Structural Equation Modeling vs. Configural Frequency Analysis: An Empirical Comparison

Structural Equation Modeling, usually shortened to SEM, covers a family of statistical techniques built mainly for data that is measured on a metric scale and follows a normal distribution. Over the past several years researchers have stretched the method to handle categorical data as well, though doing so forces you to rely on special parameter estimates and particular kinds of data matrices.

What almost nobody has published, at least up to this point, is a SEM model that works entirely with dichotomous variables. That gap is the starting point for the work described here. We set out to see whether an empirical model, one originally built from ordinal data, could still be confirmed through SEM after every variable had been collapsed into a simple two-category form.

To make a dichotomous version of SEM workable, the analysis leaned on tetrachoric correlations together with asymptotic covariances. The example came from anaesthesia: a sample of 820 patients. The path model built from these data included three exogenous variables and four endogenous ones.

That same path model was then run through a second, quite different procedure, Prediction Configural Frequency Analysis, or P-CFA. Putting the two sets of results side by side turned out to be the interesting part. The findings from SEM and from P-CFA agreed with one another, yet neither method simply duplicated the other. Each one surfaced information the other missed, which means pairing them widens what you can actually say about the data.

Both approaches carry their own strengths and limitations, and those tradeoffs are weighed against each other in the discussion.