This article discusses how several hypotheses about change in discrete variables can be tested on data obtained in a longitudinal study. A first class of hypotheses pertain to the invariance of certain characteristics of marginal distributions. A second class of hypotheses derive from assumptions about the causal relations between the variables. In this article, the authors 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 from both classes.
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