Nuisance correlations

Another important advantage of sample truncation is that it can reduce nuisance correlations. The concept of nuisance correlation is explained later in this section, but we can also discuss this concept here in terms of taxonic and continuous variance. Consider that scores on real world indicators probably reflect both taxonic and continuous variance, and the presence of the latter can skew the results. Sample truncation essentially removes a big chunk of continuous variance, which can improve the accuracy of the results. It is, of course, important to ensure that taxonic variance stays intact. Almost any screener would screen out some taxon members, but our experiences with sample truncation suggest that it is usually possible to find a cutoff that removes a substantial number of nontaxon members without losing many taxon members. 

The reason nuisance correlations cause problems for MAXCOV is that the procedure relies on a reduced, rather than the full, version of GCMT. In... 

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. 

D, will be inflated—as sizable nuisance correlations tend to lift the left end... 

Waller s MAMBAC does not perform group assignments. The reason is that MAMBAC does not actually locate the position of a hitmax, thus there is no straightforward way of calculating taxon membership probabilities. Due to these limitations, Waller s MAMBAC is not able to estimate indicator validities and nuisance correlations. 

Unfortunately, MAMBAC tends to be less robust than MAXCOV under unfavorable circumstances, such as low taxon base rates, poor indicator validities, and high nuisance correlations. Specifically, taxonic plots often look flat and sometimes concave when the validity of indicators is less than 1.5 SD or when nuisance correlations are higher than. 35 (Meehl Yonce, 1994). A low taxon base rate can obscure the plots even more. For this reason, MAMBAC findings should be interpreted with special care and should be accompanied by MAXCOV analyses whenever possible. MAXCOV can assess the extent to which ideal conditions have been violated and can provide the investigator with information needed for making sound judgments about the trustworthiness of MAMBAC results. 

To understand this formula better, suppose that the average nuisance correlation is. 33. Then MAXSLOPE will fail if the validity of the input indicator is three (or more) times greater than the validity of the output indicator. This limitation applies to both easy and difficult distributions. 

Several other useful values can be obtained with a complementary procedure, similar to MAXSLOPE except it calculates variances instead of regression slopes (see Grove Meehl, 1993). An investigator can use these values to calculate parameters of latent distributions (e.g., mean and standard deviation of the taxon). These estimates are not biased by nuisance correlations, unlike MAXCOV estimates. Unfortunately, these calculations are fairly arduous, so we will not describe them here (for more details see Grove Meehl, 1993). 

Exclude or combine indicators that have high nuisance correlations. 

Check that errors of parameter estimation are within tolerance limits. Golden proposed an index that can be used to evaluate these errors. This index specifically focuses on errors that arise from the degrading effects of nuisance correlation and ignores sampling errors, as they cannot be minimized. 

In many respects, the Waller et al. study is an exemplary taxometric report. The authors used multiple taxometric techniques and examined the construct validity of the taxon. However, three issues were not clarified in the report. First, only base rate estimates were reported and there was no discussion about shapes of the plots, so it is unclear how many of them were taxonic. Also, only one type of consistency test—cross-method consistency— was reported in the study although the different procedures were consistent with each other, it is difficult to determine the strength of each individual piece of evidence. Second, mini-scales were used for MAXSLOPE but not for the other analyses. The authors indicated that they created mini-scales because individual items are not very reliable. However, it is unclear why this would not also have been beneficial to the MAMBAC and MAXCOV analyses. Third, nuisance correlations and indicator validities were not computed. It is thus unclear how well the data conforms to CCK requirements, and how much we can trust the estimates. Moreover, this information could have been useful in assembling the DES-T. 

Harris et al. also tested the taxonic conjecture by examining one of the logical consequences of taxonicity, a prediction that taxon membership should emerge as the first unrotated component in principal component analysis (Meehl, 1992). The idea behind this corollary is that in the absence of nuisance correlations, all observed correlations between indicators are due to latent taxon membership. Furthermore, the purpose of a principal component analysis is to reduce the observed correlations to a smaller set of factors... 

Harris et al. also employed a less-known CCK procedure, which Meehl and Yonce (1996) named SQUABAC, but the authors referred to as the Parabolic Function Method. Two SQUABAC analyses were performed, one with the PCL-R total score as the input variable and criminal recidivism as the output variable, and another with adult criminal history and recidivism as input and output variables, respectively. Recidivism history was paired with the two potential taxon indicators because it is a conceptually related but distinct variable. It is expected to be a valid indicator of the taxon, but it is not redundant with other indicators, thus nuisance correlations should not be a problem. 

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