Many traits of interest in animals are measured sequentially over time and the trait is expected to change smoothly in some sense over that period. Polynomial regression is a traditional approach to modelling such data, leading to the random regression model in its various forms. However, polynomials have several drawbacks in that they represent a small subset of the correlation models that are possible. Character process models model the correlation structure using some form of stochasic model which often captures the correlation structure better than the random regression approach using fewer parameters. We consider the issue of structure of the covariance matrix over time. Both random regression and CP structures can be extended to multiple traits although it is not always obvious how to do this with CP models. Concerning unstructured matrices, we refer to developments for fitting reduced rank forms.

A. R Gilmour

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume , , 25.01, 2006
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