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Bayesian Generalized Linear Mixed Effects Models Using Normal-Independent Distributions: Formulation and Applications

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  • Adeniyi, Isaac Adeola

Abstract

A standard assumption is that the random effects of Generalized Linear Mixed Effects Models (GLMMs) follow the normal distribution. However, this assumption has been found to be quite unrealistic and sometimes too restrictive as revealed in many real-life situations. A common case of departures from normality includes the presence of outliers leading to heavy-tailed distributed random effects. This work, therefore, aims to develop a robust GLMM framework by replacing the normality assumption on the random effects by the distributions belonging to the Normal-Independent (NI) class. The resulting models are called the Normal-Independent GLMM (NI-GLMM). The four special cases of the NI class considered in these models’ formulations include the normal, Student-t, Slash and contaminated normal distributions. A full Bayesian technique was adopted for estimation and inference. A real-life data set on cotton bolls was used to demonstrate the performance of the proposed NI-GLMM methodology.

Suggested Citation

  • Adeniyi, Isaac Adeola, 2020. "Bayesian Generalized Linear Mixed Effects Models Using Normal-Independent Distributions: Formulation and Applications," MPRA Paper 99165, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:99165
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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