Bayesian Measurement Error Models Using Finite Mixtures of Scale Mixtures of Skew-Normal Distributions

TL;DR

This paper introduces a flexible Bayesian measurement error model using finite mixtures of scale mixtures of skew-normal distributions, effectively capturing skewness, heavy tails, and multi-modality in regression with measurement errors.

Contribution

It extends traditional normal models by jointly modeling unobserved covariates and errors with a novel mixture of skew-normal distributions, enhancing robustness and flexibility.

Findings

Model effectively captures skewness and heavy tails.

Provides a flexible framework for measurement error regression.

Demonstrates improved fit over normal-based models.

Abstract

We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly modeling the unobserved covariate and the random errors by a finite mixture of scale mixture of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails, and multi-modality.