Statistical model assumptions achieved by linear models: classics and generalized mixed

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

A Generalized Linear Statistical Model Approach to Monitor Profiles

Statistical process control methods for monitoring processes with univariate ormultivariate measurements are used widely when the quality variables fit to known probabilitydistributions. Some processes, however, are better characterized by a profile or a function of qualityvariables. For each profile, it is assumed that a collection of data on the response variable along withthe values of the c...

Generalized linear mixed models and modified AIC

The paper by Austin et al. refers repeatedly to generalized linear mixed models, or GLMMs. Example. Suppose we are doing a simple observational study. We observe some species of animal. N animals are selected at random and tracked. They may be observed visually, or by some sort of attached sensor. The position is recorded at short regular intervals. Say, once a minute. The variable of interest ...