Elliptical linear mixed models with a covariate subject to measurement error
| Autor: | Manuel Galea, Gilberto A. Paula, Joelmir A. Borssoi |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Mahalanobis distance 05 social sciences Conditional probability distribution Marginal model 01 natural sciences Generalized linear mixed model Hierarchical generalized linear model 010104 statistics & probability 0502 economics and business Statistics Covariate Kurtosis Errors-in-variables models REGRESSÃO LINEAR 0101 mathematics Statistics Probability and Uncertainty 050205 econometrics Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | In this paper we extend linear mixed models with elliptical errors by adding a covariate subject to measurement error in the linear predictor. The former class is defined appropriately so that the joint marginal distribution of the response and the observed covariate subject to measurement error is also elliptical. Thus, numerical integration methods are not required to obtain the marginal model and the mean and the variance–covariance structures of the hierarchical model are preserved. A kurtosis flexibility is allowed for each joint marginal distribution and since the conditional distributions are also elliptical, the predictions of the random effects as well as of the covariate subject to measurement error may be performed in a similar way of the normal case. A reweighed iterative process based on the maximum likelihood method is derived for obtaining the parameter estimates, which appear to be robust against outlying observations in the sense of the Mahalanobis distance. In order to assess the sample properties of the maximum likelihood parameter estimates as well as their asymptotic standard errors, a simulation study is performed under different parameter settings and error distributions. Goodness-of-fit measures based on the Mahalanobis distance are presented and normal curvatures of local influence are derived under three usual perturbation schemes, which are selected appropriately. Finally, an illustrative example previously analyzed under normal error models is reanalyzed by considering heavy-tailed error models. The diagnostic procedures are applied for comparing the fitted models. |
| Databáze: | OpenAIRE |
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