | -163.644 30.21884 -5.42 0.000 -222.8718 -104.4161
slope26 | -32.89317 6.588755 -4.99 0.000 -45.80689 -19.97944
_cons | 1961.893 54.6805 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(slope12) | 63954.2 13244.2 42618.17 95971.74
var(slope26) | 2617.279 636.4813 1624.992 4215.499
var(_cons) | 284312.6 42731.62 211768.9 381706.9
cov(slope12,slope26) | -1672.296 2097.085 -5782.507 2437.916
cov(slope12,_cons) | -54269.95 18230.63 -90001.32 -18538.58
cov(slope26,_cons) | -10643.8 3791.318 -18074.64 -3212.951
-----------------------------+------------------------------------------------
var(Residual) | 17673.02 1435.834 15071.46 20723.64
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 913.11 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4137.687 10 8295.374 8321.526
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 63954.2
slope26 | -1672.296 2617.279
_cons | -54269.95 -10643.8 284312.6
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | -.1292568 1
_cons | -.4024638 -.3901876 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05 2.3e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
2 | 2.3e+05 2.6e+05 2.3e+05 2.2e+05 2.0e+05 1.9e+05
3 | 2.2e+05 2.3e+05 2.4e+05 2.1e+05 2.0e+05 1.9e+05
4 | 2.1e+05 2.2e+05 2.1e+05 2.2e+05 1.9e+05 1.9e+05
5 | 2.0e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05 1.8e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 549.532 507.346 485.165 467.552 455.037 448.049
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.825 1.000
3 | 0.823 0.924 1.000
4 | 0.812 0.907 0.917 1.000
5 | 0.792 0.878 0.898 0.911 1.000
6 | 0.761 0.838 0.868 0.892 0.907 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.slope12*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 54.6805 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.slope12*1 + c.slope26*0
( 1) [rt]slope12 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 49.78476 36.12 0.000 1700.673 1895.826
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.slope12*1 + c.slope26*1
( 1) [rt]slope12 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 46.98998 37.57 0.000 1673.258 1857.455
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.slope12*1 + c.slope26*2
( 1) [rt]slope12 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 44.99354 38.50 0.000 1644.277 1820.649
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.slope12*1 + c.slope26*3
( 1) [rt]slope12 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 43.90446 38.71 0.000 1613.519 1785.621
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.slope12*1 + c.slope26*4
( 1) [rt]slope12 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 43.79051 38.06 0.000 1580.849 1752.505
------------------------------------------------------------------------------
. * Difference between slope12 and slope26
. lincom c.slope12*-1 + c.slope26*1
( 1) - [rt]slope12 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 130.7508 32.55299 4.02 0.000 66.94814 194.5535
------------------------------------------------------------------------------
. estimates store FitRand12Rand26,
. lrtest FitRand12Rand26 FitRand12Fix26,
Likelihood-ratio test LR chi2(3) = 44.24
(Assumption: FitRand12Fix26 nested in FitRand12Ra~26) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: Random Slope12, Random Slope26 Model + Fixed Quadratic Slope26"
Ch 6: Random Slope12, Random Slope26 Model + Fixed Quadratic Slope26
. mixed rt c.slope12 c.slope26 c.slope26#c.slope26, ///
> || personid: slope12 slope26, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4134.1452
Iteration 1: log restricted-likelihood = -4134.1368
Iteration 2: log restricted-likelihood = -4134.1368
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(3) = 75.90
Log restricted-likelihood = -4134.1368 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
slope12 | -151.9563 31.03041 -4.90 0.000 -212.7748 -91.13787
slope26 | -56.26845 15.56413 -3.62 0.000 -86.77358 -25.76332
|
c.slope26#c.slope26 | 5.843821 3.525181 1.66 0.097 -1.065407 12.75305
|
_cons | 1961.893 54.6805 35.88 0.000 1854.722 2069.065
-------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(slope12) | 64116.4 13242.57 42772.28 96111.62
var(slope26) | 2627.417 636.3491 1634.45 4223.635
var(_cons) | 284414 42731.42 211867 381802.4
cov(slope12,slope26) | -1692.571 2096.926 -5802.47 2417.328
cov(slope12,_cons) | -54371.32 18230.17 -90101.8 -18640.83
cov(slope26,_cons) | -10643.8 3791.318 -18074.64 -3212.95
-----------------------------+------------------------------------------------
var(Residual) | 17571.64 1429.959 14981.06 20610.2
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 913.05 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4134.137 11 8290.274 8319.04
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 64116.4
slope26 | -1692.571 2627.417
_cons | -54371.32 -10643.8 284414
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| slope12 slope26 _cons
-------------+---------------------------------
slope12 | 1
slope26 | -.1304061 1
_cons | -.4026334 -.3893648 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05
2 | 2.3e+05 2.6e+05
3 | 2.2e+05 2.3e+05 2.4e+05
4 | 2.1e+05 2.2e+05 2.1e+05 2.2e+05
5 | 2.0e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 549.532 507.306 485.092 467.465 454.959 448.003
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.825 1.000
3 | 0.823 0.924 1.000
4 | 0.813 0.907 0.917 1.000
5 | 0.792 0.879 0.899 0.912 1.000
6 | 0.761 0.838 0.868 0.892 0.907 1.000
.
