Log-Linear Modeling, Latent Class Analysis, or Correspondence Analysis Which Method Should Be Used for the Analysis of Categorical Data?

TLDR: The analysis of such data should clearly depend on the substantive questions posed by the researcher involved, although in many cases these questions will be rather vague as mentioned in this paper, and it will often be left to the statistician to clarify what is meant by such concepts and whether they are present in the investigator's data.

Abstract: Data collected by social and behavioral scientists very often consist of large multidimensional tables of subjects cross-classified according to the values or states of several categorical variables. For example, Table 1 shows a set of data on suicide victims in which the method of committing suicide is cross-classified by sex and age group (Van der Heijden & de Leeuw, 1985) and Table 2 shows counts of subjects resulting from a survey of the political attitudes of a sample from the British electorate (Butler & Stokes, 1974). The analysis of such data should clearly depend on the substantive questions posed by the researcher involved, although in many cases these questions will be rather vague. The research worker may be interested in such notions as “pattern” and “structure” but it will often be left to the statistician to clarify what is meant by such concepts and whether they are present in the investigator’s data. Finally, the statistician has the often difficult task of explaining the results.