A Stochastic Variational Framework for Fitting and Diagnosing 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...

Fitting Generalized Linear Mixed Models For Point-Referenced Spatial Data

Gaussian Variational Approximate Inference for Generalized Linear Mixed Models

Variational approximation methods have become a mainstay of contemporary Machine Learning methodology, but currently have little presence in Statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMM) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the res...

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