. display as result "Ch 6: 5a: Fixed Time, Fixed Slope26, Random Intercept Model"
Ch 6: 5a: Fixed Time, Fixed Slope26, Random Intercept Model
. mixed rt c.time1 c.slope26, ///
> || personid: , variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4191.3436
Iteration 1: log restricted-likelihood = -4191.3436
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 161.98
Log restricted-likelihood = -4191.3436 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time1 | -163.644 23.24149 -7.04 0.000 -209.1965 -118.0915
slope26 | 130.7508 26.62648 4.91 0.000 78.56389 182.9378
_cons | 1961.893 48.4187 40.52 0.000 1866.994 2056.792
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 202683.4 29469.65 152424.8 269513.6
-----------------------------+------------------------------------------------
var(Residual) | 34098.04 2150.109 30133.91 38583.65
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 805.80 Prob >= chibar2 = 0.0000
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4191.344 5 8392.687 8405.763
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| _cons
-------------+-----------
_cons | 202683.4
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| _cons
-------------+-----------
_cons | 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.4e+05
2 | 2.0e+05 2.4e+05
3 | 2.0e+05 2.0e+05 2.4e+05
4 | 2.0e+05 2.0e+05 2.0e+05 2.4e+05
5 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
6 | 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.0e+05 2.4e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 486.602 486.602 486.602 486.602 486.602 486.602
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.856 1.000
3 | 0.856 0.856 1.000
4 | 0.856 0.856 0.856 1.000
5 | 0.856 0.856 0.856 0.856 1.000
6 | 0.856 0.856 0.856 0.856 0.856 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 48.4187 40.52 0.000 1866.994 2056.792
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1 + c.slope26*0
( 1) [rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 47.00349 38.26 0.000 1706.124 1890.375
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2 + c.slope26*1
( 1) 2*[rt]time1 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 45.91347 38.45 0.000 1675.367 1855.345
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3 + c.slope26*2
( 1) 3*[rt]time1 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 45.54434 38.04 0.000 1643.198 1821.728
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4 + c.slope26*3
( 1) 4*[rt]time1 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 45.91347 37.02 0.000 1609.581 1789.559
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5 + c.slope26*4
( 1) 5*[rt]time1 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 47.00349 35.46 0.000 1574.552 1758.802
------------------------------------------------------------------------------
. * Rate of change from session 2 to 6
. lincom c.time1*1 + c.slope26*1
( 1) [rt]time1 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -32.89317 5.810373 -5.66 0.000 -44.28129 -21.50504
------------------------------------------------------------------------------
. estimates store FitFix16Fix26,
.
