title: Random regression models using  different functions to model test-day milk yield of Brazilian Holstein cows.
abstract: We  analyzed 152,145 test-day records from 7317 first lactations of Holstein cows  recorded from 1995 to 2003. Our objective was to model variations in test-day  milk yield during the first lactation of Holstein cows by random regression  model (RRM), using various functions in order to obtain adequate and  parsimonious models for the estimation of genetic parameters. Test-day milk  yields were grouped into weekly classes of days in milk, ranging from 1 to 44  weeks. The contemporary groups were defined as herd-test-day. The analyses were  performed using a single-trait RRM, including the direct additive, permanent  environmental and residual random effects. In addition, contemporary group and  linear and quadratic effects of the age of cow at calving were included as  fixed effects. The mean trend of milk yield was modeled with a fourth-order  orthogonal Legendre polynomial. The additive genetic and permanent  environmental covariance functions were estimated by random regression on two  parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions  of days in milk. The covariance components and the genetic parameters were  estimated by the restricted maximum likelihood method. Results from RRM  parametric and B-spline functions were compared to RRM on Legendre polynomials  and with a multi-trait analysis, using the same data set. Heritability  estimates presented similar trends during mid-lactation (13 to 31 weeks) and  between week 37 and the end of lactation, for all RRM. Heritabilities obtained  by multi-trait analysis were of a lower magnitude than those estimated by RRM.  The RRMs with a higher number of parameters were more useful to describe the  genetic variation of test-day milk yield throughout the lactation. RRM using  B-spline and Legendre polynomials as base functions appears to be the most  adequate to describe the covariance structure of the data.
authors: Departamento de Zootecnia, Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista Julio de Mesquita Filho, Jaboticabal, SP, Brasil. annaizabb@hotmail.com
authors: A B
authors: AB
authors: Bignardi
authors: L
authors: L
authors: El Faro
authors: R A A
authors: RA
authors: Torres Júnior
authors: V L
authors: VL
authors: Cardoso
authors: P F
authors: PF
authors: Machado
authors: L G
authors: LG
authors: Albuquerque
mesh_terms: D000818:Animals; D001938:Brazil; D002417:Cattle; D005260:Female; D006801:Humans; D040582:Inheritance Patterns / Q000235:genetics; D016013:Likelihood Functions; D008892:Milk / Q000378:metabolism*; D008954:Models, Biological; D010641:Phenotype; D019655:Quantitative Trait, Heritable; D012044:Regression Analysis