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Robust Estimation for Linear Mixed Model in the Prediction of Milk Production
Dissertation Abstract:
Milk production has become an increasingly important commodity in Thailand. Milk yield prediction models are important components of dairy milk production system from the farm management viewpoint to genetic improvement of dairy cows. The usefulness of a milk-yield prediction system relies on its accuracy in predicting daily milking patterns. The study intended to develop linear mixed model (LMM) for prediction of milk production by using a test-day model (TDM). The study aimed to demonstrate how the violations of the assumptions that underline the LMM affect the properties of the resulting estimator and compared the robust estimations to be able to be resistant to influent factors from violation of its assumptions for LMM using TDM to predict milk production.
The data set consisted of milk yield data from a total of 537 cows observed at 12 unevenly spaced time points for a total of 6,444 observations from first lactation of cows with varying proportions of Holstein Friesian genetic backgrounds. The cows were raised in four locations in western area of Thailand—namely, Tak, Ratchaburi, Phetchaburi, and Prachuap Khiri Khan provinces. Milk yield, as the animal material, was treated as dependent variable. The model contained breeding group (g), parturition season within parturition year (s), parturition month within parturition season (m), and farm location (I) as fixed effects; parturition year (d) was treated as random. The study presented general form of variance-covariance structure in case of repeated measure data and general form of parameter estimation.
According to assumption of model by univariate procedure in all combinations of independent variables, violation of independency, normality, and homoscedasticity assumption were studied to compare robustness parameter estimation of model. The study was demonstrated by TD milk yield data in which the restricted maximum likelihood (ReML) estimation under ANTE(l) covariance structure from fitted data was better than maximum likelihood estimation (MLE) among the seven models selected (SIMPLE, CS, AR(l), UN, ARH(l), and ANTE(l)) based on four fit indices criteria (-2RLL, AIC, AICC, and BIC) and F-test of fixed effects. Therefore, the study purposed the ReML estimation under ANTE(l) structure was a proper covariance structure to describe TD milk yield differences under violation of independency, normality, and homoscedasticity assumption.