Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model

Zeinolabedin Najafi, Karim Zare (), Mohammad Reza Mahmoudi, Soheil Shokri and Amir Mosavi ()
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Zeinolabedin Najafi: Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht 73711-13119, Iran
Karim Zare: Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht 73711-13119, Iran
Mohammad Reza Mahmoudi: Department of Statistics, Faculty of Science, Fasa University, Fasa 74616-86131, Iran
Soheil Shokri: Department of Statistics, Lahijan Branch, Islamic Azad University, Lahijan 44169-39515, Iran
Amir Mosavi: Faculty of Civil Engineering, Technische Universität Dresden, 01069 Dresden, Germany

Mathematics, 2022, vol. 10, issue 15, 1-21

Abstract: This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM algorithm is also implemented to extend the local influence approach under three model perturbation schemes in this model. Furthermore, a Monte Carlo simulation is conducted to evaluate the efficiency of the estimators. Finally, a real data set is used to make an illustrative comparison among the following four scenarios: normal/skew-normal errors and heteroscedasticity/homoscedasticity in random-effect factors. The empirical studies show our methodology can improve the estimates when the model errors follow from a skew-normal distribution. In addition, the local influence analysis indicates that our model can decrease the effects of anomalous observations in comparison to normal ones.

Keywords: EM algorithm; expectation–maximization algorithm; heteroscedasticity; Monte Carlo simulation; random effects; skew-normal; variance components; applied mathematics; Linear mixed models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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