Bayesian analysis of flexible measurement error models

Abstract

This paper proposes the Bayesian inference for flexible measurement error models, in which their systematic components include explanatory variable vectors with and without measurement errors, as well as nonlinear effects that are approximated by using B-splines. The model investigated is the structural version, as the error-prone variables follow scale mixtures of normal distributions such as Student-$t$, slash, contaminated normal, Laplace and symmetric hyperbolic distributions. To draw samples of the posterior distribution of the model parameters, an MCMC algorithm is proposed. The performance of this algorithm is assessed through simulations. In addition, the function fmem() of the R package BayesGESM is presented, which provides an easy way to apply the methodology presented in this paper. The proposed methodology is applied to a real data set, which shows that ignoring measurement errors (i.e., analyze the data by using the traditional methodology) can lead to wrong conclusions.