Modeling ‘repeated’ Records : Covariance Functions and Random Regression Models to Analyse Animal Breeding Data

INTRODUCTION There is a plethora of statistical literature on modeling and analysis of repeated records, often referred to as longitudinal or growth curve data. These can be analysed fitting a linear model using (restricted) maximum likelihood (Ware 1985). This framework accommodates a wide range of assumptions about the structural form of covariance matrices (e.g. Jennrich and Schluchter 1986). Until recently data from animal breeding applications have generally being analysed invoking one of the extremes of this model, namely a simple constant variance, univariate “repeatability” model or a fully parameterised, multivariate model with unstructured covariance. A specific feature of quantitative genetic analyses, not shared by other fields, is that we want to partition the variation due to individuals into its genetic and environmental components. This paper describes how an intermediate parameterisation can be achieved by fitting a covariance function (CF) for each source of variation, genetic and environmental, using a random regression (RR) model, and outlines Restricted Maximum Likelihood (REML) estimation of a parsimonious covariance structure.