Differentiating classes from dimensions under unfavorable data conditions: Monte Carlo comparisons of taxometric and latent variable mixture models
Taxometric and latent variable mixture models can aid in (1) determining whether the source of population heterogeneity, a latent variable, [straight theta], is best explain by a dimensional (one-class) or taxonic (two-class) model and (2) distinguishing between constructs continuously distributed and those that are Bernoulli distributed at the latent level. Although these models have gained widespread use in psychology research, few have been systematically evaluated to determine the robustness of their results when statistical assumptions are violated (e.g., severe skew, unequal mixing proportions, etc.). The current study examined the performance of Meehl's taxometric procedures and two latent variable mixture models: a latent profile model and a one-factor one-class factor mixture model, when assumptions of normality, homogenous variances, equal group compositions, conditional independence, and adequate class separations are violated. The shape of taxometric graphs were systematically affected by reduced class separations, taxon base rate, nuisance covariance, and skew. Whereas nuisance covariance and poor class separations increased the likelihood of misjudging taxonic samples as dimensional, skewed configurations frequently increased the likelihood of misjudging dimensional samples as taxonic. In most configurations, the factor mixture model outperformed the latent profile model, frequently producing type I error rates less than .05 with the Bayesian Information Criteria (BIC) and the Bootstrapped Likelihood Ratio Test (BLRT). Of the latent variable mixture models, the BIC and BLRT proved to be the most reliable indicators of the correct number of classes but their performance was strongly affected by skew. When multiple statistical assumptions are severely violated, all of the statistical models produced type I error rates that consistently exceeded the .05 alpha level. Application of the multiple hurdles consistency approach to Comparative Curve Fit Indices (CCFIs) with dual thresholds improved the accuracy of taxometric methods when multiple statistical assumptions are violated. Across configurations, taxometric methods produced better accuracies at distinguishing between taxonic and dimensional data, when CCFIs are compared to indices generated in the latent variable mixture models.