Chapter 7a: Descriptive Statistics for Time-Invariant Variables



Summarize



[PersonMeans7a] 


Case Processing SummaryCase Processing Summary, table, 3 levels of column headers and 1 levels of row headers, table with 7 columns and 6 rows
  Cases
Included Excluded Total
N Percent N Percent N Percent
PMwomen 105 100.0% 0 0.0% 105 100.0%
PMbaseage 105 100.0% 0 0.0% 105 100.0%
ReportReport, table, 1 levels of column headers and 1 levels of row headers, table with 3 columns and 7 rows
  PMwomen PMbaseage
N 105 105
Mean .7333 80.1297
Std. Deviation .44434 6.10501
Minimum .00 69.70
Maximum 1.00 95.31


Chapter 7a: Descriptive Statistics for Time-Varying Variables



Summarize



[Chapter7a] C:\Dropbox\PilesOfVariance\Chapter7a\SPSS\SPSS_Chapter7a.sav


Case Processing SummaryCase Processing Summary, table, 3 levels of column headers and 1 levels of row headers, table with 7 columns and 5 rows
  Cases
Included Excluded Total
N Percent N Percent N Percent
symptoms: # Daily Physical Symptoms (0=5) 509 100.0% 0 0.0% 509 100.0%
ReportReport, table, symptoms: # Daily Physical Symptoms (0=5), 1 layers, 1 levels of column headers and 0 levels of row headers, table with 5 columns and 4 rows
symptoms: # Daily Physical Symptoms (0=5)
N Mean Std. Deviation Minimum Maximum
509 1.27 1.324 0 5


Eq 7a.3: Empty Means, Random Intercept Model



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 3 rows
A(n) FIXED subcommand has no specifications and will therefore be ignored.
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 7 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 2   3  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1442.966
Akaike's Information Criterion (AIC) 1448.966
Hurvich and Tsai's Criterion (AICC) 1449.013
Bozdogan's Criterion (CAIC) 1464.663
Schwarz's Bayesian Criterion (BIC) 1461.663
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 4 rows
Source Numerator df Denominator df F Sig.
Intercept 1 102.981 133.387 .000
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 5 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.293954 .112037 102.981 11.549 .000 1.071754 1.516153
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .616175 .043462 14.177 .000 .536618 .707528
Intercept [subject = PersonID] Variance 1.189300 .183946 6.465 .000 .878291 1.610440
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Saturated Means by Day of Study; Random Intercept Only



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 8 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
studyday 14   13  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 16   16  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1434.992
Akaike's Information Criterion (AIC) 1466.992
Hurvich and Tsai's Criterion (AICC) 1468.098
Bozdogan's Criterion (CAIC) 1550.711
Schwarz's Bayesian Criterion (BIC) 1534.711
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 116.027 120.631 .000
studyday 13 415.842 .618 .839
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 20 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.027623 .255494 508.800 4.022 .000 .525671 1.529576
[studyday=1] .259300 .244576 422.130 1.060 .290 -.221439 .740040
[studyday=2] .324235 .257731 423.196 1.258 .209 -.182357 .830826
[studyday=3] .195041 .278158 422.665 .701 .484 -.351704 .741786
[studyday=4] .447323 .299455 425.500 1.494 .136 -.141273 1.035920
[studyday=5] .300503 .291765 425.821 1.030 .304 -.272976 .873981
[studyday=6] .377062 .270964 426.130 1.392 .165 -.155532 .909655
[studyday=7] .313941 .256516 421.957 1.224 .222 -.190268 .818151
[studyday=8] .235936 .256827 424.607 .919 .359 -.268875 .740747
[studyday=9] .079204 .272868 421.220 .290 .772 -.457149 .615556
[studyday=10] .451198 .291703 422.269 1.547 .123 -.122173 1.024570
[studyday=11] -.046042 .357620 422.349 -.129 .898 -.748978 .656894
[studyday=12] .223526 .331632 422.413 .674 .501 -.428329 .875381
[studyday=13] .168473 .317043 412.322 .531 .595 -.454750 .791695
[studyday=14] 0b 0 . . . . .
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. This parameter is set to zero because it is redundant.


