Theoretical basis and computational methods for different test-day genetic evaluation methods

In test-day (TD) models, records from individual test days are used to determine lactation production instead of aggregating records. Test-day models have recently gained considerable interest because they are more flexible in handling records from different recording schemes. Compared with only using records of complete lactations, they can reduce the generation interval through frequent genetic evaluations with the latest data. Test-day models can predict total production more accurately by accounting for time-dependent environmental effects. Test-day models may be separated into three groups: First, two-step models under which corrections are carried out at TD level and subsequently corrected TD records are processed in an aggregated form as lactation records. Second, fixed regression models assume that TD records within a lactation are repeated records. Because yields in the course of the lactation follow a curvilinear pattern, this curve can be considered by using suitable covariates. Third, random regression models additionally define the animal's genetic effect by using regression coefficients and allowing for covariances among them. The difference between random regression and fixed regression models is that the genetic merit of an individual is allowed to differ in the course of the lactation in random regression models. Random regressions are related to the approach of defining covariance functions for longitudinal data. Computationally, TD models are very demanding. For evaluations on a national scale, the size of the equation system can go to hundreds of millions of equations, depending on the size of the database and the specific model defined.