MAXCOV-HITMAX

All current taxometric procedures are based on a single statistical method termed Coherent Cut Kinetics (CCK). We decipher the meaning of this term in the next section in the example of the MAXCOV-HITMAX (MAXCOV stands for MAXimal COVariance the reason for this name will become clear in the next section) technique. However, we emphasize that it is not the shared statistical method that defines taxometrics. Adherence to a particular set of epistemological principles distinguishes taxometrics from other approaches. In other words, any analytic procedure that can identify taxa may... 

Let us begin by describing the logic and technique behind the most prominent taxometric analytic procedure, MAXCOV-HITMAX (Meehl Yonce, 1996), to which we refer as MAXCOV. MAXCOV is by far the oldest taxometric procedure. For example, the mathematical basis for MAXCOV was established in 1965 (Meehl), and the original version of the technique was described in 1973 (Meehl). Learning the principles employed by this classic method can facilitate understanding of the newer procedures, which are described later in the chapter. 

Meehl, P. E. (1973). MAXCOV-HITMAX A taxonomic search method for loose genetic syndromes. In P. E. Meehl (Ed.), Psychodiagnosis Selected papers (pp. 200-224). Minneapolis University of Minnesota Press. 

Meehl, P. E. (1995b). Extension of the MAXCOV-HITMAX taxometric procedure to situations of sizeable nuisance covariance. In D. Lubinski R. V. Dawis (Eds.), Assessing individual differences in human behavior new concepts, methods, and findings (pp. 81-92). Palo Alto, CA Davies-Black. 

Miller, M. B. (1996). Limitations of Meehl s MAXCOV-HITMAX procedure. American Psychologist, 51,554-556. 

A MAXCOV analysis can yield additional, potentially useful information. MAXCOV can assign individuals to categories, which in the case of psychopathology would equal assignment of diagnosis. Suppose MAXCOV located hitmaxes on all indicators and produced a coherent result that passed... 

To finish the discussion of MAXCOV, we want to note that the assumption of zero nuisance correlation is not the only assumption of MAXCOV. Our interpretation of a hitmax as an interval with the 50/50 mix of taxon and nontaxon members is based on the presumption that two unimodal distributions underlie the data. There are two components in this assumption. The first component is presuming that latent distributions are unimodal. In other words, any kind of distribution will work as long as it has only one maximum, which encompasses the majority of distributions one finds in statistics textbooks (e.g., normal, chi-square, gamma and many others). This is an extremely lenient assumption, but it does pose some constraint on the flexibility of the procedure. However, we do not consider this restriction particularly important, especially in the context of our state of knowledge regarding psychopathology. 

Unfortunately, no consistency tests were reported in this study. Furthermore, instead of reporting the 28 individual base rate estimates, the authors reported an overall base rate estimate for each item, averaging over analyses in which the item was an output variable. This can be somewhat confusing because MAXCOV base rate estimates are associated with the input variable, not the output variable. The reason for this is MAXCOV base rate estimation is tied with locating the hitmax on the input indicator so that each base rate estimate is attached to a certain input indicator. This,... 

Next, the MAXCOV analyses were repeated with smoothed plots (using Tukey s 3RH twice procedure Tukey, 1977). The general shape of the taxonic plots did not change, but the peaks shifted and the base rate estimates lost their cohesion (SD =. 10). It is notable that smoothing had this effect. This would suggest that smoothing can aid in the interpretation of the curves, but the precise estimation of the taxon base rate and location of hitmaxes may be sacrificed. 

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