Hierarchical generalized linear model

In statistics, hierarchical generalized linear models extend generalized linear models by relaxing the assumption that error components are independent.^[1] This allows models to be built in situations where more than one error term is necessary and also allows for dependencies between error terms.^[2] The error components can be correlated and not necessarily follow a normal distribution. When there are different clusters, that is, groups of observations, the observations in the same cluster are correlated. In fact, they are positively correlated because observations in the same cluster share some common features. In this situation, using generalized linear models and ignoring the correlations may cause problems.^[3]