Publication: Legendre polynomials versus linear splines in the Canadian test-day model

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Title Legendre polynomials versus linear splines in the Canadian test-day model
Authors/Editors* J. Bohmanova, J. Jamrozik, F. Miglior, I. Misztal and P.G. Sullivan
Where published* Interbull Bulleting
How published* Proceedings
Year* 2007
Volume 37
Publisher Interbull
Keywords Legendre polynomials, linear splines, random regression models
Genetic parameters were estimated for test-day (TD) milk, fat and protein yield, and somatic cell score for the first three lactations of 6,094 Holstein cows with 96,756 TD yields using six random regression models. Only TD with DIM ≤ 365 and all traits recorded on a test-day were included. Legendre polynomials of order four and linear splines with four to seven knots were fitted for the fixed, additive genetic and permanent environmental effects. The same type of function was applied for both fixed and random regressions. Residual variance was modeled by a step function with either four or twelve intervals. A single chain of Gibbs sampler with 100,000 samples was generated, with 10,000 samples as burn-in, in order to obtain posterior distribution of parameters. All models gave larger estimates of additive genetic variances at the beginning and at the end of lactation. Smaller variances at the extremes of lactation were estimated by models with linear splines compared to models with Legendre polynomials. Models were compared using Akaike’s information criterion, Bayesian information criterion, Bayes factor and Deviance information criterion. All the criteria favored the spline model with seven knots, which was the most complex model.
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