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

MAXCOV-HITMAX was invented by Paul Meehl as a tool for the detection of latent taxonic structures (i.e., structures in which the latent variable, u, 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) Taxonic structures produce single-peaked conditional covariance functions and that (R2) continuous latent structures produce flat, rather than single-peaked, curves. For neither (R1), nor (R2), have formal proofs been provided, Meehl and colleagues instead having provided an argument ("Meehl's Hypothesis") as to why they should be true, and a number of Monte Carlo studies. In an earlier article, Maraun, Slaney, and Goddyn (2003) proved that, for the case of dichotomous indicators, Meehl's Hypothesis is false and, by counterexample, that (R2) is false. In the current article (a) it is proved that, for the case of continuous indicators, Meehl's Hypothesis is false and (b) results are developed analytically on the behaviour of the conditional covariance functions produced by taxonic structures.