Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Covariance Parameter Estimates

Cov Parm Subject Estimate

Standard

Error

UN(1, 1) IDNO 8.4913 1.3877

UN(2, 1) IDNO 2.5732 2.7473

UN(2, 2) IDNO 10.5707 4.6568

Residual (VC) 0.1578 0.006670

Solutions for Fixed Effects

Effect Estimate

Standard

Error DF tValue Pr>jtj

Intercept 4.4899 1.7238 133 2.60 0.0102

BIRTHWGT 0.00046 0.000487 1038 0.94 0.3453

GENDER 0.3695 0.6908 1038 0.53 0.5928

DIARRHEA 0.6999 0.9438 28 0.74 0.4645

Estimates

Label Estimate

Standard

Error DF tValue Pr>jtj

Exponentiated

Estimate

log odds ratio
(DIARRHEA 1 vs 0)

0.6999 0.9438 28 0.74 0.4645 2.0135

TherearethreeG-sideCovarianceparametersestimated:thevarianceoftheran-
dom intercept, the variance of the random slope for DIARRHEA, and the covariance
of the random intercept and random slope. These estimates are in the table under
the heading “Covariance Parameter Estimates” and labeled by UN(1, 1), UN(2, 1),
and UN(2, 2) (the row and column of the unstructured G matrix). The estimated
correlation between the random intercept and slope is given at0.4256 (under
the heading called “Estimated G Correlation Matrix”). There is also one R-side
variance parameter estimated (obtained when using the RANDOMRESIDUAL
statement).

The odds ratio estimate for DIARRHEA¼1 vs. DIARRHEA¼0, requested with the
ESTIMATE statement, is given as 2.0135 (last row at the end of the output). The
interpretation of this odds ratio is tricky because there is a random slope component.
The odds ratio for DIARRHEA for theith subject isexp((b 3 þb 3 i), whereb 3 ifollows a
normal distribution of mean 0 and variances^20. The interpretation ofb 3 is the average
log odds ratio among all subjects.

Finally, we examine some complicated variations of the previous model. We show the
code but omit the output as with this data there were issues of model stability and
numerical convergence.

The previous model contained a random intercept and random slope as random
effects. The following code runs the same model but adds an autoregressive AR(1)
covariance structure for the residuals grouped by gender:

SAS 633