Components Analysis in Finite Mixture Model

Abstract

Determining the appropriate number of components within a finite mixture model is a challenging issue in statistical modelling. This is because the inappropriate choice misinterprets the data and could lead to poor performance. For this purpose, this study will apply empirical data on energy consumption and exchange rate in Malaysia to determine the suitable number of components using the finite mixture model. This study applies Akaike Information Criterion and Bayesian Information Criterion model selection criteria for considering model adequacy. The results demonstrated that the log-likelihood increases as the number of components increases. Indeed, even Akaike Information Criterion still favoured more complex models. However, Bayesian Information Criterion reached a minimum value of three components, which resulted in choosing the most suitable model structure. These results also indicated that Akaike Information Criterion overestimates the number of components. However, Bayesian Information Criterion yielded a more parsimonious and interpretable solution. This study tries to give practical meaning to model selection in mixture modelling. This study also points out the effectiveness of Bayesian Information Criterion in identifying meaningful group structures when the data are heterogeneous.