NOTE: Copyright (c) 1999-2000 by SAS Institute Inc., Cary, NC, USA. NOTE: SAS (r) Proprietary Software Release 8.1 (TS1M0) Licensed to NEW YORK UNIVERSITY, Site 0011830001. NOTE: This session is executing on the WIN_98 platform. NOTE: SAS initialization used: real time 12.40 seconds 1 filename myimport 'c:\mixedex.por'; 2 proc convert spss=myimport out=sasuser.mixedex; 3 TITLE1 'SMALL SIMULATED RANDOM COEFFICIENTS DATA'; 4 run; NOTE: SPSS Portable File (Creation Date=24FEB01:16:06:37). NOTE: The data set SASUSER.MIXEDEX has 24 observations and 21 variables. NOTE: PROCEDURE CONVERT used: real time 1.21 seconds 5 proc mixed covtest; 6 class sub; 7 model y=g time g*time /s; 8 random intercept / subject=sub; 9 TITLE2 'RANDOM INTERCEPT ONLY'; NOTE: Convergence criteria met. NOTE: There were 24 observations read from the data set SASUSER.MIXEDEX. NOTE: PROCEDURE MIXED used: real time 2.40 seconds 10 proc mixed covtest; 11 class sub; 12 model y=g time g*time /s; 13 random intercept time / subject=sub g gcorr type=un; 14 TITLE2 'RANDOM INTERCEPT AND SLOPE'; NOTE: Convergence criteria met. NOTE: There were 24 observations read from the data set SASUSER.MIXEDEX. NOTE: PROCEDURE MIXED used: real time 0.16 seconds 15 proc mixed covtest; 16 class sub; 17 model y=g time g*time /s; 18 random intercept time / subject=sub g gcorr type=un; 19 REPEATED /TYPE=AR(1) SUBJECT=SUB R RCORR; 20 TITLE2 'RANDOM INTERCEPT ONLY WITH CORRELATED RESIDUALS'; 21 run; NOTE: Convergence criteria met. NOTE: There were 24 observations read from the data set SASUSER.MIXEDEX. NOTE: PROCEDURE MIXED used: real time 0.16 seconds 22 proc mixed covtest; 23 class sub; 24 model y=g time g*time /s; 25 random intercept / subject=sub g gcorr type=un; 26 REPEATED /TYPE=AR(1) SUBJECT=SUB R RCORR; 27 TITLE2 'RANDOM INTERCEPT AND SLOPE WITH CORRELATED RESIDUALS'; 28 run; NOTE: Convergence criteria met. NOTE: Estimated G matrix is not positive definite. NOTE: There were 24 observations read from the data set SASUSER.MIXEDEX. NOTE: PROCEDURE MIXED used: real time 0.17 seconds SMALL SIMULATED RANDOM COEFFICIENTS DATA 1 RANDOM INTERCEPT ONLY 07:57 Wednesday, February 28, 2001 The Mixed Procedure Model Information Data Set SASUSER.MIXEDEX Dependent Variable Y Covariance Structure Variance Components Subject Effect SUB Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values SUB 8 a b c d e f g h Dimensions Covariance Parameters 2 Columns in X 4 Columns in Z Per Subject 1 Subjects 8 Max Obs Per Subject 4 Observations Used 24 Observations Not Used 0 Total Observations 24 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 34.63795793 1 2 20.57050637 0.04946249 2 1 20.07499353 0.01199419 3 1 19.95860344 0.00111538 4 1 19.94861831 0.00001284 5 1 19.94850951 0.00000000 Convergence criteria met. SMALL SIMULATED RANDOM COEFFICIENTS DATA 2 RANDOM INTERCEPT ONLY 07:57 Wednesday, February 28, 2001 The Mixed Procedure Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z Intercept SUB 0.2086 0.1307 1.60 0.0553 Residual 0.04186 0.01590 2.63 0.0042 Fit Statistics -2 Res Log Likelihood 19.9 AIC (smaller is better) 23.9 AICC (smaller is better) 24.7 BIC (smaller is better) 24.1 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 