Estimation of genetic and phenotypic covariance functions for
longitudinal data by Restricted Maximum Likelihood
K. Meyer and W.G.Hill
Livestock Production Science 47 : 185-200.
Abstract
Covariance functions are the equivalent of covariance matrices for
traits with many, potentially infinitely many, records in which the
covariances are defined as a function of age or time. They can be
fitted for any source of variation, e.g. genetic, permanent
environment or phenotypic. A suitable family of functions for
covariance functions are orthogonal polynomials. These give the
covariance between measurements at any two ages as a higher order
polynomial of the ages at recording. Polynomials can be fitted to full
or reduced order. The former is equivalent to a multivariate analysis
estimating covariance components. A reduced order fit involves less
parameters and smoothes out differences in estimates of covariances.
It gives predicted covariance matrices of rank equal to the order of
fit.
The coefficients of covariance functions can be
estimated by Restricted Maximum Likelihood through a
reparameterisation of existing algorithms to estimate covariance
components. For a simple animal model with equal design matrices for
all traits, computational requirements to estimate covariance
functions are proportional to the order of fit for the genetic
covariance function. Applications to simulated data and a set of beef
cattle data are shown.
Key words :
Genetic parameters, covariance functions, repeated
records, Restricted Maximum Likelihood
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K.Meyer, Nov. 30, 1996