Modelling test day data

Four statistical models for genetic evaluations utilising dairy test day data are considered. These are: a fixed regression model, a random regression model, an autoregressive model and a multiple trait model. The emphasis is put on the comparison of these models in terms of their assumed covariance structure, modelling and prediction of breeding values and parameterisation. In the future one of the models should be used for a routine genetic evaluation of the Polish Black-and-White dairy cattle. Therefore, characteristics of test day data from the Polish population are given. In conclusion, it appears that thanks to its flexibility in handling heterogeneous variances during lactation, variable autocorrelation, and nonuniform spacing between tests, random regression model forms the most suitable approach. Key-words: dairy cattle, genetic evaluation, statistical modelling , test day data Introduction Longitudinal data consist of sets of multiple observations scored on one subject (e.g., a person or an animal) repeatedly in time. Milk production measured on cows on several test days during lactation forms a classical example of longitudinal data. From the statistical perspective, the most important feature of the analysis of such repeated observations is the ability to model the correlation between them. During the last two decades appropriate statistical methods have been developed and applied mainly in the analysis of small, experimental data sets (for overview see: DIGGLE et al. 1994). Thanks to the progress in computer hardware technology, the analysis of large amounts of data has become feasible also for modelling of test day data in dairy cattle (PTAK, SCHAEFFER 1993, SCHAEFFER, DEKKERS 1994, JAMROZIK et al. 1997). Moreover, attempts have been made recently to use test day information in national genetic evaluations for dairy cattle (REENTS et al. 1995, JAMROZIK et al. 1997). The main objective of this paper is to compare four models available for genetic evaluation based on dairy test day yields. The model which suites best the characteristics of test day data from the dairy population of the Polish Black-and-White cattle is chosen, as a desirable model for a routine genetic evaluation. Genetic evaluation models for dairy test day data Modelling of test day data Test day data sets resulting from routine milk recording programs are considerably larger and have a more complicated covariance structure than data from designed experiments. The most characteristic features of test day data comprise: (i) between-subject correlation, (ii) differences between means and variances of measurements taken at different stages of lactation, (iii) correlation between test day yields decaying with increasing time between test days, meaning that outcomes of adjacent tests are more correlated than outcomes of remote tests, (iv) unequal spacing of test days throughout lactation. In the modelling of test day data the aforementioned features have to be accounted for. Traditionally, cow milk production measured on consecutive test days has been transformed into an aggregated 305-day yield. Such assembling of data on the phenotypic level has many disadvantages, such as the need for projecting of partially terminated records or inability to model changes in environment throughout the lactation. In order to avoid using the aggregated 305-day lactation records, various approaches to modelling of test day data directly have been developed. These are: (i) fixed and random regression models (PTAK, SCHAEFFER 1993, SCHAEFFER, DEKKERS 1994, REENTS et al. 1995, JAMROZIK et al. 1997, MEYER 1997), (ii) first-order autoregressive models (CARVALHEIRA et al. 1998), (iii) multiple trait models (WIGGANS, GODDARD 1997; GENGLER et al. 1999). The most important characteristics of these models are outlined below. Fixed regression model The fixed regression model (FRM) was the first model proposed for modelling of dairy test day data (PTAK, SCHAEFFER 1993, REENTS et al. 1995): ∑ = + + + + = + + + + =