Linear Mixed Models: Gum and Beyond

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...

Linear quantile mixed models

Dependent data arise in many studies. For example, children with the same parents or living in neighboring geographic areas tend to be more alike in many characteristics than individuals chosen at random from the population at large; observations taken repeatedly on the same individual are likely to be more similar than observations from different individuals. Frequently adopted sampling design...

Generalized Linear Mixed Models

Comparison of Different Estimation Methods for Linear Mixed Models and Generalized Linear Mixed Models

Linear mixed models (LMM) and generalized linear mixed models (GLMM) are widely used in regression analyses. With the variance structure dependent on the random effects with their variance components, the parameter estimation of LMMs is more complicated than linear models (LM). Generally, we use maximum likelihood estimation (MLE) together with some procedure such as derivative free optimizatio...