Generalized Linear Mixed Models With Crossed Effects and Unit-specific Survey Weights

Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

Random Effects in Generalized Linear Mixed Models

In this chapter, we examine the use of special forms of correlated random e ects in the generalized linear mixed model (GLMM) setting. A special feature of our GLMM is the inclusion of random residual e ects to account for lack of t due to extra variation, outliers and other unexplained sources of variation. For random e ects, we consider, in particular, the correlation structure and improper p...

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