Generalized semiparametrically structured mixed models

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

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...

Bayesian Generalized Kernel Mixed Models

We propose a fully Bayesian methodology for generalized kernel mixed models (GKMMs), which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of a generalized kernel model (GKM). This mixture prior allows a fraction of the components of the regres...

Got Randomness? SAS® for Mixed and Generalized Linear Mixed Models

SAS® PROC GLIMMIX fits generalized linear mixed models for nonnormal data with random effects, thus combining features of both PROC GENMOD and PROC MIXED. I will review the ideas behind PROC GLIMMIX and offer examples of Poisson and binary data. PROC NLMIXED also has the capacity to fit these kinds of models. After a brief introduction to that procedure, I will show an example of a zero-inflate...