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Selection of locations of knots for linear splines in random regression test‐day models
Author(s) -
Jamrozik J.,
Bohmanova J.,
Schaeffer L.R.
Publication year - 2010
Publication title -
journal of animal breeding and genetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.689
H-Index - 51
eISSN - 1439-0388
pISSN - 0931-2668
DOI - 10.1111/j.1439-0388.2009.00829.x
Subject(s) - mathematics , covariance , selection (genetic algorithm) , knot (papermaking) , regression , spline (mechanical) , covariance function , linear regression , statistics , goodness of fit , linear model , legendre polynomials , computer science , artificial intelligence , mathematical analysis , structural engineering , chemical engineering , engineering
Summary Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test‐day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single‐ and multiple‐trait test‐day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness‐of‐fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test‐day models when analysing milk production traits.