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Generalized Linear Mixed Effects Models

Generalized Linear Mixed Models (GLMMs) are an extension of linear mixed models to allow response variables from different distributions (such as binary or multi-nomial responses). Think of it as an extension of generalized linear models (e.g. logistic regression) to include both fixed and random effects.

  • The general form of the model is:      y = Xβ + Zu + ε
    • y is a N*1 column vector of the dependent (outcome) variable
    • X is a N*p of the p predictor variables
    • Z is the N*q design matrix for q random effects (the random complement to the fixed X)
    • u is a q*1 vector of the random effects
    • ε is an N*1 column of vector of the residuals (the part not explained by Xβ + Zu)

 

 

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