Abstract
One of the greatest challenges in the application of finite mixture models is model comparison. A variety of statistical fit indices exist, including information criteria, approximate likelihood ratio tests, and resampling techniques; however, none of these indices describe the amount of improvement in model fit when a latent class is added to the model. We review these model fit statistics and propose a novel approach, the likelihood increment percentage per parameter (LIPpp), targeting the relative improvement in model fit when a class is added to the model. Simulation work based on two previous simulation studies highlighted the potential for the LIPpp to identify the correct number of classes, and provide context for the magnitude of improvement in model fit. We conclude with recommendations and future research directions.
Highlights
Finite mixture modeling (FMM) is a broad class of statistical models to examine whether model parameters vary over unmeasured groups of individuals
The likelihood increment percentage per parameter (LIPpp) was proposed as a measure of relative improvement in model fit for comparing FMMs
The LIPpp was able to discern the number of classes relatively well
Summary
Finite mixture modeling (FMM) is a broad class of statistical models to examine whether model parameters vary over unmeasured groups of individuals. A series of FMMs, differing in the number of latent classes and the nature of model constraints, are specified, fit, and compared. FMMs that differ in the number of classes, but have the same parameter constraints are nested; the difference in −2 log-likelihood is not chi-square distributed under the null hypothesis. Because of these issues, different model fit criteria are used for model selection. We review model fit criteria to compare FMMs and Monte Carlo simulation studies that have investigated the performance of these model comparison approaches. We propose a novel approach to model comparison for FMMs based on the relative improvement in model fit
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