Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

Document Type : Final File

Authors
L. Kalhori Nadrabadi
M. Mohhamadzadeh
1 Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran
10.22059/jsciences.2018.65022
Abstract
In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symmetric and skewed families. In this paper, a beta generalized linear mixed model with spatial random effect is proposed emphasizing on small values of the spatial range parameter and small sample sizes. Then some models with both fixed and varying precision parameter and different combinations of priors and sample sizes are discussed. Next, the Bayesian estimation of the model parameters is evaluated in an intensive simulation study. Selected priors improved the Bayesian estimation of the parameters, especially for small sample sizes and small values of range parameter. Finally, an application of the proposed model on data provided by Household Income and Expenditure Survey (HIES) of Tehran city is presented.
Keywords
Bayesian estimation
Beta regression model
Household income and expenditure data
Spatial random effect
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Appendix I:

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Journal of Sciences, Islamic Republic of Iran
Volume 29, Issue 2
Spring 2018
Pages 173-185