2.0290 0.2504 6 8.10 0.0002 G 1.1680 0.3509 14 3.33 0.0050 TIME 0.5139 0.05854 14 8.78 <.0001 G*TIME -0.5469 0.07753 14 -7.05 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F G 1 14 11.08 0.0050 TIME 1 14 77.06 <.0001 G*TIME 1 14 49.75 <.0001 SMALL SIMULATED RANDOM COEFFICIENTS DATA 3 RANDOM INTERCEPT AND SLOPE 07:57 Wednesday, February 28, 2001 The Mixed Procedure Model Information Data Set SASUSER.MIXEDEX Dependent Variable Y Covariance Structure Unstructured Subject Effect SUB Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values SUB 8 a b c d e f g h Dimensions Covariance Parameters 4 Columns in X 4 Columns in Z Per Subject 2 Subjects 8 Max Obs Per Subject 4 Observations Used 24 Observations Not Used 0 Total Observations 24 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 34.63795793 1 2 13.91812695 0.07570676 2 1 12.80396229 0.03262924 3 1 12.31559189 0.00925827 4 1 12.18174684 0.00114670 5 1 12.16644886 0.00002362 6 1 12.16615425 0.00000001 7 1 12.16615411 0.00000000 Convergence criteria met. SMALL SIMULATED RANDOM COEFFICIENTS DATA 4 RANDOM INTERCEPT AND SLOPE 07:57 Wednesday, February 28, 2001 The Mixed Procedure Estimated G Matrix Row Effect SUB Col1 Col2 1 Intercept a 0.06084 0.01862 2 TIME a 0.01862 0.06337 Estimated G Correlation Matrix Row Effect SUB Col1 Col2 1 Intercept a 1.0000 0.2999 2 TIME a 0.2999 1.0000 Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) SUB 0.06084 0.04197 1.45 0.0736 UN(2,1) SUB 0.01862 0.03336 0.56 0.5767 UN(2,2) SUB 0.06337 0.04701 1.35 0.0888 Residual 0.01191 0.006250 1.91 0.0284 Fit Statistics -2 Res Log Likelihood 12.2 AIC (smaller is better) 20.2 AICC (smaller is better) 22.8 BIC (smaller is better) 20.5 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 3 22.47 <.0001 SMALL SIMULATED RANDOM COEFFICIENTS DATA 5 RANDOM INTERCEPT AND SLOPE 07:57 Wednesday, February 28, 2001 The Mixed Procedure Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 2.1768 0.1388 6 15.68 <.0001 G 1.0221 0.1920 8 5.32 0.0007 TIME 0.4355 0.1319 6 3.30 0.0164 G*TIME -0.4683 0.1846 8 -2.54 0.0349 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F G 1 8 28.33 0.0007 TIME 1 6 10.90 0.0164 G*TIME 1 8 6.43 0.0349 SMALL SIMULATED RANDOM COEFFICIENTS DATA 6 RANDOM INTERCEPT ONLY WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Model Information Data Set SASUSER.MIXEDEX Dependent Variable Y Covariance Structures Unstructured, Autoregressive Subject Effects SUB, SUB Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values SUB 8 a b c d e f g h Dimensions Covariance Parameters 5 Columns in X 4 Columns in Z Per Subject 2 Subjects 8 Max Obs Per Subject 4 Observations Used 24 Observations Not Used 0 Total Observations 24 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 34.63795793 1 3 12.58906886 0.13263692 2 3 12.51891150 . 