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .605363 .042725 14.169 .000 .527157 .695172
Intercept [subject = PersonID] Variance 1.181284 .182952 6.457 .000 .872016 1.600237
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Estimated Marginal Means



studyday: Actual Day in Study (1-14)


EstimatesaEstimates, table, 2 levels of column headers and 1 levels of row headers, table with 6 columns and 18 rows
studyday: Actual Day in Study (1-14) Mean Std. Error df 95% Confidence Interval
Lower Bound Upper Bound
1 1.287 .131 187.186 1.029 1.545
2 1.352 .151 288.973 1.055 1.648
3 1.223 .184 428.318 .861 1.585
4 1.475 .209 482.540 1.064 1.886
5 1.328 .200 465.806 .936 1.721
6 1.405 .166 362.453 1.077 1.732
7 1.342 .152 296.643 1.042 1.641
8 1.264 .147 268.610 .975 1.552
9 1.107 .178 409.023 .757 1.457
10 1.479 .206 476.910 1.074 1.884
11 .982 .291 504.189 .411 1.552
12 1.251 .260 508.985 .741 1.762
13 1.196 .260 508.984 .686 1.707
14 1.028 .255 508.800 .526 1.530
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Pairwise ComparisonsaPairwise Comparisons, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 188 rows
(I) studyday: Actual Day in Study (1-14) (J) studyday: Actual Day in Study (1-14) Mean Difference (I-J) Std. Error df Sig.b 95% Confidence Interval for Differenceb
Lower Bound Upper Bound
1 2 -.065 .131 407.463 .621 -.323 .193
3 .064 .169 413.352 .704 -.267 .396
4 -.188 .196 415.225 .337 -.573 .197
5 -.041 .186 416.830 .825 -.407 .325
6 -.118 .149 412.189 .431 -.412 .176
7 -.055 .133 408.551 .682 -.317 .208
8 .023 .127 406.800 .854 -.226 .273
9 .180 .162 411.772 .267 -.138 .499
10 -.192 .192 416.682 .319 -.570 .186
11 .305 .281 418.684 .278 -.247 .858
12 .036 .249 418.909 .886 -.454 .526
13 .091 .249 418.742 .716 -.399 .580
14 .259 .245 422.130 .290 -.221 .740
2 1 .065 .131 407.463 .621 -.193 .323
3 .129 .183 412.307 .481 -.231 .490
4 -.123 .208 414.424 .555 -.533 .286
5 .024 .204 420.414 .908 -.378 .425
6 -.053 .168 415.027 .754 -.384 .278
7 .010 .153 411.395 .947 -.291 .312
8 .088 .147 409.786 .549 -.201 .378
9 .245 .178 412.219 .169 -.105 .595
10 -.127 .207 418.107 .541 -.535 .281
11 .370 .292 419.267 .205 -.204 .944
12 .101 .264 421.577 .703 -.417 .619
13 .156 .262 420.077 .552 -.359 .670
14 .324 .258 423.196 .209 -.182 .831
3 1 -.064 .169 413.352 .704 -.396 .267
2 -.129 .183 412.307 .481 -.490 .231
4 -.252 .231 413.352 .275 -.706 .202
5 -.105 .231 421.806 .648 -.559 .348
6 -.182 .204 422.049 .373 -.583 .219
7 -.119 .187 416.335 .526 -.487 .249
8 -.041 .183 416.027 .823 -.401 .319
9 .116 .207 414.209 .575 -.290 .522
10 -.256 .232 417.639 .269 -.711 .199
11 .241 .306 416.323 .431 -.360 .842
12 -.028 .285 422.848 .921 -.589 .532
13 .027 .285 421.892 .926 -.533 .586
14 .195 .278 422.665 .484 -.352 .742
4 1 .188 .196 415.225 .337 -.197 .573
2 .123 .208 414.424 .555 -.286 .533
