An Analysis of Meehl's MAXCOV-HITMAX Procedure for the Case of Dichotomous Indicators

MAXCOV-HITMAX was invented by Paul Meehl for the detection of latent taxonic structures (i.e., structures in which the latent variable, _, is not continuously, but rather Bernoulli, distributed). It involves the examination of the shape of a certain conditional covariance function, and is based on Meehl's claims that: (R1) Given a latent taxonic structure, this conditional covariance function is single peaked; and that (R2), continuous latent structures produce a flat, rather than single-peaked, curve. While Meehl has recommended that continuous indicators be used as input into MAXCOV-HITMAX, the use of dichotomous indicators has become popular. The current work investigates whether (R1) and (R2) are true for the case of dichotomous indicators. The conclusions will be that, for dichotomous indicators: (a) (R1) is not true; (b) (R1) is made true given that there are a large number of indicators; and (c) (R2) is not true, certain unexceptional Rasch structures, for example, producing single-peaked curves. Implications are briefly discussed of these results for the case of MAXCOV-HITMAX with continuous indicators.