Conjugate and Other Distributional Methods in Configural Frequency Analysis

Abstract

AbstractConfigural Frequency Analysis (CFA) is being increasingly used by psychologists and other researchers to test for the presence of combinations of categorical variables which occur more frequently or less frequently than expected under a particular model of chance. Configurations which occur more frequently than chance are known as “Types”‐Configurations which are conspicuous by their absence or rarity are known as “Antitypes”. Most configural frequency test theory consists of binomial tests applied to the cells of a cross‐tabulation table. The wide variety of statistical tests described in papers and books on CFA are approximations to the binomial test, due to the computational intensity associated with performing binomial tests directly (VON EYE, 1990b). This paper advocates direct computation of binomial probabilities instead of the usual approximations used in CFA. Mathematical relationships of the binomial distribution with the F and incomplete beta distributions are described which enable the researcher to efficiently compute binomial probabilities using functions available in common statistical software. The classical inference approach adopted by traditional CFA makes it difficult to make conclusions regarding the likely prevalence rates of types or antitypes in the reference population. It is also not possible to exploit additional information about the sample which, while not known precisely, is known with a degree of confidence and can aid in the identification of types and antitypes. A Bayesian conjugate distributions approach based on the incomplete beta distribution is proposed. Bayesian extensions of this model to both classical CFA and a sequential CFA analysis advanced by KIESER and VICTOR (1991) are described.