A new test procedure in the CFA

Configural Frequency Analysis, or CFA, sets out among other things to find configurations of symptoms that stand out as types or as anti-types. Working from the logic of an efficient regression algorithm devised by Cierzynski and von Weber, the authors of this paper built a gradient method for that search.

The procedure runs iteratively. At each step it lowers the total chi-square of a contingency table by shaving a small amount off the frequency of the cell that looks most suspect. When the cell points to an anti-type rather than a type, the frequency is nudged upward instead. Repeated across many steps, this drives the table toward a state that satisfies the hypothesis of independence exactly.

From that final table one can read off expectation values, the quantities known in the literature as Victor-expectation values. Pairing those values with the original cell frequencies lets the authors apply the trustworthy small-group test of Dunkl and von Eye, after which the Holm procedure supplies confirmation.

A Bayesian step pushes the results further. Its starting assumption is that types tend to stay hidden inside cells with high frequencies, and accounting for that tendency sharpens what the method recovers.

Numerical simulations back up the approach and indicate that it behaves correctly. Set against the "new approach" of Kieser and Victor, the findings agree to a large degree.