. display as result "Ch 6: 5b: Random Time, Fixed Slope26 Model"
Ch 6: 5b: Random Time, Fixed Slope26 Model
. mixed rt c.time1 c.slope26, ///
> || personid: time1, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4166.6906
Iteration 1: log restricted-likelihood = -4166.6906
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 101.87
Log restricted-likelihood = -4166.6906 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time1 | -163.644 20.83445 -7.85 0.000 -204.4788 -122.8092
slope26 | 130.7508 23.22133 5.63 0.000 85.23785 176.2638
_cons | 1961.893 52.67356 37.25 0.000 1858.655 2065.132
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 2346.464 551.3954 1480.437 3719.098
var(_cons) | 254290.5 37895.39 189880.6 340549
cov(time1,_cons) | -12982.37 3620.524 -20078.47 -5886.277
-----------------------------+------------------------------------------------
var(Residual) | 25934.4 1827.001 22589.76 29774.25
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 855.10 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4166.691 7 8347.381 8365.687
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 2346.464
_cons | -12982.37 254290.5
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time1 _cons
-------------+----------------------
time1 | 1
_cons | -.5314741 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 2.8e+05 2.4e+05 2.3e+05 2.2e+05 2.0e+05 1.9e+05
2 | 2.4e+05 2.6e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
3 | 2.3e+05 2.2e+05 2.4e+05 2.0e+05 2.0e+05 1.9e+05
4 | 2.2e+05 2.1e+05 2.0e+05 2.2e+05 1.9e+05 1.9e+05
5 | 2.0e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05 1.8e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.1e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 529.363 506.564 487.526 472.704 462.503 457.234
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.900 1.000
3 | 0.885 0.891 1.000
4 | 0.861 0.874 0.883 1.000
5 | 0.827 0.848 0.866 0.876 1.000
6 | 0.782 0.812 0.838 0.859 0.872 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 52.67356 37.25 0.000 1858.655 2065.132
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1 + c.slope26*0
( 1) [rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 49.37559 36.42 0.000 1701.475 1895.024
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2 + c.slope26*1
( 1) 2*[rt]time1 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 46.6212 37.87 0.000 1673.98 1856.732
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3 + c.slope26*2
( 1) 3*[rt]time1 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 44.79893 38.67 0.000 1644.659 1820.267
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4 + c.slope26*3
( 1) 4*[rt]time1 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 44.02466 38.60 0.000 1613.283 1785.857
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5 + c.slope26*4
( 1) 5*[rt]time1 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 44.35333 37.58 0.000 1579.746 1753.608
------------------------------------------------------------------------------
. * Rate of change from session 2 to 6
. lincom c.time1*1 + c.slope26*1
( 1) [rt]time1 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -32.89317 6.993564 -4.70 0.000 -46.6003 -19.18603
------------------------------------------------------------------------------
. estimates store FitRand16Fix26,
. lrtest FitRand16Fix26 FitFix16Fix26,
Likelihood-ratio test LR chi2(2) = 49.31
(Assumption: FitFix16Fix26 nested in FitRand16Fix26) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: 5c: Random Time, Random Slope26 Model"
Ch 6: 5c: Random Time, Random Slope26 Model
. mixed rt c.time1 c.slope26, ///
> || personid: time1 slope26, variance reml covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -4154.8797 (not concave)
Iteration 1: log restricted-likelihood = -4153.1166
Iteration 2: log restricted-likelihood = -4143.8006
Iteration 3: log restricted-likelihood = -4141.8746
Iteration 4: log restricted-likelihood = -4137.7303
Iteration 5: log restricted-likelihood = -4137.6872
Iteration 6: log restricted-likelihood = -4137.6872
Computing standard errors:
Mixed-effects REML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 73.15
Log restricted-likelihood = -4137.6872 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time1 | -163.644 30.21889 -5.42 0.000 -222.8719 -104.416
slope26 | 130.7508 32.55304 4.02 0.000 66.94804 194.5536
