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Mixed Effects Model for log(FEV1) with Random Intercept and Slopes for Age and Log Height |
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Six Cities Study |
|
The Mixed Procedure |
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Model Information |
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Data Set |
WORK.FEV |
|
Dependent Variable |
logfev1 |
|
Covariance Structure |
Unstructured |
|
Subject Effect |
id |
|
Estimation Method |
REML |
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Residual Variance Method |
Profile |
|
Fixed Effects SE Method |
Model-Based |
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Degrees of Freedom Method |
Containment |
|
Class Level Information |
||
|
Class |
Levels |
Values |
|
id |
299 |
not printed |
|
Dimensions |
|
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Covariance Parameters |
7 |
|
Columns in X |
5 |
|
Columns in Z Per Subject |
3 |
|
Subjects |
299 |
|
Max Obs Per Subject |
12 |
|
Observations Used |
1993 |
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Observations Not Used |
0 |
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Total Observations |
1993 |
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Iteration History |
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Iteration |
Evaluations |
-2 Res Log Like |
Criterion |
|
0 |
1 |
-2961.45030802 |
|
|
1 |
2 |
-4525.34587509 |
1.08900123 |
|
2 |
1 |
-4526.52099519 |
0.21154590 |
|
3 |
1 |
-4534.30743803 |
7.32006321 |
|
4 |
1 |
-4544.85801410 |
219.20495583 |
|
5 |
1 |
-4548.65364068 |
5.27040271 |
|
6 |
1 |
-4550.87935831 |
0.00485639 |
|
7 |
3 |
-4560.41529524 |
. |
|
8 |
2 |
-4580.64140277 |
. |
|
9 |
2 |
-4588.90623048 |
. |
|
10 |
1 |
-4589.86323392 |
0.00000850 |
|
11 |
1 |
-4589.89930825 |
0.00000002 |
|
12 |
1 |
-4589.89938271 |
0.00000000 |
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Convergence criteria met. |
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Estimated G Matrix |
|||||
|
Row |
Effect |
id |
Col1 |
Col2 |
Col3 |
|
1 |
Intercept |
1 |
0.01337 |
-0.00007 |
-0.01663 |
|
2 |
age |
1 |
-0.00007 |
0.000012 |
-0.00036 |
|
3 |
loght |
1 |
-0.01663 |
-0.00036 |
0.07984 |
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Estimated G Correlation Matrix |
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|
Row |
Effect |
id |
Col1 |
Col2 |
Col3 |
|
1 |
Intercept |
1 |
1.0000 |
-0.1648 |
-0.5091 |
|
2 |
age |
1 |
-0.1648 |
1.0000 |
-0.3731 |
|
3 |
loght |
1 |
-0.5091 |
-0.3731 |
1.0000 |
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Estimated V Correlation Matrix for id 35 |
||||||||||||
|
Row |
Col1 |
Col2 |
Col3 |
Col4 |
Col5 |
Col6 |
Col7 |
Col8 |
Col9 |
Col10 |
Col11 |
Col12 |
|
1 |
1.0000 |
0.7180 |
0.7003 |
0.6652 |
0.6274 |
0.5704 |
0.5109 |
0.4887 |
0.4811 |
0.4803 |
0.4793 |
0.4707 |
|
2 |
0.7180 |
1.0000 |
0.7042 |
0.6792 |
0.6494 |
0.6020 |
0.5505 |
0.5310 |
0.5242 |
0.5234 |
0.5223 |
0.5145 |
|
3 |
0.7003 |
0.7042 |
1.0000 |
0.6913 |
0.6720 |
0.6371 |
0.5961 |
0.5800 |
0.5743 |
0.5733 |
0.5721 |
0.5652 |
|
4 |
0.6652 |
0.6792 |
0.6913 |
1.0000 |
0.6929 |
0.6760 |
0.6504 |
0.6391 |
0.6346 |
0.6331 |
0.6315 |
0.6257 |
|
5 |
0.6274 |
0.6494 |
0.6720 |
0.6929 |
1.0000 |
0.6983 |
0.6855 |
0.6784 |
0.6752 |
0.6735 |
0.6717 |
0.6670 |
|
6 |
0.5704 |
0.6020 |
0.6371 |
0.6760 |
0.6983 |
1.0000 |
0.7180 |
0.7159 |
0.7141 |
0.7120 |
0.7097 |
0.7063 |
|
7 |
0.5109 |
0.5505 |
0.5961 |
0.6504 |
0.6855 |
0.7180 |
1.0000 |
0.7381 |
0.7376 |
0.7350 |
0.7324 |
0.7302 |
|
8 |
0.4887 |
0.5310 |
0.5800 |
0.6391 |
0.6784 |
0.7159 |
0.7381 |
1.0000 |
0.7430 |
0.7410 |
0.7388 |
0.7375 |
|
9 |
0.4811 |
0.5242 |
0.5743 |
0.6346 |
0.6752 |
0.7141 |
0.7376 |
0.7430 |
1.0000 |
0.7427 |
0.7410 |
0.7405 |
|
10 |
0.4803 |
0.5234 |
0.5733 |
0.6331 |
0.6735 |
0.7120 |
0.7350 |
0.7410 |
0.7427 |
1.0000 |
0.7415 |
0.7416 |
|
11 |
0.4793 |
0.5223 |
0.5721 |
0.6315 |
0.6717 |
0.7097 |
0.7324 |
0.7388 |
0.7410 |
0.7415 |
1.0000 |
0.7421 |
|
12 |
0.4707 |
0.5145 |
0.5652 |
0.6257 |
0.6670 |
0.7063 |
0.7302 |
0.7375 |
0.7405 |
0.7416 |
0.7421 |
1.0000 |
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Fit Statistics |
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-2 Res Log Likelihood |
-4589.9 |
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AIC (smaller is better) |
-4575.9 |
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AICC (smaller is better) |
-4575.8 |
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BIC (smaller is better) |
-4550.0 |
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Solution for Fixed Effects |
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|
Effect |
Estimate |
Standard Error |
DF |
t Value |
Pr > |t| |
|
Intercept |
-0.2857 |
0.03903 |
297 |
-7.32 |
<.0001 |
|
age |
0.02344 |
0.001278 |
251 |
18.34 |
<.0001 |
|
loght |
2.2476 |
0.04692 |
227 |
47.90 |
<.0001 |
|
baseage |
-0.01610 |
0.007429 |
1213 |
-2.17 |
0.0304 |
|
logbht |
0.1774 |
0.1454 |
1213 |
1.22 |
0.2225 |
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Type 3 Tests of Fixed Effects |
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|
Effect |
Num DF |
Den DF |
Chi-Square |
F Value |
Pr > ChiSq |
Pr > F |
|
age |
1 |
251 |
336.50 |
336.50 |
<.0001 |
<.0001 |
|
loght |
1 |
227 |
2294.67 |
2294.67 |
<.0001 |
<.0001 |
|
baseage |
1 |
1213 |
4.70 |
4.70 |
0.0302 |
0.0304 |
|
logbht |
1 |
1213 |
1.49 |
1.49 |
0.2222 |
0.2225 |