Estimation in skew-normal linear mixed measurement error models

Abstract

a b s t r a c tIn 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.

Bayesian Estimation of Spatial Regression Models with Skew-normally Covariates Measured with Errors: Evidence from Monte Carlo Simulations

“…The linear models with Skew-normal measurement error models perform better when there is evidence of departure from symmetry or normality [7]. Furthermore, the Skew-normal linear mixed measurement error outperform the normal mixed measurement error model when the actual covariate distribution has a Skew-normal [8].…”

“…The error-prone covariates and the random errors are usually assumed to be symmetrically, normally distribution [4][5][6]. However, the assumption of normality may be too restrictive in many applications [7,8]. The linear models with Skew-normal measurement error models perform better when there is evidence of departure from symmetry or normality [7].…”

Score Tests for Intercept and Slope Parameters of Doubly Multivariate Linear Models with Skew-Normal Errors

“…No attempt was made therein to develop the Fisher information matrix for a wide array of cases where was structured since the monograph had other aims in mind. Some structured covariance matrices are considered in the multivariate linear mixed models developed in Kheradmandi et al [14], Lachos et al [15], Lin and Wang [18], and Wang [35]; however, the Fisher information matrices were unreported or undeveloped since these papers aimed at fitting their models and recommending variants of the EM algorithm. In fact, it appears that no systematic development of the Fisher information matrix of parameters of a multivariate linear model with a skew-normal errors and structured covariance matrices has been performed, and only mentions of approximating the observed information matrix numerically are made.…”

Some extensions in measurement error models

“…However, for the estimation of the skewness parameter λ , a larger sample size is needed, as can be seen for n = 500. Regarding the estimation of this parameter, and Kheradmandi and Rasekh (2015) mentioned that in some samples, the probability of having λ = ∞ can be positive. Alternative methods of estimation of λ are part of ongoing work.…”

“…For instance, it is often doubtful and suffers from a lack of robustness against influential observations on the parameter estimates. For this reason, several works have considered relaxations of the normality assumption, such as considering asymmetric distributions, see , Kheradmandi and Rasekh (2015) and models based on distributions with tails heavier than the ones of a normal distribution, see Cao, Lin and Zhu (2012), Melo, Ferrari and Patriota (2014).…”