Configural Frequency Analysis, Multiple Correspondence Analysis and Latent Class Analysis: An Empirical Comparison

Researchers working with categorical data have long relied on three established approaches: Configural Frequency Analysis (CFA), Multiple Correspondence Analysis (MCA) and Latent Class Analysis (LCA). Each answers a somewhat different question, and this study puts them side by side to see what they contribute when used together rather than in isolation.

The division of labor here is deliberate. CFA does the exploratory and confirmatory work of locating types, meaning the particular combinations of response categories that occur more often than chance would predict. Once those types are on the table, MCA and LCA take over the job of describing and explaining them in finer detail.

For the empirical demonstration, Lautsch and Plichta draw on the 14th Shell Youth Study from 2002, narrowing their attention to how young adults regard social organizations and political institutions. That dataset gives the methods something concrete to work on: patterns of confidence (or its absence) across a set of attitude items.

CFA isolates three types in these data. MCA and LCA then represent and interpret the relational structure of those three, and they do so at two measurement levels that complement each other. On the manifest level the types read as positions along an ordinal confidence scale. Looked at through the latent lens, each of the three occupies a distinct place within a latent space, which gives a second line of evidence for treating them as genuinely different configurations rather than artifacts of the coding.

All three analyses were carried out in the same program, LEM (Vermunt, 1997), which let the authors run CFA, MCA and LCA on one footing and compare their outputs directly. The broader point of the exercise is less about any single result from the Shell data and more about showing that these techniques can be chained: exploration and confirmation of types from one method, richer interpretation on manifest and latent levels from the others.