_cons | 1961.893 54.68051 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 63954.53 13246.07 42616.04 95977.52
var(slope26) | 69916.44 15434.44 45359.87 107767.2
var(_cons) | 284312.8 42738.48 211759.1 381725.1
cov(time1,slope26) | -65626.84 14155.3 -93370.72 -37882.96
cov(time1,_cons) | -54270.24 18252.61 -90044.69 -18495.79
cov(slope26,_cons) | 43626.45 19072.94 6244.168 81008.74
-----------------------------+------------------------------------------------
var(Residual) | 17673 1435.833 15071.44 20723.62
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 913.11 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4137.687 10 8295.374 8321.526
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat recovariance, relevel(personid),
Random-effects covariance matrix for level personid
| time1 slope26 _cons
-------------+---------------------------------
time1 | 63954.53
slope26 | -65626.84 69916.44
_cons | -54270.24 43626.45 284312.8
. estat recovariance, relevel(personid) correlation,
Random-effects correlation matrix for level personid
| time1 slope26 _cons
-------------+---------------------------------
time1 | 1
slope26 | -.9814229 1
_cons | -.4024648 .3094298 1
. estat wcorrelation, covariance,
Covariances for personid = 101:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 3.0e+05 2.3e+05 2.2e+05 2.1e+05 2.0e+05 1.9e+05
2 | 2.3e+05 2.6e+05 2.3e+05 2.2e+05 2.0e+05 1.9e+05
3 | 2.2e+05 2.3e+05 2.4e+05 2.1e+05 2.0e+05 1.9e+05
4 | 2.1e+05 2.2e+05 2.1e+05 2.2e+05 1.9e+05 1.9e+05
5 | 2.0e+05 2.0e+05 2.0e+05 1.9e+05 2.1e+05 1.8e+05
6 | 1.9e+05 1.9e+05 1.9e+05 1.9e+05 1.8e+05 2.0e+05
. estat wcorrelation,
Standard deviations and correlations for personid = 101:
Standard deviations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
sd | 549.532 507.346 485.165 467.552 455.037 448.049
Correlations:
obs | 1 2 3 4 5 6
-------------+------------------------------------------------
1 | 1.000
2 | 0.825 1.000
3 | 0.823 0.924 1.000
4 | 0.812 0.907 0.917 1.000
5 | 0.792 0.878 0.898 0.911 1.000
6 | 0.761 0.838 0.868 0.892 0.907 1.000
. * Intercept at Session=1 Time=0
. lincom _cons*1 + c.time1*0 + c.slope26*0
( 1) [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1961.893 54.68051 35.88 0.000 1854.722 2069.065
------------------------------------------------------------------------------
. * Intercept at Session=2 Time=1
. lincom _cons*1 + c.time1*1 + c.slope26*0
( 1) [rt]time1 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1798.249 49.78475 36.12 0.000 1700.673 1895.826
------------------------------------------------------------------------------
. * Intercept at Session=3 Time=2
. lincom _cons*1 + c.time1*2 + c.slope26*1
( 1) 2*[rt]time1 + [rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1765.356 46.98997 37.57 0.000 1673.258 1857.455
------------------------------------------------------------------------------
. * Intercept at Session=4 Time=3
. lincom _cons*1 + c.time1*3 + c.slope26*2
( 1) 3*[rt]time1 + 2*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1732.463 44.99353 38.50 0.000 1644.277 1820.649
------------------------------------------------------------------------------
. * Intercept at Session=5 Time=4
. lincom _cons*1 + c.time1*4 + c.slope26*3
( 1) 4*[rt]time1 + 3*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1699.57 43.90445 38.71 0.000 1613.519 1785.621
------------------------------------------------------------------------------
. * Intercept at Session=6 Time=5
. lincom _cons*1 + c.time1*5 + c.slope26*4
( 1) 5*[rt]time1 + 4*[rt]slope26 + [rt]_cons = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1666.677 43.7905 38.06 0.000 1580.849 1752.505
------------------------------------------------------------------------------
. * Rate of change from session 2 to 6
. lincom c.time1*1 + c.slope26*1
( 1) [rt]time1 + [rt]slope26 = 0
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -32.89317 6.588756 -4.99 0.000 -45.80689 -19.97944
------------------------------------------------------------------------------
. estimates store FitRand16Rand26,
. lrtest FitRand16Rand26 FitRand16Fix26,
Likelihood-ratio test LR chi2(3) = 58.01
(Assumption: FitRand16Fix26 nested in FitRand16Ra~26) 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.
Note: LR tests based on REML are valid only when the fixed-effects specification is identical for both models.
.