3 .252 .231 413.352 .275 -.202 .706
5 .147 .243 415.325 .546 -.331 .625
6 .070 .224 419.090 .754 -.370 .510
7 .133 .213 418.169 .532 -.286 .553
8 .211 .209 417.526 .312 -.199 .622
9 .368 .233 418.849 .115 -.090 .827
10 -.004 .253 419.416 .988 -.502 .494
11 .493 .320 416.192 .124 -.136 1.123
12 .224 .303 422.418 .460 -.371 .819
13 .279 .301 422.120 .355 -.314 .871
14 .447 .299 425.500 .136 -.141 1.036
5 1 .041 .186 416.830 .825 -.325 .407
2 -.024 .204 420.414 .908 -.425 .378
3 .105 .231 421.806 .648 -.348 .559
4 -.147 .243 415.325 .546 -.625 .331
6 -.077 .209 413.392 .714 -.487 .334
7 -.013 .201 415.887 .947 -.409 .382
8 .065 .199 417.555 .745 -.326 .455
9 .221 .225 420.945 .326 -.221 .664
10 -.151 .250 424.745 .548 -.643 .341
11 .347 .322 421.792 .282 -.286 .979
12 .077 .282 413.082 .785 -.478 .632
13 .132 .295 422.819 .655 -.448 .712
14 .301 .292 425.821 .304 -.273 .874
6 1 .118 .149 412.189 .431 -.176 .412
2 .053 .168 415.027 .754 -.278 .384
3 .182 .204 422.049 .373 -.219 .583
4 -.070 .224 419.090 .754 -.510 .370
5 .077 .209 413.392 .714 -.334 .487
7 .063 .168 411.904 .707 -.266 .393
8 .141 .162 410.417 .383 -.177 .459
9 .298 .195 418.388 .128 -.086 .682
10 -.074 .222 422.155 .738 -.510 .362
11 .423 .302 421.513 .162 -.171 1.017
12 .154 .268 417.495 .567 -.373 .680
13 .209 .269 419.231 .439 -.320 .737
14 .377 .271 426.130 .165 -.156 .910
7 1 .055 .133 408.551 .682 -.208 .317
2 -.010 .153 411.395 .947 -.312 .291
3 .119 .187 416.335 .526 -.249 .487
4 -.133 .213 418.169 .532 -.553 .286
5 .013 .201 415.887 .947 -.382 .409
6 -.063 .168 411.904 .707 -.393 .266
8 .078 .147 408.238 .597 -.212 .368
9 .235 .182 415.685 .198 -.123 .592
10 -.137 .212 421.435 .517 -.553 .279
11 .360 .296 421.690 .224 -.222 .942
12 .090 .262 419.316 .730 -.425 .606
13 .145 .263 420.488 .581 -.372 .663
14 .314 .257 421.957 .222 -.190 .818
8 1 -.023 .127 406.800 .854 -.273 .226
2 -.088 .147 409.786 .549 -.378 .201
3 .041 .183 416.027 .823 -.319 .401
4 -.211 .209 417.526 .312 -.622 .199
5 -.065 .199 417.555 .745 -.455 .326
6 -.141 .162 410.417 .383 -.459 .177
7 -.078 .147 408.238 .597 -.368 .212
9 .157 .177 414.506 .375 -.190 .504
10 -.215 .205 419.324 .295 -.619 .189
11 .282 .292 420.906 .335 -.292 .856
12 .012 .258 419.088 .962 -.495 .520
13 .067 .261 421.247 .796 -.446 .581
14 .236 .257 424.607 .359 -.269 .741
9 1 -.180 .162 411.772 .267 -.499 .138
2 -.245 .178 412.219 .169 -.595 .105
3 -.116 .207 414.209 .575 -.522 .290
4 -.368 .233 418.849 .115 -.827 .090
5 -.221 .225 420.945 .326 -.664 .221
6 -.298 .195 418.388 .128 -.682 .086
7 -.235 .182 415.685 .198 -.592 .123
8 -.157 .177 414.506 .375 -.504 .190
10 -.372 .226 415.981 .100 -.815 .071
11 .125 .305 417.801 .681 -.473 .724
12 -.144 .279 420.588 .605 -.692 .404
13 -.089 .277 418.748 .747 -.634 .455
14 .079 .273 421.220 .772 -.457 .616
10 1 .192 .192 416.682 .319 -.186 .570
