Generalized linear mixed models

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Generalized linear mixed models , also generalized linear mixed models ( English Generalized Linear Mixed Models , GLMM ), are a class of regression models . Depending on the point of view, a generalized linear mixed model is a generalization of a linear mixed model ( English Linear Mixed Models , LMM) to more than one distribution of the target variable , or it is used as an extension of the generalized linear models ( English Generalized Linear Model , GLM) to include random ones Effects seen. They are therefore used when the application of the covariates on the target variable is linear, different in clusters and is not necessarily normally distributed .

example

In a worldwide study, the relationship between several environmental influences ( ) and the number of children conceived in the family ( ) is to be modeled. Modeling by means of the Poisson distribution would be more appropriate than the normal distribution . Furthermore, one can assume that the number of children conceived differs between different geographical areas, without this being due to the measured environmental influences, but rather to “random” local peculiarities. These are adequately modeled by the random effects. Another example is longitudinal data , for example when it is recorded on a monthly basis whether a schizophrenia patient has had an episode or not.

estimate

Estimating a generalized linear mixed model by means of the maximum likelihood estimation includes integrating over the random effects. In general, the resulting integrals cannot be represented in closed form . Various approximation methods were developed for the integrals, but none had convincing properties for all types of models and data. For this reason, numerical integration and MCMC methods were increasingly used with increasing computing power and methodological advances .

See also

Web links