. display as result "Ch 6: 0: Saturated Means, Unstructured Variance Model"
Ch 6: 0: Saturated Means, Unstructured Variance Model
. display as result "Using ML Instead of REML"
Using ML Instead of REML
. mixed rt i.session, ///
> || personid: , noconstant variance mle covariance(unstructured) ///
> residuals(unstructured,t(session)),
Obtaining starting values by EM:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4606.4947 (not concave)
Iteration 1: log likelihood = -4228.9442 (not concave)
Iteration 2: log likelihood = -4192.7953
Iteration 3: log likelihood = -4154.9762
Iteration 4: log likelihood = -4139.4083
Iteration 5: log likelihood = -4139.0458
Iteration 6: log likelihood = -4139.0444
Iteration 7: log likelihood = -4139.0444
Computing standard errors:
Mixed-effects ML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(5) = 84.44
Log likelihood = -4139.0444 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
session |
2 | -146.721 29.67288 -4.94 0.000 -204.8788 -88.56321
3 | -211.8587 31.21012 -6.79 0.000 -273.0294 -150.688
4 | -244.0969 33.47577 -7.29 0.000 -309.7082 -178.4856
5 | -254.7176 35.66764 -7.14 0.000 -324.6249 -184.8103
6 | -289.7574 32.53768 -8.91 0.000 -353.53 -225.9847
|
_cons | 1961.893 54.4089 36.06 0.000 1855.254 2068.533
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: (empty) |
-----------------------------+------------------------------------------------
Residual: Unstructured |
var(e1) | 298993.1 42064.31 226938.7 393925.2
var(e2) | 256583 36093.01 194756.1 338037.3
var(e3) | 231056.4 32501.71 175381.2 304405.7
var(e4) | 215388.9 30298.22 163488.4 283765.6
var(e5) | 209996.8 29540.36 159394.6 276663.4
var(e6) | 194784.5 27400.15 147848.4 256620.9
cov(e1,e2) | 233323.8 36022.3 162721.4 303926.2
cov(e1,e3) | 215834.1 33827.79 149532.9 282135.4
cov(e1,e4) | 200599.3 32174.04 137539.4 263659.3
cov(e1,e5) | 190249.8 31291.76 128919.1 251580.6
cov(e1,e6) | 193424.4 30761.66 133132.7 253716.1
cov(e2,e3) | 227936.2 33173.66 162917 292955.4
cov(e2,e4) | 211119.4 31426.76 149524.1 272714.7
cov(e2,e5) | 200090.1 30480.41 140349.6 259830.6
cov(e2,e6) | 191353.6 29267.63 133990.1 248717.1
cov(e3,e4) | 203176.2 30011.63 144354.5 261997.9
cov(e3,e5) | 194968 29257.95 137623.5 252312.5
cov(e3,e6) | 186736.1 28109.72 131642 241830.1
cov(e4,e5) | 191757.2 28482.16 135933.1 247581.2
cov(e4,e6) | 183485.2 27351.31 129877.6 237092.8
cov(e5,e6) | 185979.7 27328.79 132416.2 239543.2
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(20) = 934.90 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.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4139.044 27 8332.089 8402.697
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estimates store FitMLSatUN,
.
. display as result "Ch 6: 1b: Empty Means, Random Intercept Model"
Ch 6: 1b: Empty Means, Random Intercept Model
. display as result "Using ML Instead of REML"
Using ML Instead of REML
. mixed rt , ///
> || personid: , variance mle covariance(unstructured) ///
> residuals(independent,t(session)),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4273.1628
Iteration 1: log likelihood = -4273.1628
Computing standard errors:
Mixed-effects ML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(0) = .
Log likelihood = -4273.1628 Prob > chi2 = .
