The following chapters introduce methods of longitudinal CFA. Simple longitudinal designs involve two observation points for one variable. In complex designs several variables are observed for several samples over many points in time. CFA enables one to analyze contingency tables displaying patterns of constancy and change in a unique way. Rather than identifying models of interrelationships among variables across time, CFA identifies cases with patterns that remain stable or show specific changes in behavior. CFA shows which patterns occur more often than expected by chance and what other patterns are very unlikely.

Longitudinal CFA deals with several types of change. For instance, systematic shifts in means may be described as trends, and systematic changes in variability may be described as examples of the “Law of Initial Values” (cf. Wall 1977). The following sections pay special attention to specifying the particular type of change under study, and to the model under which the expected frequencies are estimated.

Most of the models discussed in the above chapters assume independent samples. In longitudinal CFA, samples are no longer independent. Therefore, repeated observations cannot be analyzed with, for instance, k-sample CFA. This approach assumes the k samples to be independent. Treating repeated observations as independent would lead to an artificial increase of the sample size and, therefore, to grossly nonconservative statistical decisions. Thus, the following chapters present methods for the investigation of longitudinal data that avoid these problems.