2 .127 .207 418.107 .541 -.281 .535
3 .256 .232 417.639 .269 -.199 .711
4 .004 .253 419.416 .988 -.494 .502
5 .151 .250 424.745 .548 -.341 .643
6 .074 .222 422.155 .738 -.362 .510
7 .137 .212 421.435 .517 -.279 .553
8 .215 .205 419.324 .295 -.189 .619
9 .372 .226 415.981 .100 -.071 .815
11 .497 .321 417.866 .122 -.133 1.127
12 .228 .301 424.535 .450 -.365 .820
13 .283 .294 418.651 .336 -.294 .860
14 .451 .292 422.269 .123 -.122 1.025
11 1 -.305 .281 418.684 .278 -.858 .247
2 -.370 .292 419.267 .205 -.944 .204
3 -.241 .306 416.323 .431 -.842 .360
4 -.493 .320 416.192 .124 -1.123 .136
5 -.347 .322 421.792 .282 -.979 .286
6 -.423 .302 421.513 .162 -1.017 .171
7 -.360 .296 421.690 .224 -.942 .222
8 -.282 .292 420.906 .335 -.856 .292
9 -.125 .305 417.801 .681 -.724 .473
10 -.497 .321 417.866 .122 -1.127 .133
12 -.270 .361 421.508 .456 -.980 .440
13 -.215 .360 420.578 .552 -.923 .494
14 -.046 .358 422.349 .898 -.749 .657
12 1 -.036 .249 418.909 .886 -.526 .454
2 -.101 .264 421.577 .703 -.619 .417
3 .028 .285 422.848 .921 -.532 .589
4 -.224 .303 422.418 .460 -.819 .371
5 -.077 .282 413.082 .785 -.632 .478
6 -.154 .268 417.495 .567 -.680 .373
7 -.090 .262 419.316 .730 -.606 .425
8 -.012 .258 419.088 .962 -.520 .495
9 .144 .279 420.588 .605 -.404 .692
10 -.228 .301 424.535 .450 -.820 .365
11 .270 .361 421.508 .456 -.440 .980
13 .055 .337 421.489 .870 -.607 .718
14 .224 .332 422.413 .501 -.428 .875
13 1 -.091 .249 418.742 .716 -.580 .399
2 -.156 .262 420.077 .552 -.670 .359
3 -.027 .285 421.892 .926 -.586 .533
4 -.279 .301 422.120 .355 -.871 .314
5 -.132 .295 422.819 .655 -.712 .448
6 -.209 .269 419.231 .439 -.737 .320
7 -.145 .263 420.488 .581 -.663 .372
8 -.067 .261 421.247 .796 -.581 .446
9 .089 .277 418.748 .747 -.455 .634
10 -.283 .294 418.651 .336 -.860 .294
11 .215 .360 420.578 .552 -.494 .923
12 -.055 .337 421.489 .870 -.718 .607
14 .168 .317 412.322 .595 -.455 .792
14 1 -.259 .245 422.130 .290 -.740 .221
2 -.324 .258 423.196 .209 -.831 .182
3 -.195 .278 422.665 .484 -.742 .352
4 -.447 .299 425.500 .136 -1.036 .141
5 -.301 .292 425.821 .304 -.874 .273
6 -.377 .271 426.130 .165 -.910 .156
7 -.314 .257 421.957 .222 -.818 .190
8 -.236 .257 424.607 .359 -.741 .269
9 -.079 .273 421.220 .772 -.616 .457
10 -.451 .292 422.269 .123 -1.025 .122
11 .046 .358 422.349 .898 -.657 .749
12 -.224 .332 422.413 .501 -.875 .428
13 -.168 .317 412.322 .595 -.792 .455
Based on estimated marginal means
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate TestsaUnivariate Tests, table, 1 levels of column headers and 0 levels of row headers, table with 4 columns and 5 rows
Numerator df Denominator df F Sig.
13 415.859 .618 .839
The F tests the effect of studyday: Actual Day in Study (1-14). This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Fixed Linear Effect of Day of Study; Random Intercept Only



