Understanding heterogeneity in generalized mixed and frailty models

Variance components are useful parameters to quantify the different sources of randomness in hierarchical models. Interpreting the variance components in generalized mixed and frailty models is not straightforward because the variance is not directly related to quantities with a biological meaning. We therefore investigate how the estimated values of the variance components affect the variability of specific quantities of interest such as the prevalence or the median time to event. We discuss two examples from veterinary science with clustering between animals and show for these examples how variance components can be interpreted in the case of a binary and time-to-event response variable.