Estimating covariance functions for longitudinal data using a random regression model

A method is described to estimate genetic and environmental covariance functions for traits measured repeatedly per individual along some continuous scale, such as time, directly from the data by restricted maximum likelihood. It relies on the equivalence of a covariance function and a random regression model. By regressing on random, orthogonal polynomials of the continuous scale variable, the coefficients of covariance functions can be estimated as the covariances among the regression coefficients. A parameterisation is described which allows the rank of estimated covariance matrices and functions to be restricted, thus facilitating a highly parsimonious description of the covariance structure. The procedure and the type of results which can be obtained are illustrated with an application to mature weight records of beef cows.