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 8 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
studyday1 1   1  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 3   4  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1442.156
Akaike's Information Criterion (AIC) 1450.156
Hurvich and Tsai's Criterion (AICC) 1450.236
Bozdogan's Criterion (CAIC) 1471.086
Schwarz's Bayesian Criterion (BIC) 1467.086
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 138.682 121.724 .000
studyday1 1 413.376 .810 .369
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.335096 .121011 138.682 11.033 .000 1.095831 1.574361
studyday1 -.008930 .009920 413.376 -.900 .369 -.028429 .010569
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .614894 .043371 14.177 .000 .535502 .706056
Intercept [subject = PersonID] Variance 1.189959 .183995 6.467 .000 .878854 1.611193
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Random Linear Effect of Day of Study



Mixed Model Analysis


Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 9 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
studyday1 1   1  
Random Effects Intercept + studyday1b 2 Unstructured 3 PersonID
Residual     1  
Total 4   6  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information.
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1440.173
Akaike's Information Criterion (AIC) 1452.173
Hurvich and Tsai's Criterion (AICC) 1452.340
Bozdogan's Criterion (CAIC) 1483.567
Schwarz's Bayesian Criterion (BIC) 1477.567
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 102.429 121.367 .000
studyday1 1 92.196 .600 .441
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.333354 .121030 102.429 11.017 .000 1.093303 1.573406
studyday1 -.008375 .010811 92.196 -.775 .441 -.029846 .013097
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 8 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .583490 .046410 12.573 .000 .499264 .681924
Intercept + studyday1 [subject = PersonID] UN (1,1) 1.203731 .215703 5.581 .000 .847224 1.710254
UN (2,1) -.005019 .014841 -.338 .735 -.034107 .024069
UN (2,2) .002000 .001660 1.204 .228 .000393 .010178
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Saturated Means by Day of Week; Random Intercept Only



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 8 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
dayofweek 7   6  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 9   9  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1442.300
Akaike's Information Criterion (AIC) 1460.300
Hurvich and Tsai's Criterion (AICC) 1460.660
Bozdogan's Criterion (CAIC) 1507.392
Schwarz's Bayesian Criterion (BIC) 1498.392
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 109.781 131.102 .000
dayofweek 6 417.574 .111 .995
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 13 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.265010 .137287 215.847 9.214 .000 .994415 1.535606
[dayofweek=1] .072105 .143515 414.586 .502 .616 -.210004 .354214
[dayofweek=2] .057351 .176377 419.279 .325 .745 -.289342 .404044
[dayofweek=3] .029285 .171795 427.657 .170 .865 -.308382 .366953
[dayofweek=4] .087225 .145473 418.825 .600 .549 -.198722 .373173
[dayofweek=5] .020387 .133660 415.659 .153 .879 -.242348 .283121
[dayofweek=6] .009694 .106463 410.660 .091 .927 -.199587 .218975
[dayofweek=7] 0b 0 . . . . .
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. This parameter is set to zero because it is redundant.


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .615212 .043407 14.173 .000 .535757 .706451
Intercept [subject = PersonID] Variance 1.189075 .184104 6.459 .000 .877846 1.610647
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Estimated Marginal Means



