|
Mixed Effects Model for log(FEV1) with Random Intercept and Slope for Age |
|
Six Cities Study |
|
The Mixed Procedure |
|
Model Information |
|
|
Data Set |
WORK.FEV |
|
Dependent Variable |
logfev1 |
|
Covariance Structure |
Unstructured |
|
Subject Effect |
id |
|
Estimation Method |
REML |
|
Residual Variance Method |
Profile |
|
Fixed Effects SE Method |
Model-Based |
|
Degrees of Freedom Method |
Containment |
|
Class Level Information |
||
|
Class |
Levels |
Values |
|
id |
299 |
not printed |
|
Dimensions |
|
|
Covariance Parameters |
4 |
|
Columns in X |
5 |
|
Columns in Z Per Subject |
2 |
|
Subjects |
299 |
|
Max Obs Per Subject |
12 |
|
Observations Used |
1993 |
|
Observations Not Used |
0 |
|
Total Observations |
1993 |
|
Iteration History |
|||
|
Iteration |
Evaluations |
-2 Res Log Like |
Criterion |
|
0 |
1 |
-2961.45030802 |
|
|
1 |
2 |
-4567.61910964 |
0.00006041 |
|
2 |
1 |
-4567.88023186 |
0.00000041 |
|
3 |
1 |
-4567.88194328 |
0.00000000 |
|
Convergence criteria met. |
|
Estimated G Matrix |
||||
|
Row |
Effect |
id |
Col1 |
Col2 |
|
1 |
Intercept |
1 |
0.01221 |
-0.00043 |
|
2 |
age |
1 |
-0.00043 |
0.000050 |
|
Estimated G Correlation Matrix |
||||
|
Row |
Effect |
id |
Col1 |
Col2 |
|
1 |
Intercept |
1 |
1.0000 |
-0.5531 |
|
2 |
age |
1 |
-0.5531 |
1.0000 |
|
Estimated V Correlation Matrix for id 35 |
||||||||||||
|
Row |
Col1 |
Col2 |
Col3 |
Col4 |
Col5 |
Col6 |
Col7 |
Col8 |
Col9 |
Col10 |
Col11 |
Col12 |
|
1 |
1.0000 |
0.7001 |
0.6939 |
0.6843 |
0.6719 |
0.6574 |
0.6414 |
0.6216 |
0.6037 |
0.5819 |
0.5640 |
0.5429 |
|
2 |
0.7001 |
1.0000 |
0.6985 |
0.6930 |
0.6847 |
0.6740 |
0.6615 |
0.6455 |
0.6305 |
0.6119 |
0.5963 |
0.5778 |
|
3 |
0.6939 |
0.6985 |
1.0000 |
0.6992 |
0.6950 |
0.6882 |
0.6793 |
0.6671 |
0.6552 |
0.6400 |
0.6269 |
0.6110 |
|
4 |
0.6843 |
0.6930 |
0.6992 |
1.0000 |
0.7028 |
0.7002 |
0.6953 |
0.6872 |
0.6786 |
0.6670 |
0.6565 |
0.6436 |
|
5 |
0.6719 |
0.6847 |
0.6950 |
0.7028 |
1.0000 |
0.7089 |
0.7078 |
0.7038 |
0.6984 |
0.6903 |
0.6826 |
0.6725 |
|
6 |
0.6574 |
0.6740 |
0.6882 |
0.7002 |
0.7089 |
1.0000 |
0.7168 |
0.7167 |
0.7145 |
0.7098 |
0.7046 |
0.6973 |
|
7 |
0.6414 |
0.6615 |
0.6793 |
0.6953 |
0.7078 |
0.7168 |
1.0000 |
0.7263 |
0.7270 |
0.7255 |
0.7228 |
0.7182 |
|
8 |
0.6216 |
0.6455 |
0.6671 |
0.6872 |
0.7038 |
0.7167 |
0.7263 |
1.0000 |
0.7377 |
0.7397 |
0.7396 |
0.7379 |
|
9 |
0.6037 |
0.6305 |
0.6552 |
0.6786 |
0.6984 |
0.7145 |
0.7270 |
0.7377 |
1.0000 |
0.7490 |
0.7511 |
0.7517 |
|
10 |
0.5819 |
0.6119 |
0.6400 |
0.6670 |
0.6903 |
0.7098 |
0.7255 |
0.7397 |
0.7490 |
1.0000 |
0.7614 |
0.7646 |
|
11 |
0.5640 |
0.5963 |
0.6269 |
0.6565 |
0.6826 |
0.7046 |
0.7228 |
0.7396 |
0.7511 |
0.7614 |
1.0000 |
0.7728 |
|
12 |
0.5429 |
0.5778 |
0.6110 |
0.6436 |
0.6725 |
0.6973 |
0.7182 |
0.7379 |
0.7517 |
0.7646 |
0.7728 |
1.0000 |
|
Covariance Parameter Estimates |
|||||
|
Cov Parm |
Subject |
Estimate |
Standard Error |
Z Value |
Pr Z |
|
UN(1,1) |
id |
0.01221 |
0.001924 |
6.34 |
<.0001 |
|
UN(2,1) |
id |
-0.00043 |
0.000122 |
-3.55 |
0.0004 |
|
UN(2,2) |
id |
0.000050 |
9.801E-6 |
5.11 |
<.0001 |
|
Residual |
|
0.003629 |
0.000133 |
27.21 |
<.0001 |
|
Fit Statistics |
|
|
-2 Res Log Likelihood |
-4567.9 |
|
AIC (smaller is better) |
-4559.9 |
|
AICC (smaller is better) |
-4559.9 |
|
BIC (smaller is better) |
-4545.1 |
|
Solution for Fixed Effects |
|||||
|
Effect |
Estimate |
Standard Error |
DF |
t Value |
Pr > |t| |
|
Intercept |
-0.2883 |
0.03872 |
297 |
-7.45 |
<.0001 |
|
age |
0.02353 |
0.001395 |
251 |
16.86 |
<.0001 |
|
loght |
2.2372 |
0.04354 |
1440 |
51.39 |
<.0001 |
|
baseage |
-0.01651 |
0.007458 |
1440 |
-2.21 |
0.0270 |
|
logbht |
0.2182 |
0.1455 |
1440 |
1.50 |
0.1340 |
|
Type 3 Tests of Fixed Effects |
||||||
|
Effect |
Num DF |
Den DF |
Chi-Square |
F Value |
Pr > ChiSq |
Pr > F |
|
age |
1 |
251 |
284.34 |
284.34 |
<.0001 |
<.0001 |
|
loght |
1 |
1440 |
2640.50 |
2640.50 |
<.0001 |
<.0001 |
|
baseage |
1 |
1440 |
4.90 |
4.90 |
0.0269 |
0.0270 |
|
logbht |
1 |
1440 |
2.25 |
2.25 |
0.1337 |
0.1340 |