Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution

TL;DR

This paper introduces a flexible finite mixture model using multivariate skew-normal distributions to analyze censored and missing data, effectively capturing skewness and multimodality, with an efficient EM algorithm for parameter estimation.

Contribution

It proposes a novel robust modeling approach for censored and missing data using mixtures of multivariate skew-normal distributions, including an efficient EM algorithm and implementation in R.

Findings

Effective modeling of skewed, multimodal data with censoring and missingness.

Successful application to simulated and real datasets demonstrating robustness.

Availability of an R package CensMFM for practical use.

Abstract

Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, for instance, asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, EM- type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.