CERES Plot in Generalized Linear 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...

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 Models

Generalized Linear Models

Binary Logistic Regressions The classic example of a generalized linear model is when our response data y is binary, so that we can code it as zero/one. For example, one has the disease/does not have the disease, lives/dies, the device fails/device does not fail. To model binary data, a quite reasonable and very general approach is to use the predictor variables (the x’s) to estimate the probab...

Overdispersed Generalized Linear Models

Generalized linear models have become a standard class of models for data analysts. However in some applications, heterogeneity in samples is too great to be explained by the simple variance function implicit in such models. Utilizing a two parameter exponential family which is overdispersed relative to a speciied one parameter exponential family enables the creation of classes of overdispersed...