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1770.701 45.19521 39.18 0.000 1682.12 1859.282
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 198820 29034.73 149332.6 264707.1
-----------------------------+------------------------------------------------
var(Residual) | 44899.96 2825.63 39689.76 50794.13
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 690.12 Prob >= chibar2 = 0.0000
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4273.163 3 8552.326 8560.171
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estat icc,
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid | .8157723 .0240389 .7639505 .8583271
------------------------------------------------------------------------------
. estimates store FitMLEmptyRI,
. lrtest FitMLSatUN FitMLEmptyRI,
Likelihood-ratio test LR chi2(24) = 268.24
(Assumption: FitMLEmptyRI nested in FitMLSatUN) 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 6: 3b: Random Quadratic Time Model"
Ch 6: 3b: Random Quadratic Time Model
. display as result "Using ML instead of REML"
Using ML instead of REML
. mixed rt c.time1 c.time1#c.time1, ///
> || personid: time1 time1sq, variance mle covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4163.25
Iteration 1: log likelihood = -4161.2927
Iteration 2: log likelihood = -4160.8836
Iteration 3: log likelihood = -4160.8833
Computing standard errors:
Mixed-effects ML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 72.45
Log likelihood = -4160.8833 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
time1 | -120.8999 19.94803 -6.06 0.000 -159.9973 -81.80251
|
c.time1#c.time1 | 13.86561 3.398459 4.08 0.000 7.204756 20.52647
|
_cons | 1945.85 53.58259 36.31 0.000 1840.83 2050.87
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(time1) | 25437.86 5781.419 16293.81 39713.52
var(time1sq) | 622.8 169.99 364.7687 1063.358
var(_cons) | 273306.9 40831.76 203930.4 366285.1
cov(time1,time1sq) | -3837.723 968.8047 -5736.545 -1938.9
cov(time1,_cons) | -35261.67 11771.5 -58333.38 -12189.95
cov(time1sq,_cons) | 3845.378 1921.468 79.37031 7611.386
-----------------------------+------------------------------------------------
var(Residual) | 20298.2 1649.119 17310.2 23801.98
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 891.99 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4160.883 10 8341.767 8367.918
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estimates store FitMLRandQuad,
. lrtest FitMLRandQuad FitMLEmptyRI,
Likelihood-ratio test LR chi2(7) = 224.56
(Assumption: FitMLEmptyRI nested in FitMLRandQuad) 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.
. lrtest FitMLSatUN FitMLRandQuad,
Likelihood-ratio test LR chi2(17) = 43.68
(Assumption: FitMLRandQuad nested in FitMLSatUN) Prob > chi2 = 0.0004
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 6: 4c: Random Slope12, Random Slope26 Model"
Ch 6: 4c: Random Slope12, Random Slope26 Model
. display as result "Using ML instead of REML"
Using ML instead of REML
. mixed rt c.slope12 c.slope26, ///
> || personid: slope12 slope26, variance mle covariance(unstructured) ///
> residuals(independent,t(session)),
Note: t() not required for this residual structure; ignored
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4149.4821
Iteration 1: log likelihood = -4149.4733
Iteration 2: log likelihood = -4149.4733
Computing standard errors:
Mixed-effects ML regression Number of obs = 606
Group variable: personid Number of groups = 101
Obs per group: min = 6
avg = 6.0
max = 6
Wald chi2(2) = 73.88
Log likelihood = -4149.4733 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
rt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
slope12 | -163.644 30.06887 -5.44 0.000 -222.5779 -104.7101
slope26 | -32.89317 6.556056 -5.02 0.000 -45.7428 -20.04353
_cons | 1961.893 54.40913 36.06 0.000 1855.253 2068.533
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(slope12) | 63041.03 13053.94 42011.15 94598.01
var(slope26) | 2573.867 627.5353 1596.079 4150.666
var(_cons) | 281322.7 42099.28 209809.1 377211.6
cov(slope12,slope26) | -1620.742 2066.603 -5671.209 2429.725
cov(slope12,_cons) | -53557.65 17962.22 -88762.96 -18352.34
cov(slope26,_cons) | -10538.41 3735.149 -17859.17 -3217.655
-----------------------------+------------------------------------------------
var(Residual) | 17673.02 1435.834 15071.46 20723.64
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 914.40 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(101),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 101 . -4149.473 10 8318.947 8345.098
-----------------------------------------------------------------------------
Note: N=101 used in calculating BIC
. estimates store FitMLRand12Rand26,
. lrtest FitMLRand12Rand26 FitMLEmptyRI,
Likelihood-ratio test LR chi2(7) = 247.38
(Assumption: FitMLEmptyRI nested in FitMLRand12~26) 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.
. lrtest FitMLSatUN FitMLRand12Rand26,
Likelihood-ratio test LR chi2(17) = 20.86
(Assumption: FitMLRand12~26 nested in FitMLSatUN) Prob > chi2 = 0.2327
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 6 MODELS ******
.
. * Close log
. log close STATA_Chapter6
name: STATA_Chapter6
log: C:\Dropbox\PilesOfVariance\Chapter6\STATA\STATA_Chapter6_Output.smcl
log type: smcl
closed on: 6 Jan 2015, 12:53:50
------------------------------------------------------------------------------------------------------------------------------------------------------