A useful new type of random regressions based on biological differences among repeated records, application to longevity.

Abstract

peer reviewedA major problem in random regression models is that it is not always obvious what type of regressions to use. Different types of functions were identified and use. The first type used where functions that described lactation shapes. These functions did an excellent job to describe the mean, however were very poor in modeling of (co)variance structures. The second group of functions was based on strictly mathematical ones as polynomials. Polynomials were excellent for modeling the (co)variances as long as high order polynomials could be used. Different alternative functions were proposed over time (e.g., splines). Recently another alternative method was proposed by Wiggans and Van Raden (2004) based on the concept of parity differences (PD). Instead of using predefined functions they defined as regressions differences among repeated records. This can be considered an approximation of expected a priory change in genetic merit across those repetitions where the relative size of genetic differences by parity were derived from genetic correlations. We will use the word biological differences as the idea is to base it on individual difference corrected for the environment. The following example might clarify the general idea. Wiggans and Van Raden (2004) defined relative PD among the first five lactation for milk yield as -0.9, 0.1, 0.4, 0.6 and 0.7 which means that differences from second to third, from third to fourth and from fourth to five represent 30%, 20% respectively 10% of the difference from first to second. This has the side effect that (co)variance structures are modelled as quadratic functions of regressors. Through the use of these PD they linearized changes from one lactation to the next. The objective of this paper was to present this idea and to use it for multi-lactation longevity evaluations