Determining the number of classes in latent class regression models

Abstract

Latent class regression (LCR) is a statistical method used to identify qualitatively different groups or latent classes within a heterogeneous population and commonly used in the behavioural, health, and social sciences. Despite the vast applications, an agreed fit index to correctly determine the number of latent classes is hotly debated. To add, there are also conflicting views on whether covariates should or should not be included into the class enumeration process. We conduct a simulation study to determine the impact of covariates on the class enumeration accuracy as well as study the performance of several commonly used fit indices under different population models and modelling conditions. Our results indicate that of the eight fit indices considered, the aBIC and BLRT proved to be the best performing fit indices for class enumeration. Furthermore, we found that covariates should not be included into the enumeration procedure. Our results illustrate that an unconditional LCA model can enumerate equivalently as well as a conditional LCA model with its true covariate specification. Even with the presence of large covariate effects in the population, the unconditional model is capable of enumerating with high accuracy. As noted by Nylund and Gibson (2016), a misspecified covariate specification can easily lead to an overestimation of latent classes.

Therefore, we recommend to perform class enumeration without covariates and determine a set of candidate latent class models with the aBIC. Once that is determined, the BLRT can be utilized on the set of candidate models and confirm whether results obtained by the BLRT match the results of the aBIC. By separating the enumeration procedure of the BLRT, it still allows one to use the BLRT but reduce the heavy computational burden that is associated with this fit index. Subsequent analysis can then be pursued accordingly after the number of latent classes is determined.