ACKNOWLEDGEMENTS xviii 1 INTRODUCTION 1 2 LITERATURE REVIEW 3 Milking cows three times a day 3 Parity number and milking three times a day 4 Stage of lactation and milking three times a day 5 Feed intake, body weight and milking three times a day 6 Milk components and quality, and milking three times a day ..... 7 Udder health and milking three times a day 8 Reproductive performance and milking three times a day 8 Test-day model First approach Second approach Third approach Expected advantages of test-day-models Variance components and heritability estimates using test-day models 13 Correlations among test-days within the same trait Approaches to handle large data 15 Use of covariance functions in genetic evaluation 17 Taking into account contemporary groups and heterogeneous variance Regression coefficients in a test-day model 19 Use of adjustment factors in livestock species 20 iv 3 MATERIAL AND METHODS 23 Data 23 Management code 24 Model 28 Model in matrix notation Model assumptions 31 Mixed model equations Estimation of covariance components, heritabilities, genetic and phenotypic correlation Analyses of variance of fixed effects .35 Estimation of adjustment factors 4 RESULTS AND DISCUSSION Number of levels for each factor in each sample and in the whole data set Descriptive statistics for the three samples and for the whole data set Trait peak yield and cumulative means across days-in-milk within man agement groups Profiles of raw means of test-day yields Profiles of raw means of test-day yields across days-in-milk Profiles of raw means of test-day yield across days pregnant Profiles of raw means of test-day yield across levels of parity 57 Estimates of covariance components 61 Heritability, genetic and phenotypic correlation estimates 63 Analyses of variance of fixed effects 71 Estimates of adjustment factors 73 Profiles of adjusted yield-trait means 80 Profiles of adjusted yield-trait means across days-in-milk 80 Profiles of adjusted yield-trait means across days pregnant 80 Profiles of adjusted yield-trait means across parities 99 V General discussion about profiles of adjusted means across days-inmilk, days pregnant, and parities 99 Evaluation of adjustment factors Further discussion about adjustment factor estimates, based on literature review Suggested adjustment factors Ill Profiles of estimated difference in production across days-in-milk Cumulative estimated difference in production across days-in-milk General discussion about 3x versus 2x based on the results of estimated difference in production Profiles of estimated difference in production across days pregnant ....