3 1 12.26135046 0.01926457 4 1 12.21600110 0.01278109 5 1 12.05024590 0.00017120 6 1 12.04810204 0.00000014 7 1 12.04810029 0.00000000 SMALL SIMULATED RANDOM COEFFICIENTS DATA 7 RANDOM INTERCEPT ONLY WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Convergence criteria met. Estimated R Matrix for SUB a Row Col1 Col2 Col3 1 0.008378 -0.00319 0.001212 2 -0.00319 0.008378 -0.00319 3 0.001212 -0.00319 0.008378 Estimated R Correlation Matrix for SUB a Row Col1 Col2 Col3 1 1.0000 -0.3803 0.1446 2 -0.3803 1.0000 -0.3803 3 0.1446 -0.3803 1.0000 Estimated G Matrix Row Effect SUB Col1 Col2 1 Intercept a 0.06585 0.01915 2 TIME a 0.01915 0.06393 Estimated G Correlation Matrix Row Effect SUB Col1 Col2 1 Intercept a 1.0000 0.2951 2 TIME a 0.2951 1.0000 Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) SUB 0.06585 0.04352 1.51 0.0651 UN(2,1) SUB 0.01915 0.03311 0.58 0.5631 UN(2,2) SUB 0.06393 0.04636 1.38 0.0839 AR(1) SUB -0.3803 0.8057 -0.47 0.6369 Residual 0.008378 0.006161 1.36 0.0869 SMALL SIMULATED RANDOM COEFFICIENTS DATA 8 RANDOM INTERCEPT ONLY WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Fit Statistics -2 Res Log Likelihood 12.0 AIC (smaller is better) 22.0 AICC (smaller is better) 26.3 BIC (smaller is better) 22.4 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 4 22.59 0.0002 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 2.1864 0.1388 6 15.75 <.0001 G 1.0088 0.1925 8 5.24 0.0008 TIME 0.4351 0.1310 6 3.32 0.0160 G*TIME -0.4652 0.1836 8 -2.53 0.0350 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F G 1 8 27.47 0.0008 TIME 1 6 11.03 0.0160 G*TIME 1 8 6.42 0.0350 SMALL SIMULATED RANDOM COEFFICIENTS DATA 9 RANDOM INTERCEPT AND SLOPE WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Model Information Data Set SASUSER.MIXEDEX Dependent Variable Y Covariance Structures Unstructured, Autoregressive Subject Effects SUB, SUB Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values SUB 8 a b c d e f g h Dimensions Covariance Parameters 3 Columns in X 4 Columns in Z Per Subject 1 Subjects 8 Max Obs Per Subject 4 Observations Used 24 Observations Not Used 0 Total Observations 24 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 34.63795793 1 2 18.84124229 1.11093219 2 2 18.74723803 0.00418811 3 3 18.70663804 0.00000003 4 1 18.70663781 0.00000000 Convergence criteria met. SMALL SIMULATED RANDOM COEFFICIENTS DATA 10 RANDOM INTERCEPT AND SLOPE WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Estimated R Matrix for SUB a Row Col1 Col2 Col3 1 0.2395 0.2033 0.1726 2 0.2033 0.2395 0.2033 3 0.1726 0.2033 0.2395 Estimated R Correlation Matrix for SUB a Row Col1 Col2 Col3 1 1.0000 0.8491 0.7210 2 0.8491 1.0000 0.8491 3 0.7210 0.8491 1.0000 Estimated G Matrix Row Effect SUB Col1 1 Intercept a Estimated G Correlation Matrix Row Effect SUB Col1 1 Intercept a 1.0000 Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) SUB 2.69E-18 . . . AR(1) SUB 0.8491 0.09181 9.25 <.0001 Residual 0.2395 0.1221 1.96 0.0250 Fit Statistics -2 Res Log Likelihood 18.7 AIC (smaller is better) 22.7 AICC (smaller is better) 23.4 BIC (smaller is better) 22.9 SMALL SIMULATED RANDOM COEFFICIENTS DATA 11 RANDOM INTERCEPT AND SLOPE WITH CORRELATED RESIDUALS 07:57 Wednesday, February 28, 2001 The Mixed Procedure Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 15.93 <.0001 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 2.0457 0.2509 6 8.15 0.0002 G 1.1856 0.3480 14 3.41 0.0043 TIME 0.4869 0.07739 14 6.29 <.0001 G*TIME -0.5339 0.09794 14 -5.45 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F G 1 14 11.61 0.0043 TIME 1 14 39.58 <.0001 G*TIME 1 14 29.72 <.0001