title: Quantifying intraclass correlations for count and time-to-event data.
abstract: The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter-rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult 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 for overdispersion. Furthermore, because the models admit closed-form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies.
authors.affiliation: Department of Exact Sciences, Federal University of Lavras, 37200-000 Lavras, Brazil.|I-BioStat, Universiteit Hasselt, B-3500 Hasselt, Belgium.|Department of Exact Sciences, ESALQ/USP, 13418-900 Piracicaba, Brazil.
authors.forename: Izabela R C
authors.initials: IR
authors.lastname: Oliveira
authors.affiliation: I-BioStat, Universiteit Hasselt, B-3500 Hasselt, Belgium.|I-BioStat, KU Leuven, B-3000 Leuven, Belgium.
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
authors.affiliation: Department of Exact Sciences, ESALQ/USP, 13418-900 Piracicaba, Brazil.
authors.forename: Clarice G B
authors.initials: CG
authors.lastname: Demétrio
authors.affiliation: Department of Exact Sciences, ESALQ/USP, 13418-900 Piracicaba, Brazil.
authors.forename: Carlos T S
authors.initials: CT
authors.lastname: Dias
authors.affiliation: Department of Statistics, Federal University of Paraná, 80060-000 Curitiba, Brazil.
authors.forename: Suely R
authors.initials: SR
authors.lastname: Giolo
authors.affiliation: Department of Biology, Federal University of Lavras, 37200-000 Lavras, Brazil.
authors.forename: Marcela C
authors.initials: MC
authors.lastname: Andrade
mesh_terms: D000383:Agriculture / Q000706:statistics & numerical data; D000818:Animals; D001699:Biometry / Q000379:methods*; D016014:Linear Models; D058751:Livestock; D015203:Reproducibility of Results; D013223:Statistics as Topic
keywords: Generalized linear mixed model; ICC; Overdispersion; Poisson distribution; Weibull distribution