Page 146 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

9 Analysis of Longitudinal Data

9.1 Introduction

In Chapter 4, the use of a repeatability model to analyse repeated measurements on
individuals was discussed and illustrated. The basic assumption of the model was that
repeated measurements were regarded as expression of the same trait over time. In
other words, a genetic correlation of unity was assumed between repeated measure-
ments. The model has been employed mostly in the genetic evaluation of milk pro-
duction traits of dairy cattle in most countries up to 1999 (Interbull, 2000). The main
advantages of this model are its simplicity, fewer computation requirements and
fewer parameters compared to a multivariate model (see Chapter 5). However, the
model has some drawbacks. First, test day records within lactation are assumed to
measure the same trait during the whole lactation length and are used to compute
305-day yields. These test day records are actually repeated observations measured
along a trajectory (days in milk), and the mean and covariance between measure-
ments change gradually along the trajectory. Several studies have reported that herit-
ability of daily milk yields varied with days in milk. In addition, genetic correlations
between repeated measurements usually tended to decrease as the time between them
increases (Meyer, 1989; Pander et al., 1992). The extension of test records to compute
305-day yields is unable to account for these changes in the covariance structure.
Second, the assumption that 305-day yields across parities measure the same trait
suffers from the same limitations.
However, in beef cattle, repeated measurements of growth have been analysed
somewhat differently, with the assumption that measurements are genetically differ-
ent but correlated traits. Usually, a multivariate model has been employed in the
genetic evaluation of these traits. While the multivariate model is an improvement
on the repeatability model by accounting for the genetic correlations among differ-
ent records, it would be highly over-parameterized if records were available at
many ages or time periods. For instance, a multivariate model for daily body weight
up to yearly weight in beef cattle as different traits will not only be over-parameterized
but it will be difficult to obtain accurate estimates of the necessary genetic
parameters.
An appropriate model for the analysis of repeated measurements over time or age
(also termed longitudinal data) should account for the mean and covariance structure
that changes with time or age and should be feasible in terms of estimating the
required genetic parameters. In 1994, Schaeffer and Dekkers introduced the concept
of the random regression (RR) model for the analysis of test day records in dairy
cattle as a means of accounting for the covariance structure of repeated records over
time or age. Almost at the same time, Kirkpatrick et al. (1990, 1994) introduced

130 © R.A. Mrode 2014. Linear Models for the Prediction of Animal Breeding Values,
3rd Edition (R.A. Mrode)