Jason T. Newsom,
Richard N. Jones, & Scott M. Hofer.
Longitudinal
data analysis: A practical guide for researchers in aging, health, and social
sciences
CHAPTER 7
Shaw BA & Liang J
Table 7.1 Multilevel
Regression of BMI over Time &
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 1
Bmi =
body mass index
Ctime =
time centered
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime /SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 471
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 4
Columns in X 2
Columns in Z Per Subject 2
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42721
Number of Observations Not Used 1541
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264692.46803175
1 2 193433.41107227 0.00000663
2 1 193433.02543010 0.00000000
Convergence criteria met.
Estimated G Correlation Matrix
Row Effect id Col1 Col2
1 Intercept 1 1.0000 0.2084
2 ctime 1 0.2084 1.0000
The SAS System 09:44 Monday, April 11, 2011 472
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 26.0290 0.4352 59.81 <.0001
UN(2,1) id 0.2662 0.01880 14.16 <.0001
UN(2,2) id 0.06267 0.001593 39.34 <.0001
Residual 2.1710 0.01836 118.23 <.0001
Fit Statistics
-2 Res Log Likelihood 193433.0
AIC (smaller is better) 193441.0
AICC (smaller is better) 193441.0
BIC (smaller is better) 193468.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 71259.44 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 28.0979 0.05985 7375 469.47 <.0001
ctime 0.05382 0.003594 7254 14.97 <.0001
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 2
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime Zage
zage*ctime /SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 473
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 4
Columns in X 4
Columns in Z Per Subject 2
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42721
Number of Observations Not Used 1541
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264554.78052201
1 2 193292.38565887 0.00000530
2 1 193292.07813591 0.00000000
Convergence criteria met.
Estimated G Correlation Matrix
Row Effect id Col1 Col2
1 Intercept 1 1.0000 0.2019
2 ctime 1 0.2019 1.0000
The SAS System 09:44 Monday, April 11, 2011 474
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 25.9435 0.4338 59.81 <.0001
UN(2,1) id 0.2536 0.01857 13.66 <.0001
UN(2,2) id 0.06082 0.001563 38.92 <.0001
Residual 2.1711 0.01836 118.23 <.0001
Fit Statistics
-2 Res Log Likelihood 193292.1
AIC (smaller is better) 193300.1
AICC (smaller is better) 193300.1
BIC (smaller is better) 193327.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 71262.70 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 28.0981 0.05975 7373 470.23 <.0001
ctime 0.05395 0.003559 7252 15.16 <.0001
Zage -0.2985 0.05977 7377 -4.99 <.0001
ctime*Zage -0.04315 0.003565 7270 -12.10 <.0001
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 3
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime Zage Zgender zage*ctime zgender*ctime /SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 475
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 4
Columns in X 6
Columns in Z Per Subject 2
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42721
Number of Observations Not Used 1541
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264565.95297507
1 2 193301.13661251 0.00000513
2 1 193300.83898603 0.00000000
Convergence criteria met.
Estimated G Correlation Matrix
Row Effect id Col1 Col2
1 Intercept 1 1.0000 0.2018
2 ctime 1 0.2018 1.0000
The SAS System 09:44 Monday, April 11, 2011 476
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 25.9434 0.4338 59.80 <.0001
UN(2,1) id 0.2534 0.01856 13.65 <.0001
UN(2,2) id 0.06078 0.001562 38.90 <.0001
Residual 2.1711 0.01836 118.23 <.0001
Fit Statistics
-2 Res Log Likelihood 193300.8
AIC (smaller is better) 193308.8
AICC (smaller is better) 193308.8
BIC (smaller is better) 193336.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 71265.11 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 28.0980 0.05975 7372 470.23 <.0001
ctime 0.05397 0.003558 7251 15.17 <.0001
Zage -0.2847 0.06140 7376 -4.64 <.0001
Zgender -0.06057 0.06138 7371 -0.99 0.3238
ctime*Zage -0.04149 0.003661 7264 -11.33 <.0001
ctime*Zgender -0.00725 0.003652 7238 -1.99 0.0471
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 4
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime Zage Zgender zage*ctime zgender*ctime genderage /SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 477
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 4
Columns in X 7
Columns in Z Per Subject 2
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42721
Number of Observations Not Used 1541
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264565.90064867
1 2 193302.97579931 0.00000524
2 1 193302.67136322 0.00000000
Convergence criteria met.
