Properties of random regression models using linear splines.

Properties of random regression models using linear splines (RRMS) were evaluated with respect to scale of parameters, numerical properties, changes in variances and strategies to select the number and positions of knots. Parameters in RRMS are similar to those in multiple trait models with traits corresponding to points at knots. RRMS have good numerical properties because of generally superior numerical properties of splines compared with polynomials and sparser system of equations. These models also contain artefacts in terms of depression of variances and predictions in the middle of intervals between the knots, and inflation of predictions close to knots; the artefacts become smaller as correlations corresponding to adjacent knots increase. The artefacts can be greatly reduced by a simple modification to covariables. With the modification, the accuracy of RRMS increases only marginally if the correlations between the adjacent knots are > or =0.6. In practical analyses the knots for each effect in RRMS can be selected so that: (i) they cover the entire trajectory; (ii) changes in variances in intervals between the knots are approximately linear; and (iii) the correlations between the adjacent knots are at least 0.6. RRMS allow for simple and numerically stable implementations of genetic evaluations with artefacts present but transparent and easily controlled.