This post captures key concepts, comparisons, and design criteria for random regression models (RRMs) used to analyze longitudinal phenotypic and genomic data.

1. Comparison of Covariate Functions for Random Regression

When modeling longitudinal trajectories (such as milk yield or growth curves), the time covariate must be modeled using mathematical functions. The table below compares the most common choices:

1.1 Legendre Polynomials (Orthogonal Polynomials)

Traditionally the most popular choice in animal breeding (Kirkpatrick & Heckman, 1989; Meyer, 1998). Time is scaled to the interval $[-1, 1]$ and orthogonal polynomial terms are evaluated.