Fixed effect and covariance parameter estimates (generalized linear mixed models)

Figure 1. Covariance parameters for model with after_t as a random effect, Block 1

Still in the viewer for the model with after_t as a random effect, click the Covariance Parameters view thumbnail.
From the Effect dropdown, select Block 1.
The order of parameters along the diagonal of the covariance matrix corresponds to the order of effects on the Random Effect Block dialog.
- UN(1,1) is the variance estimate for the random effect intercept term.
- UN(2,1) is the covariance between the intercept and after_t.
- UN(2,2) is the variance estimate for the after_t.
You can test the statistical significance of parameters in the covariance matrix with a simple Wald test; for example, for UN(2,2) compute a z statistic equal to the ratio of the estimate and its standard error, 0.187 / 0.022 = 8.5. A z statistic with a value of 8.5 has a p-value near 0, which suggests that including after_t as a random effect is necessary to account for heterogeneity among patients between the baseline and after treatment periods

Figure 2. Fixed coefficients for model with intercept-only random effect, table style
Now let's compare the fixed coefficients. Activate (double-click) the model object for the model with an intercept-only random effect.
Click the Fixed Coefficients view thumbnail.
From the Style dropdown of the Coefficients view, select Table.
In the parameter estimates table, click the Coefficient cell. This displays the standard error, t statistic, and confidence interval.
The coefficient for after_t is statistically significant and its estimate of −0.086 implies that the expected seizure rate for a typical patient would be reduced by 1−exp(−0.086) = 8.2% after starting the trial on placebo. It's possible that there is a placebo effect, but we don't expect it to be that large.

Figure 3. Fixed coefficients for model with after_t as a random effect, table style
For comparison, back in the viewer for the model with after_t as a random effect, click the Fixed Coefficients view thumbnail.
From the Style dropdown of the Coefficients view, select Table.
In the parameter estimates table, click the Coefficient cell. This displays the standard error, t statistic, and confidence interval.

On the other hand, the after_t effect is not significant in the model with after_t as a random effect, which makes more intuitive sense. For this model, the expected seizure rate for a typical patient would reduce by 1−exp(−0.012−0.191) = 18.4% after taking the anticonvulsant, so the drug seems to have a modest effect.