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Mixed Effects Model for log(FEV1) with Random Intercept and Slope for Log Height |
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Six Cities Study |
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The Mixed Procedure |
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Model Information |
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Data Set |
WORK.FEV |
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Dependent Variable |
logfev1 |
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Covariance Structure |
Unstructured |
|
Subject Effect |
id |
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Estimation Method |
REML |
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Residual Variance Method |
Profile |
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Fixed Effects SE Method |
Model-Based |
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Degrees of Freedom Method |
Containment |
|
Class Level Information |
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|
Class |
Levels |
Values |
|
id |
299 |
not printed |
|
Dimensions |
|
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Covariance Parameters |
4 |
|
Columns in X |
5 |
|
Columns in Z Per Subject |
2 |
|
Subjects |
299 |
|
Max Obs Per Subject |
12 |
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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 |
3 |
-4589.31545000 |
0.00003664 |
|
2 |
1 |
-4589.47260066 |
0.00000016 |
|
3 |
1 |
-4589.47325326 |
0.00000000 |
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Convergence criteria met. |
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Estimated G Matrix |
||||
|
Row |
Effect |
id |
Col1 |
Col2 |
|
1 |
Intercept |
1 |
0.01330 |
-0.01855 |
|
2 |
loght |
1 |
-0.01855 |
0.06849 |
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Estimated G Correlation Matrix |
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Row |
Effect |
id |
Col1 |
Col2 |
|
1 |
Intercept |
1 |
1.0000 |
-0.6146 |
|
2 |
loght |
1 |
-0.6146 |
1.0000 |
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Estimated V Correlation Matrix for id 35 |
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|
Row |
Col1 |
Col2 |
Col3 |
Col4 |
Col5 |
Col6 |
Col7 |
Col8 |
Col9 |
Col10 |
Col11 |
Col12 |
|
1 |
1.0000 |
0.7223 |
0.7050 |
0.6706 |
0.6336 |
0.5776 |
0.5187 |
0.4968 |
0.4895 |
0.4895 |
0.4895 |
0.4823 |
|
2 |
0.7223 |
1.0000 |
0.7088 |
0.6842 |
0.6551 |
0.6085 |
0.5575 |
0.5382 |
0.5317 |
0.5317 |
0.5317 |
0.5253 |
|
3 |
0.7050 |
0.7088 |
1.0000 |
0.6957 |
0.6767 |
0.6423 |
0.6017 |
0.5857 |
0.5804 |
0.5804 |
0.5804 |
0.5750 |
|
4 |
0.6706 |
0.6842 |
0.6957 |
1.0000 |
0.6962 |
0.6790 |
0.6533 |
0.6423 |
0.6385 |
0.6385 |
0.6385 |
0.6347 |
|
5 |
0.6336 |
0.6551 |
0.6767 |
0.6962 |
1.0000 |
0.7004 |
0.6872 |
0.6804 |
0.6779 |
0.6779 |
0.6779 |
0.6754 |
|
6 |
0.5776 |
0.6085 |
0.6423 |
0.6790 |
0.7004 |
1.0000 |
0.7179 |
0.7164 |
0.7157 |
0.7157 |
0.7157 |
0.7148 |
|
7 |
0.5187 |
0.5575 |
0.6017 |
0.6533 |
0.6872 |
0.7179 |
1.0000 |
0.7378 |
0.7386 |
0.7386 |
0.7386 |
0.7392 |
|
8 |
0.4968 |
0.5382 |
0.5857 |
0.6423 |
0.6804 |
0.7164 |
0.7378 |
1.0000 |
0.7440 |
0.7440 |
0.7440 |
0.7451 |
|
9 |
0.4895 |
0.5317 |
0.5804 |
0.6385 |
0.6779 |
0.7157 |
0.7386 |
0.7440 |
1.0000 |
0.7455 |
0.7455 |
0.7468 |
|
10 |
0.4895 |
0.5317 |
0.5804 |
0.6385 |
0.6779 |
0.7157 |
0.7386 |
0.7440 |
0.7455 |
1.0000 |
0.7455 |
0.7468 |
|
11 |
0.4895 |
0.5317 |
0.5804 |
0.6385 |
0.6779 |
0.7157 |
0.7386 |
0.7440 |
0.7455 |
0.7455 |
1.0000 |
0.7468 |
|
12 |
0.4823 |
0.5253 |
0.5750 |
0.6347 |
0.6754 |
0.7148 |
0.7392 |
0.7451 |
0.7468 |
0.7468 |
0.7468 |
1.0000 |
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Covariance Parameter Estimates |
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Cov Parm |
Subject |
Estimate |
Standard Error |
Z Value |
Pr Z |
|
UN(1,1) |
id |
0.01330 |
0.002132 |
6.24 |
<.0001 |
|
UN(2,1) |
id |
-0.01855 |
0.004666 |
-3.98 |
<.0001 |
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UN(2,2) |
id |
0.06849 |
0.01267 |
5.40 |
<.0001 |
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Residual |
|
0.003533 |
0.000131 |
27.03 |
<.0001 |
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Fit Statistics |
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-2 Res Log Likelihood |
-4589.5 |
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AIC (smaller is better) |
-4581.5 |
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AICC (smaller is better) |
-4581.5 |
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BIC (smaller is better) |
-4566.7 |
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Solution for Fixed Effects |
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Effect |
Estimate |
Standard Error |
DF |
t Value |
Pr > |t| |
|
Intercept |
-0.2846 |
0.03901 |
297 |
-7.30 |
<.0001 |
|
age |
0.02327 |
0.001247 |
1440 |
18.65 |
<.0001 |
|
loght |
2.2523 |
0.04613 |
251 |
48.82 |
<.0001 |
|
baseage |
-0.01630 |
0.007439 |
1440 |
-2.19 |
0.0286 |
|
logbht |
0.1808 |
0.1455 |
1440 |
1.24 |
0.2142 |
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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 |
1440 |
348.01 |
348.01 |
<.0001 |
<.0001 |
|
loght |
1 |
251 |
2383.77 |
2383.77 |
<.0001 |
<.0001 |
|
baseage |
1 |
1440 |
4.80 |
4.80 |
0.0285 |
0.0286 |
|
logbht |
1 |
1440 |
1.54 |
1.54 |
0.2140 |
0.2142 |