dayofweek: 1=Monday to 7=Sunday


EstimatesaEstimates, table, 2 levels of column headers and 1 levels of row headers, table with 6 columns and 11 rows
dayofweek: 1=Monday to 7=Sunday Mean Std. Error df 95% Confidence Interval
Lower Bound Upper Bound
1 1.337 .157 315.554 1.028 1.646
2 1.322 .186 430.125 .956 1.689
3 1.294 .178 400.170 .944 1.644
4 1.352 .156 309.813 1.046 1.659
5 1.285 .146 259.933 .998 1.573
6 1.275 .123 147.469 1.032 1.518
7 1.265 .137 215.847 .994 1.536
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Pairwise ComparisonsaPairwise Comparisons, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 48 rows
(I) dayofweek: 1=Monday to 7=Sunday (J) dayofweek: 1=Monday to 7=Sunday Mean Difference (I-J) Std. Error df Sig.b 95% Confidence Interval for Differenceb
Lower Bound Upper Bound
1 2 .015 .189 416.246 .938 -.356 .386
3 .043 .190 430.038 .822 -.331 .417
4 -.015 .168 424.599 .928 -.345 .315
5 .052 .156 420.526 .740 -.254 .357
6 .062 .132 416.558 .636 -.197 .321
7 .072 .144 414.586 .616 -.210 .354
2 1 -.015 .189 416.246 .938 -.386 .356
3 .028 .210 423.932 .894 -.384 .441
4 -.030 .194 423.421 .878 -.412 .352
5 .037 .187 423.668 .844 -.331 .405
6 .048 .166 420.114 .774 -.279 .374
7 .057 .176 419.279 .745 -.289 .404
3 1 -.043 .190 430.038 .822 -.417 .331
2 -.028 .210 423.932 .894 -.441 .384
4 -.058 .181 419.277 .749 -.414 .298
5 .009 .175 422.178 .960 -.335 .353
6 .020 .156 423.256 .900 -.288 .327
7 .029 .172 427.657 .865 -.308 .367
4 1 .015 .168 424.599 .928 -.315 .345
2 .030 .194 423.421 .878 -.352 .412
3 .058 .181 419.277 .749 -.298 .414
5 .067 .152 415.068 .659 -.231 .365
6 .078 .129 413.961 .549 -.177 .332
7 .087 .145 418.825 .549 -.199 .373
5 1 -.052 .156 420.526 .740 -.357 .254
2 -.037 .187 423.668 .844 -.405 .331
3 -.009 .175 422.178 .960 -.353 .335
4 -.067 .152 415.068 .659 -.365 .231
6 .011 .117 411.274 .927 -.219 .241
7 .020 .134 415.659 .879 -.242 .283
6 1 -.062 .132 416.558 .636 -.321 .197
2 -.048 .166 420.114 .774 -.374 .279
3 -.020 .156 423.256 .900 -.327 .288
4 -.078 .129 413.961 .549 -.332 .177
5 -.011 .117 411.274 .927 -.241 .219
7 .010 .106 410.660 .927 -.200 .219
7 1 -.072 .144 414.586 .616 -.354 .210
2 -.057 .176 419.279 .745 -.404 .289
3 -.029 .172 427.657 .865 -.367 .308
4 -.087 .145 418.825 .549 -.373 .199
5 -.020 .134 415.659 .879 -.283 .242
6 -.010 .106 410.660 .927 -.219 .200
Based on estimated marginal means
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate TestsaUnivariate Tests, table, 1 levels of column headers and 0 levels of row headers, table with 4 columns and 5 rows
Numerator df Denominator df F Sig.
6 417.573 .111 .995
The F tests the effect of dayofweek: 1=Monday to 7=Sunday. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Fixed Effect of Weekend; Random Intercept Only



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 8 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
weekend 1   1  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 3   4  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1442.563
Akaike's Information Criterion (AIC) 1450.563
Hurvich and Tsai's Criterion (AICC) 1450.643
Bozdogan's Criterion (CAIC) 1471.493
Schwarz's Bayesian Criterion (BIC) 1467.493
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 126.431 124.361 .000
weekend 1 411.330 .403 .526
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.317625 .118154 126.431 11.152 .000 1.083809 1.551441
weekend -.046416 .073141 411.330 -.635 .526 -.190192 .097360
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .615331 .043404 14.177 .000 .535879 .706561
Intercept [subject = PersonID] Variance 1.191384 .184237 6.467 .000 .879874 1.613180
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Ch 7a: Testing Random Effect of Weekend



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
Iteration was terminated but convergence has not been achieved. The MIXED procedure continues despite this warning. Subsequent results produced are based on the last iteration. Validity of the model fit is uncertain.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 9 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
weekend 1   1  
Random Effects Intercept + weekendb 2 Unstructured 3 PersonID
Residual     1  
Total 4   6  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information.
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1442.321
Akaike's Information Criterion (AIC) 1454.321
Hurvich and Tsai's Criterion (AICC) 1454.489
Bozdogan's Criterion (CAIC) 1485.716
Schwarz's Bayesian Criterion (BIC) 1479.716
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 99.061 120.175 .000
weekend 1 417.127 .408 .523
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.318624 .120286 99.061 10.962 .000 1.079953 1.557296
weekend -.046755 .073178 417.127 -.639 .523 -.190598 .097087
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 9 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .613163 .043184 14.199 .000 .534107 .703922
Intercept + weekend [subject = PersonID] UN (1,1) 1.245040 .214999 5.791 .000 .887553 1.746516
UN (2,1) -.059213 .090683 -.653 .514 -.236947 .118522
UN (2,2) .002817b .000000 . . . .
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
b. This covariance parameter is redundant. The test statistic and confidence interval cannot be computed.


