Multivariate Cluster Weighted Models Using Skewed Distributions

TL;DR

This paper introduces a new family of 24 multivariate cluster weighted models that incorporate skewed distributions for both covariates and responses, extending existing models to better handle asymmetry in data.

Contribution

It proposes the first CWMs to include skewed distributions for covariates and responses, broadening the modeling capabilities of traditional CWMs.

Findings

Successful parameter estimation via EM algorithm.

Demonstrated improved modeling with simulated data.

Validated with real data examples.

Abstract

Much work has been done in the area of the cluster weighted model (CWM), which extends the finite mixture of regression model to include modelling of the covariates. Although many types of distributions have been considered for both the response and covariates, to our knowledge skewed distributions have not yet been considered in this paradigm. Herein, a family of 24 novel CWMs are considered which allows both the covariates and response variables to be modelled using one of four skewed distributions, or the normal distribution. Parameter estimation is performed using the expectation-maximization algorithm and both simulated and real data are used for illustration.