To fit a model of graduation with fixed coefficient on x1 and random coefficient on x2 at the school level and with random intercepts at both the school and class-within-school level, you type
. xtmelogit graduate x1 x2 || school: x2 || class:
The results show that the average coefficient across schools on x2 is 1.31 with standard deviation .83. There is also a significant overall effect due to school and a somewhat significant effect due to class. The LR test shows that the three random effects, taken together, provide a substantially better fit than standard (marginal) logistic regression.
Estimation is by ML, and standard errors and confidence intervals (in fact, the full covariance matrix) are estimated for all variance components.
xtmelogit and xtmepoisson provide four random-effects variance structures—identity, independent, exchangeable, and unstructured—and you can combine them to form even more complex block-diagonal structures.
predict after xtmelogit and xtmepoisson will calculate predicted random effects.