Eq 7a.4: Adding Sex and Age to the Model for the Means



Mixed Model Analysis


WarningsWarnings, table, 0 levels of column headers and 0 levels of row headers, table with 1 columns and 2 rows
The covariance structure for random effect with only one level will be changed to Identity.
Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 6 columns and 10 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
women 1   1  
age80 1   1  
women * age80 1   1  
Random Effects Intercept 1 Identity 1 PersonID
Residual     1  
Total 5   6  
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Log Likelihood 1432.578
Akaike's Information Criterion (AIC) 1444.578
Hurvich and Tsai's Criterion (AICC) 1444.745
Bozdogan's Criterion (CAIC) 1475.973
Schwarz's Bayesian Criterion (BIC) 1469.973
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 7 rows
Source Numerator df Denominator df F Sig.
Intercept 1 106.047 66.032 .000
women 1 105.414 4.686 .033
age80 1 107.877 7.282 .008
women * age80 1 106.968 6.847 .010
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 8 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1.712739 .210773 106.047 8.126 .000 1.294863 2.130615
women -.530642 .245132 105.414 -2.165 .033 -1.016672 -.044612
age80 .099999 .037057 107.877 2.698 .008 .026544 .173455
women * age80 -.110428 .042201 106.968 -2.617 .010 -.194087 -.026769
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Covariance Matrix for Estimates of Fixed EffectsaCovariance Matrix for Estimates of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 7 rows
Parameter Intercept women age80 women * age80
Intercept .044425 -.044425 .001315 -.001315
women -.044425 .060090 -.001315 .001114
age80 .001315 -.001315 .001373 -.001373
women * age80 -.001315 .001114 -.001373 .001781
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual .615189 .043329 14.198 .000 .535866 .706254
Intercept [subject = PersonID] Variance 1.072737 .166721 6.434 .000 .791047 1.454736
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Covariance Matrix for Estimates of Covariance ParametersaCovariance Matrix for Estimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 4 columns and 6 rows
Parameter Residual Intercept [subject = PersonID]
Variance
Residual .001877 -.000421
Intercept [subject = PersonID] Variance -.000421 .027796
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Custom Hypothesis Test 1 (Multivariate Test of Fixed Effects)


Contrast Estimatesa,bContrast Estimates, table, 2 levels of column headers and 1 levels of row headers, table with 9 columns and 8 rows
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 -.530642 .245132 105.414 0 -2.165 .033 -1.016672 -.044612
L2 .099999 .037057 107.877 0 2.698 .008 .026544 .173455
L3 -.110428 .042201 106.968 0 -2.617 .010 -.194087 -.026769
a. Multivariate Test of Fixed Effects
b. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).
Test of ContrastsaTest of Contrasts, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 4 rows
Source Numerator df Denominator df F Sig.
Multivariate Test of Fixed Effects 3 105.555 3.615 .016
a. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Custom Hypothesis Test 2 (Age Slope for Men)


Contrast Estimatesa,bContrast Estimates, table, 2 levels of column headers and 1 levels of row headers, table with 9 columns and 6 rows
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 .099999 .037057 107.877 0 2.698 .008 .026544 .173455
a. Age Slope for Men
b. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Custom Hypothesis Test 3 (Age Slope for Women)


Contrast Estimatesa,bContrast Estimates, table, 2 levels of column headers and 1 levels of row headers, table with 9 columns and 6 rows
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 -.010428 .020191 103.979 0 -.516 .607 -.050469 .029612
a. Age Slope for Women
b. Dependent Variable: symptoms: # Daily Physical Symptoms (0=5).


Correlations


CorrelationsCorrelations, table, 1 levels of column headers and 2 levels of row headers, table with 4 columns and 8 rows
  symptoms: # Daily Physical Symptoms (0=5) Fixed Predicted Values
symptoms: # Daily Physical Symptoms (0=5) Pearson Correlation 1 .220
Sig. (2-tailed)   .000
N 509 509
Fixed Predicted Values Pearson Correlation .220 1
Sig. (2-tailed) .000  
N 509 509