# Solved – Interpretation of covariance estimates glmm (proc glimmix)

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 ``
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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.

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