A Bayesian Skew-Normal Independent Mixture Measurement Error Model

The traditional regression model with measurement errors assumes normal distributions for the error terms and unobserved latent covariate. These assumptions are not appropriate when asymmetry, outliers, and multi-modality occur simultaneously. We propose a model that presents robustness against violations of these assumptions, assuming that the distribution of the covariate belongs to a highly flexible family of distributions, defined as a finite mixture of skew-normal independent distributions. The model can be applied in many practical situations such as comparative calibration of instruments, where the bias and precision of measurements made using some instruments are
evaluated based on measurements made by a reference one. The main goals are (i) develop algorithms for Bayesian estimation of the parameters of the proposed model; (ii) investigate, through simulation, the performance of the model selection criterion DIC (Deviance Information Criterion) as a suitable method to choose between the different considered models, including the determination of the number of component mixtures and (iii) apply the proposed methodology by considering the analysis of simulated and real data sets.