AUTHOR=Grimm Kevin J. , Houpt Russell , Rodgers Danielle 

TITLE=Model Fit and Comparison in Finite Mixture Models: A Review and a Novel Approach

JOURNAL=Frontiers in Education

VOLUME=6

YEAR=2021

URL=https://www.frontiersin.org/journals/education/articles/10.3389/feduc.2021.613645

DOI=10.3389/feduc.2021.613645

ISSN=2504-284X

ABSTRACT=<p>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 <italic>likelihood increment percentage per parameter</italic> (<italic>LIPpp</italic>), 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 <italic>LIPpp</italic> 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.</p>