Linear and Generalized Linear Mixed Models and Their Applications

Linear and Generalized Linear Mixed Models and Their Applications

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Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

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 symm...

Generalized Linear Mixed Models

Generalized linear models (GLMs) represent a class of fixed effects regression models for several types of dependent variables (i.e., continuous, dichotomous, counts). McCullagh and Nelder [32] describe these in great detail and indicate that the term ‘generalized linear model’ is due to Nelder and Wedderburn [35] who described how a collection of seemingly disparate statistical techniques coul...

Generalized Linear Mixed Models

Generalized Linear Models and Their Applications to Actuarial Modeling

This paper will discuss the basic principles underlying the theory of generalized linear models and the advantages of using generalized linear models over more traditional methods of actuarial modeling. Generalized linear models offer the flexibility needed to model real world data that does not conform to the strict assumptions underlying these traditional methods. The second part ofthis paper...