This article discusses how several hypotheses about change in discrete vari
ables can be rested on data obtained in a longitudinal study. A first class
of hypotheses pertain to the invariance of certain characteristics of marg
inal distributions. A second class of hypotheses derive from assumptions ab
out the causal relations between the variables. In this article, the author
s show how all these hypotheses can be tested by means of a generalization
of log-linear modeling developed by Lang and Agresti. By means of the same
approach, it is also possible to test conjunctions of several hypotheses fr
om both classes.