Interpretation of covariance estimates glmm (proc glimmix)

Question

I am using the glimmix procedure in SAS to model a generalize linear mixed model with and binomial distribution and a logit link function. I am modeling both the G-side and the R-side covariance structure due to the nature of my data (repeated measures for 43 participants).

Specifically I use a random intercept model for subjects and G-side covariance matrix following a variance component structure. To account for the repeated measures the model also included random residuals for subjects with the R-side covariance matrix modeled as first order auto regressive.

My question now is; how do I interpret the covariance parameter estimates (an example is provided below))?

Covariance Parameter Estimates          
Cov Parm    Subject     Estimate    Standard Error
Intercept   Subject     1.233       0.2133
AR(1)       Subject     0.1113      0.004561
Residual                0.9964      0.00651

Answer 1

The estimates are just estimates of the parameters specified in the random statements.

• The estimate of 1.233 for intercept is an estimate of the parameter $\tau$ in the G-side matrix. Essentially the variance (between subjects) of the model intercept.
• The estimate of 0.9964 for residuals is an estimate of the parameter $\sigma^2$ in the R-side matrix
• The estimate of 0.1113 for AR(1) is an estimate of the parameter $\rho$ in the R-side matrix.

($\tau$, $\sigma$ and $\rho$ are used based on notation from e.g. Multilevel Analysis by Snijders & Bosker (2012))

I hope this will help others as well.