Estimated G Correlation Matrix
Row Effect id Col1 Col2
1 Intercept 1 1.0000 0.2024
2 ctime 1 0.2024 1.0000
The SAS System 09:44 Monday, April 11, 2011 478
The Mixed Procedure
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 25.9444 0.4339 59.80 <.0001
UN(2,1) id 0.2542 0.01857 13.69 <.0001
UN(2,2) id 0.06078 0.001562 38.90 <.0001
Residual 2.1711 0.01836 118.23 <.0001
Fit Statistics
-2 Res Log Likelihood 193302.7
AIC (smaller is better) 193310.7
AICC (smaller is better) 193310.7
BIC (smaller is better) 193338.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 71263.23 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 28.1173 0.06132 7389 458.53 <.0001
ctime 0.05397 0.003558 7251 15.17 <.0001
Zage -0.2763 0.06169 7379 -4.48 <.0001
Zgender -0.05808 0.06141 7370 -0.95 0.3443
ctime*Zage -0.04150 0.003661 7264 -11.34 <.0001
ctime*Zgender -0.00725 0.003652 7238 -1.99 0.0471
genderage -0.08409 0.06019 7366 -1.40 0.1624
Table 7.3 Multilevel
Regression of BMI over Time and time-varying marital status
Model 5
GENDER*AGE INTERACTION EFFECT DIFFERS FROM THE HLM ANALYSIS, MOST LIKELY
DUE TO DIFFERENT CASES INCLUDED IN THE ANALYSIS DUE TO MISSING VALUES.
DF IN HLM ANALYSIS IS 7373, BUT ONLY 7180 FOR TH IS COEFFICIENT IN
SAS. ALL OTHER COEFFICIENTS ARE
NEARLY IDENTICAL.;
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime Zage Zgender zage*ctime zgender*ctime genderage married
/SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime married /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 479
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 7
Columns in X 8
Columns in Z Per Subject 3
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42713
Number of Observations Not Used 1549
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264495.87052990
1 3 193824.65240761 0.01386982
2 1 193364.91414239 0.00307672
3 1 193150.38640398 0.00067145
4 1 193105.42808783 0.00007634
5 1 193100.66868827 0.00000172
6 1 193100.56852481 0.00000000
Convergence criteria met.
The SAS System 09:44 Monday, April 11, 2011 480
The Mixed Procedure
Estimated G Correlation Matrix
Row Effect id Col1 Col2 Col3
1 Intercept 1 1.0000 0.1757 -0.2153
2 ctime 1 0.1757 1.0000 0.1451
3 married 1 -0.2153 0.1451 1.0000
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 26.8595 0.5994 44.81 <.0001
UN(2,1) id 0.2218 0.02318 9.57 <.0001
UN(2,2) id 0.05934 0.001582 37.50 <.0001
UN(3,1) id -1.5850 0.3239 -4.89 <.0001
UN(3,2) id 0.05023 0.02015 2.49 0.0127
UN(3,3) id 2.0182 0.2426 8.32 <.0001
Residual 2.1325 0.01832 116.43 <.0001
Fit Statistics
-2 Res Log Likelihood 193100.6
AIC (smaller is better) 193114.6
AICC (smaller is better) 193114.6
BIC (smaller is better) 193162.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
6 71395.30 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 27.8818 0.07711 4052 361.58 <.0001
ctime 0.05808 0.003583 7054 16.21 <.0001
Zage -0.2628 0.06165 7262 -4.26 <.0001
Zgender -0.08256 0.06165 7380 -1.34 0.1805
ctime*Zage -0.04092 0.003652 7247 -11.21 <.0001
ctime*Zgender -0.00916 0.003646 7211 -2.51 0.0120
genderage -0.1028 0.06005 7180 -1.71 0.0871
married 0.3108 0.06150 1405 5.05 <.0001
Table 7.3
Multilevel Regression of BMI over Time and time-varying marital status
Model 5
GENDER*AGE AND GENDER*AGE*MARRIED INTERACTION EFFECTS DIFFER FROM THE
HLM ANALYSIS, MOST LIKELY DUE TO DIFFERENT CASES INCLUDED IN THE ANALYSIS DUE
TO MISSING VALUES.
