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

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • Mohammad Reza Mahmoudi

    (Department of Statistics, Faculty of Science, Fasa University, Fasa 74616-86131, Iran
    These authors contributed equally to this work.)

  • 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
    John von Neumann Faculty of Informatics, Obuda University, 1034 Budapest, Hungary
    Institute of Information Society, University of Public Service, 1083 Budapest, Hungary
    Institute of Information Engineering, Automation and Mathematics, Slovak University of Technology in Bratislava, 81243 Bratislava, Slovakia)

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.

Suggested Citation

  • Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2820-:d:883339
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    References listed on IDEAS

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