Does nature have joints worth carving? A discussion of taxometrics, model-based clustering and latent variable mixture modeling

Abstract

Taxometric procedures, model-based clustering and latent variable mixture modeling (LVMM) are statistical methods that use the inter-relationships of observed symptoms or questionnaire items to investigate empirically whether the underlying psychiatric or psychological construct is dimensional or categorical. In this review we show why the results of such an investigation depend on the characteristics of the observed symptoms (e.g. symptom prevalence in the sample) and of the sample (e.g. clinical, population sample). Furthermore, the three methods differ with respect to their assumptions and therefore require different types of a priori knowledge about the observed symptoms and their inter-relationships. We argue that the choice of method should optimally match and make use of the existing knowledge about the data that are analyzed.

Keywords: taxometrics.

Fig. 1

(a) Path diagram showing p observed variables, Y₁−Y_p, and an underlying latent variable (LV), which represents the construct. The LV can be either categorical (latent class variable) or continuous (latent factor or trait). (b) Path diagram for a hybrid model with a continuous factor (F) within each latent class of the latent class variable C.

Fig. 2

(a) The three thin lines show the probability of endorsing three severe symptoms of an underlying continuous construct (thick curve). Only individuals with very high scores on the construct have a non-zero probability of endorsing the items, and a large proportion of the population will score zero on all items. (b) The thick lines show two latent classes, a taxon and a complement. The thin lines reflect again the probability of endorsing symptoms, which are here spread over the range of the construct.

Fig. 3

(a) A smaller sample from a truly categorical construct consisting of a complement (black) and a taxon (red) might not suffice to detect taxonicity. There are too few red dots belonging to the taxon to clearly show a separate cluster. (b) In a larger sample, the power is more likely to be sufficient to detect the taxon.

Fig. 4

(a) A skewed observed distribution (thick line) resulting from a population mixture distribution (dashed lines) consisting of three classes with equal variance. (b) The same skewed observed distribution can be due to a mixture with two components that have unequal variance.