DF IN HLM ANALYSIS IS 7373, BUT ONLY 7180 FOR TH IS COEFFICIENT IN
SAS. ALL OTHER COEFFICIENTS ARE
NEARLY IDENTICAL.
;
PROC MIXED data=chpt7
COVTEST ;
CLASS id;
MODEL bmi = ctime Zage Zgender zage*ctime zgender*ctime genderage married
zage*married zgender*married genderage*married /SOLUTION NOTEST DDFM=KR;
RANDOM INTERCEPT ctime married /TYPE=UN SUBJECT=id GCORR;
RUN;
The SAS System 09:44 Monday, April 11, 2011 481
The Mixed Procedure
Model Information
Data Set WORK.CHPT7
Dependent Variable bmi
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
id 7377 not printed
Dimensions
Covariance Parameters 7
Columns in X 11
Columns in Z Per Subject 3
Subjects 7377
Max Obs Per Subject 6
Number of Observations
Number of Observations Read 44262
Number of Observations Used 42713
Number of Observations Not Used 1549
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 264331.43193472
1 3 197200.05753046 9099.0175428
2 2 194653.83100140 0.62068328
3 1 193490.79454445 0.00517776
4 2 193197.85722744 0.00121649
5 1 193116.48017523 0.00014172
6 1 193107.54211058 0.00000458
7 1 193107.27287702 0.00000001
Convergence criteria met.
The SAS System 09:44 Monday, April 11, 2011 482
The Mixed Procedure
Estimated G Correlation Matrix
Row Effect id Col1 Col2 Col3
1 Intercept 1 1.0000 0.1755 -0.2152
2 ctime 1 0.1755 1.0000 0.1450
3 married 1 -0.2152 0.1450 1.0000
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 26.8253 0.5993 44.76 <.0001
UN(2,1) id 0.2214 0.02318 9.55 <.0001
UN(2,2) id 0.05935 0.001583 37.50 <.0001
UN(3,1) id -1.5925 0.3242 -4.91 <.0001
UN(3,2) id 0.05047 0.02017 2.50 0.0123
UN(3,3) id 2.0412 0.2441 8.36 <.0001
Residual 2.1326 0.01832 116.43 <.0001
Fit Statistics
-2 Res Log Likelihood 193107.3
AIC (smaller is better) 193121.3
AICC (smaller is better) 193121.3
BIC (smaller is better) 193169.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
6 71224.16 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 27.8393 0.07993 3646 348.30 <.0001
ctime 0.05785 0.003585 7066 16.13 <.0001
Zage -0.2203 0.08089 3544 -2.72 0.0065
Zgender -0.1811 0.08187 3489 -2.21 0.0270
ctime*Zage -0.04123 0.003706 7141 -11.13 <.0001
ctime*Zgender -0.00849 0.003675 7033 -2.31 0.0209
genderage -0.03267 0.08147 3410 -0.40 0.6884
married 0.3522 0.06487 1334 5.43 <.0001
Zage*married -0.05008 0.06322 1258 -0.79 0.4284
Zgender*married 0.1205 0.06690 1305 1.80 0.0720
genderage*married -0.07574 0.06322 1177 -1.20 0.2311