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15 Examples 292105Residual0-5-10200 400 600 800 1000 1200 1400 1600ageFigure 15.16 Plot of the residuals from the nonlinear model of Pinheiro and Bates15.10 Multivariate animal genetics data - SheepThe analysis of incomplete or unbalanced multivariate data often presents computationaldifficulties. These difficulties are exacerbated by either the number ofrandom effects in the linear mixed model, the number of traits, the complexity ofthe variance models being fitted to the random effects or the size of the problem.In this section we illustrate two approaches to the analysis of a complex set ofincomplete multivariate data.Much of the difficulty in conducting such analyses in ASReml centres on obtaininggood starting values. Derivative based algorithms such as the AI algorithm can beunreliable when fitting complex variance structures unless good starting valuesare available. Poor starting values may result in divergence of the algorithmor slow convergence. A particular problem with fitting unstructured variancemodels is keeping the estimated variance matrix positive definite. These are notsimple issues and in the following we present a pragmatic approach to them.