Fitting LVMMs requires the specification of all relationships between the observed variables within a class, for instance that the covariation of items within a class is due to an underlying factor. Furthermore, the user has to specify whether the related parameters are class specific or class invariant. This leads to an extremely large number of possible models. Although multiple different models can be fitted to the data, the user has to limit the number of models a priori to a reasonably small number of models to minimize multiple testing. This selection requires additional a priori knowledge about the data. If such knowledge is available and integrated in a fitted model, the power to detect the correct cluster structure is improved (Lubke & Neale, 2006; Tueller & Lubke, 2010). Model misspecifications such as incorrectly specifying that the covariances within a class are zero can lead to accepting too many classes (Lubke & Neale, 2006). In both model-based clustering and LVMM the model selection can be based on the BIC or bootstrapped likelihood ratio tests. If a single class model with a continuous latent variable representing the construct fits best, then the hypothesis of taxonicity can be rejected.
