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The studies described in this thesis were achieved within the graduate school Wageningen Institute of Animal Science (WIAS), carried out at the Institute for Animal Science and Health (ID-Lelystad BV) at the department of Genetics and Reproduction, and financially supported by the product division NRS of CR-DELTA.This thesis describes choices and decisions made to develop a random regression test-day model. Studies included were performed on Dutch dairy cattle data. Random regression test-day models are preferred above lactation models, because they model both the level and shape of the lactation curve. Single test-day records are used instead of cumulative lactation yields. Therefore, the correction of fixed effects is better and more precise, herd-test-date effects can be accounted for, and if the lactation curve is modeled by a covariance function (i.e., with a random regression function) information from the number, intervals and ordering of test-day records is included. The trend in breeding values for sires was 94 kg of milk per year compared to 106 kg in a repeatability model. Selection in the past was for the level of production and has not influenced the shape of the lactation curve. Correlations between breeding values were high and standard deviations were slightly higher in the test-day model. But for sires with more persistent daughters breeding values seemed to fluctuate less in the random regression test-day model.For correct modeling of the variance structure higher order functions are needed. A fourth order Legendre polynomials was sufficient for both the genetic and permanent environmental effect. More complete information and a correction for heterogeneity of variance over days in milk allowed a reduction in the least order of fit. However, a multiple-trait random regression test-day model with three parities and a full fit is huge (i.e., 2 × 15 parameters to be estimated per animal) and probably overparameterized. Therefore, a stepwise-reduced rank procedure was applied, which allowed to half the number of parameter without reducing the goodness of fit considerably. For further extension of the random regression test-day model for the traits milk, fat and protein the stepwise-reduced rank procedure is suggested.

The studies described in this thesis were achieved within the graduate school Wageningen Institute of Animal Science (WIAS), carried out at the Institute for Animal Science and Health (ID-Lelystad BV) at the department of Genetics and Reproduction, and financially supported by the product division NRS of CR-DELTA.This thesis describes choices and decisions made to develop a random regression test-day model. Studies included were performed on Dutch dairy cattle data. Random regression test-day models are preferred above lactation models, because they model both the level and shape of the lactation curve. Single test-day records are used instead of cumulative lactation yields. Therefore, the correction of fixed effects is better and more precise, herd-test-date effects can be accounted for, and if the lactation curve is modeled by a covariance function (i.e., with a random regression function) information from the number, intervals and ordering of test-day records is included. The trend in breeding values for sires was 94 kg of milk per year compared to 106 kg in a repeatability model. Selection in the past was for the level of production and has not influenced the shape of the lactation curve. Correlations between breeding values were high and standard deviations were slightly higher in the test-day model. But for sires with more persistent daughters breeding values seemed to fluctuate less in the random regression test-day model.For correct modeling of the variance structure higher order functions are needed. A fourth order Legendre polynomials was sufficient for both the genetic and permanent environmental effect. More complete information and a correction for heterogeneity of variance over days in milk allowed a reduction in the least order of fit. However, a multiple-trait random regression test-day model with three parities and a full fit is huge (i.e., 2 × 15 parameters to be estimated per animal) and probably overparameterized. Therefore, a stepwise-reduced rank procedure was applied, which allowed to half the number of parameter without reducing the goodness of fit considerably. For further extension of the random regression test-day model for the traits milk, fat and protein the stepwise-reduced rank procedure is suggested.

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