Base Models for Configural Frequency Analysis

This article sorts the base models used in Configural Frequency Analysis (CFA) into categories and explains what distinguishes each one. Four groupings emerge from that work.

The first draws on log-linear models. Here the expected frequency for each cell is estimated from what the observed cell frequencies already tell us, so the model builds its predictions out of the data at hand.

A second group starts instead from a priori probabilities. Those probabilities might come from outside the sample entirely, for example as population parameters that are known or assumed before any counting begins.

The third group also works from a priori probabilities, but ties them to substantive theory. The probabilities are chosen so they match a model that carries real content about the phenomenon being studied, rather than being left as generic assumptions.

The fourth group is aimed at the shape of the multivariate distribution in a cross-classification. Base models of this kind encode hypotheses about that distribution, and CFA is then used to ask whether the data depart from the assumed distribution and, if so, in which cells those departures show up.

To keep the discussion concrete, von Eye works through data drawn from three different areas: politics, birth statistics, and aggressive behavior among adolescents.

The closing section turns to how log-linear modeling and CFA relate to one another. A common assumption is that CFA amounts to little more than residual analysis within a log-linear model. That reading sells the method short. The groundwork beneath CFA reaches considerably further than that equivalence would suggest.