Model Fit and Comparison in Finite Mixture Models: A Review and a Novel Approach - Grimm, Kevin J.; Houpt, Russell; Rodgers, Danielle (Frontiers in Education, 2021)
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 per parameter likelihood increment percentage (per parameter LIP), 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 per parameter LIP to identify the correct number of classes, and describe the importance of the improvement in model fit. We conclude with recommendations and future research directions.