Estimation in skew-normal linear mixed measurement error models

Abstract

In this paper we define a class of skew-normal linear mixed measurement error models. This class provides a useful generalization of normal linear mixed models with measurement error in fixed effects variables. It is assumed that the random effects, model errors and measurement errors follow a skew-normal distribution, extending usual symmetric normal model in order to avoid data transformation. We find the likelihood function of the observed data, which can be maximized by using standard optimization techniques. Next, an EM-type algorithm is proposed for estimating the parameters that seems to provide some advantages over a direct maximization of the likelihood. Finally, we propose results of a simulation study and an example of real data for illustration.