

You can fit a wide variety of randomintercept and randomslope models.
Let us show you an example with an ordered categorical outcome, random intercepts, and threelevel data.
Using a fourlevel Likert scale, we ran an experiment measuring students' attitudes toward statistics after taking an introductory statistics class. In some of the classes, Stata was used. Other packages were used in the remaining classes. The question is, does exposure to Stata result in a more positive attitude toward statistics?
In the model we fit, we control for use of Stata, each student's average score in previous math courses, and whether either of the student's parents is in a sciencerelated profession.
We will imagine that the fictional data were collected from various courses at various undergraduate schools. School may have an effect, as might class within school.
The results are
No. of Observations per Group  
Group Variable  Groups Minimum Average Maximum  
school  28 18 57.1 137  
class  135 1 11.9 28  
attitude  Coef. Std. Err. z P>z [95% Conf. Interval]  
mathscore  .4085273 .039616 10.31 0.000 .3308814 .4861731  
1.stata  .8844369 .2099124 4.21 0.000 .4730161 1.295858  
1.science  .236448 .2049065 1.15 0.249 .1651614 .6380575  
stata#science  
1 1  .3717699 .2958887 1.26 0.209 .951701 .2081612  
/cut1  .0959459 .1688988 0.57 0.570 .4269815 .2350896  
/cut2  1.177478 .1704946 6.91 0.000 .8433151 1.511642  
/cut3  2.383672 .1786736 13.34 0.000 2.033478 2.733865  
school  
var(_cons)  .0448735 .0425387 .0069997 .2876749  
school>class  
var(_cons)  .1482157 .0637521 .063792 .3443674  
(stata##science is how we introduce a full factorial interaction of stata and school in Stata; see Factor variables and value labels.)
We discover that exposure to Stata does indeed improve students' attitudes toward statistics.
The effect of school is minimal (the variance is small).
Class has a larger effect as revealed by its larger variance, so teachers matter.
Above we showed you an example with random intercepts. We could just as easily have shown you an example with random slopes.
See the allnew 358page Multilevel MixedEffects Reference Manual.
The manual demonstrates many of the possible models, links, and families, including:
Introduction to multilevel mixedeffects models
Multilevel mixedeffects generalized linear model
Multilevel mixedeffects logistic regression
Multilevel mixedeffects probit regression
Multilevel mixedeffects complementary loglog regression
Multilevel mixedeffects ordered logistic regression
Multilevel mixedeffects ordered probit regression
Multilevel mixedeffects Poisson regression
Multilevel mixedeffects negative binomial regression
In multilevel data, observations—subjects, for want of a better term—can be divided into groups that have something in common:
See New in Stata 13 for more about what was added in Stata 13.