Logistic Regression and Prediction Configural Frequency Analysis: A Comparison

This paper sets two analytic approaches side by side: logistic regression (LR) and Prediction Configural Frequency Analysis (PCFA). Both are tools for studying how predictors relate to an outcome, but they rest on different assumptions and answer different questions. Our aim is to lay out where they overlap, where they part ways, and what a researcher gains or loses by picking one over the other.

We begin with the statistical machinery behind each method. LR models the probability of an outcome as a function of predictor variables, estimating coefficients that describe the relationship between each predictor and the log odds of the result. PCFA, by contrast, works at the level of configurations: specific combinations of predictor and outcome categories, asking whether particular patterns of predictor values occur together with particular outcomes more or less often than chance would suggest.

From there we turn to the design matrices that each procedure relies on. Spelling out these matrices makes the structural contrast concrete, because the way predictors are coded and entered differs between the two models. The design matrix for LR encodes main effects and any interaction terms the analyst specifies, while the base model of PCFA is built to detect types and antitypes, configurations that stand out against an expected frequency.

Two data sets illustrate the methods in practice. The first is artificial, constructed so the properties of each analysis can be seen plainly. The second comes from a study of domestic violence, which gives the comparison a grounding in real research questions rather than a purely numerical exercise. Running both methods on the same data shows where they agree in their verdicts and where they diverge.

The deeper difference is one of orientation. LR is variable-oriented: it asks how variables, taken as dimensions, predict an outcome across the sample. PCFA is person-oriented: it asks which combinations of characteristics describe actual groups of individuals and how those groups relate to the outcome. A researcher interested in average effects of predictors will gravitate toward LR; one interested in characteristic patterns among subgroups of people will find PCFA more natural.

We close with a practical suggestion for anyone who wants to use both approaches together and read their results in parallel. In its standard form, LR does not map cleanly onto the base model of PCFA. To let the two methods inform each other, the standard LR model has to be extended so that its structure matches the PCFA base model. Done that way, results from the two can be compared term for term, and each enriches the reading of the other.