Semiparametric animal models via penalized splines as alternatives to models with contemporary groups1

Abstract

Contemporary groups (CG) are used in genetic evaluation to account for systematic environmental effects of management, nutritional level, or any other differentially expressed group effect; however, because the functional form of the distribution of those effects is unknown, CG serve as an approximation to a time-varying mean. Conversely, in semiparametric models, there is no need to assume any functional form for the time-varying effects. In this research, we present a semiparametric animal model (AMS) using the covariate day of birth (DOB) by means of penalized splines (P-splines), as an alternative to fitting CG. In the AMS, the functionality of the data on DOB is expressed by means of a Basic segmented polynomial line (B-spline) basis, and proper covariance matrices are used to reflect the serial correlation among the points of support (or knots) at different times. Three different covariance matrices that reflect either short- or long-range dependences among knots are discussed. Different models were fitted to birth weight data from Polled Hereford calves. Models compared were an animal model with CG, an animal model with CG and the covariate DOB nested within CG (CG + DOB), and P-splines with the first difference penalty matrix and three different AMS with 20, 40, 60, 80, or 120 knots. Models were compared using a modified Akaike information criterion (AICC), which was calculated as a byproduct of the estimation of variance components by REML using the expectation maximization algorithm. All three AMS had smaller (better) values of AICC than the regular model with CG, while producing almost the same ranking of predicted breeding values and similar average predicted error variance. In all AMS, the inference and all measures of comparison were similar when the number of knots was equal > or = 40. The model CG + DOB had analogous performance to the AMS, but at the expense of using more parameters. It is concluded that the use of penalized regression splines using a B-spline basis with proper covariance matrices is a competitive method to the fitting of CG into animal models for genetic evaluation, without having to assume any functional form for the covariate DOB.

Trajectory of body weight of performance tested dual-purpose bulls

“…Knots were located equally at the same distance covering the whole age range of 3-420 days. The formulation of SP function was described by De Boor (1993), Bohmanová et al (2005) or Cantet et al (2005).…”

Two-dimensional penalized splines via Gibbs sampling to account for spatial variability in forest genetic trials with small amount of information available

“…However, there are several examples of the use of spline functions with different degree only in one dimension when analyzing breeding data. Thus, animal breeders have used linear splines to model growth in beef cattle (BOHMANOVA et al, 2005;IWAISAKI et al, 2005) or cubic B-spline to smoothing of lactation curves (WHITE et al, 1999) and to model the effects of management unit and time (CANTET et al, 2005). MEYER (2005) used linear to cubic B-splines to model growth of Australian Angus cattle.…”

Comparison of different traits to evaluate the growth of bulls

“…Covariance components for live weight develop notably with the age of the animal (Albuquerque and Meyer, 2001;Meyer, 2001;Nobre et al, 2003;Legarra et al, 2004;Bohmanová et al, 2005;Cantet et al, 2005;Přibyl et al, 2007Přibyl et al, , 2008.…”

“…Different methodologies of linear and nonlinear growth curves have been used (Hyánek and Hyánková 1995;Nešetřilová, 2005;Vuori et al, 2006 Albuquerque and Meyer (2001), Nobre et al (2003), Legarra et al (2004), Bohmanová et al (2005), Cantet et al (2005), Meyer (2005) and Přibyl et al (2007Přibyl et al ( , 2008. Different types of growth functions and comparisons of RR with multipletrait AM methodology were examined.…”