Incorporating Clustering Techniques into GAMLSS

Abstract

A method for statistical analysis of multimodal and/or highly distorted data is presented. The new methodology combines different clustering methods with the GAMLSS (generalized additive models for location, scale, and shape) framework, and is therefore called c-GAMLSS, for “clustering GAMLSS. ” In this new extended structure, a latent variable (cluster) is created to explain the response-variable (target). Any and all parameters of the distribution for the response variable can also be modeled by functions of the new covariate added to other available resources (features). The method of selecting resources to be used is carried out in stages, a step-based method. A simulation study considering multiple scenarios is presented to compare the c-GAMLSS method with existing Gaussian mixture models. We show by means of four different data applications that in cases where other authentic explanatory variables are or are not available, the c-GAMLSS structure outperforms mixture models, some recently developed complex distributions, cluster-weighted models, and a mixture-of-experts model. Even though we use simple distributions in our examples, other more sophisticated distributions can be used to explain the response variable.