Quantifying intraclass correlations for nonnegative traits

Abstract

The intraclass correlation is an important quantity in various areas of application. It is estimated based on fitting a model to hierarchical data and leads, in turn, to several concepts such as reliability, heritability, interrater agreement, etc. For data where linear models can be used, these attributes are conveniently defined as ratios of variance components. Matters are less simple for non-Gaussian outcomes. The focus here is on count and time-to-event outcomes where so-called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as overdispersion. Furthermore, because the models admit closed-form expressions for the mean, variances, higher moments, and even the joint marginal distribution, the derivation of intraclass correlations is convenient. The proposed methodology is illustrated using data from agricultural and livestock studies.