A Review of Multivariate Taxometric Procedures: Distinguishing Types from Continua
Roderick P. McDonald · Journal of Educational and Behavioral Statistics · 2003
It is an easy but unfair tactic for a reviewer to complain that the title of a text is misleading. The stated objectives of Waller and Meehl's brief monograph are (a) to describe Meehl's MAXCOV device for detecting taxonicity-that is to say, for detecting a latent profile model with just two latent classes, (b) to describe two further procedures for this purpose-MAXEIG and L-mode, and (c) to discuss some of the philosophical misconceptions pertaining to taxonic notions-notions concerning types versus traits. Paul Meehl's inventive spirit informed much of the social science philosophy I learned from my undergraduate days. I consider it my own fault that I had not previously come into contact with his contributions to this class of psychometric problem. The basic insight behind the MAXCOV device has the admirable quality of all truly inventive devices. It is perfectly obvious as soon as it is stated, but it is not a solution that springs to mind easily in response to the stated problem. Essentially, Meehl's conception is this: If each of a set of individuals belongs to one of just two latent classes, and within each, p quantitative indicator variables are uncorrelated (at least to a good approximation), membership is probabilistically indicated by any one of the p variables. Accordingly, when conditioned on one (input) indicator, a number of statistics of other (output) indicators will vary as a function of the conditioning variable. We could call this wide-sense heteroskedasticity. If, in particular, we compute the covariance of two output variables within successive fractiles defined by an input variable, a plot of the sequence will show covariances lowest at the extremes, where the input indicator selects nearly pure types, and a maximum at the cut-point where members of the two classes are selected about equally into the fractile. Given more than three indicators, we may condition on each in turn and average results to get a best cut-point. It does not trouble this reviewer that the resulting MAXCOV device requires judgment, and does not supply standard errors or tests of significance. Chapter 3 treats this device, but for a more general account the reader must pursue the references. Chapter 4 describes MAXEIG, an extension of the principle to conditioning the largest eigenvalue of the covariance matrix of remaining indicators on overlapping fractiles of one quantitative indicator. An adjustment intended to eliminate the