Estimating covariance functions for longitudinal data using a random regression model.

摘要

A method is described for the estimation of 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. The method 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 parameterization is described which allows the rank of estimated covariance matrices and functions to be restricted, allowing a highly parsimonious description of the covariance structure. The procedure and the type of results whichcan be obtained are illustrated using body weight records of beef cattle.