Polynomial order selection in random regression models via penalizing adaptively the likelihood.

Area of Science:

• Animal Breeding and Genetics
• Statistical Genetics
• Quantitative Genetics

Background:

• Random regression models (RRM) utilize orthogonal Legendre polynomials (LP) to describe genetic and environmental effects.
• Akaike (AIC) and Bayesian (BIC) information criteria are commonly used for selecting LP order but have theoretical limitations in optimality.
• The need for a more robust criterion for LP order selection in RRM is evident.

Purpose of the Study:

• To introduce and evaluate the 'penalizing adaptively the likelihood' (PAL) method for selecting LP order in RRM.
• To compare the performance of PAL against AIC and BIC using simulated and real data.
• To assess the ability of PAL to identify the correct model order, even when the true model is not among the candidates.

Main Methods:

• Fitting nested models to simulated and real datasets (60,513 records from 6675 Colombian Holstein cows).
• Calculating Akaike (AIC), Bayesian (BIC), and penalizing adaptively the likelihood (PAL) for each fitted model.
• Evaluating the probability of each criterion selecting the true or best model order.

Main Results:

• PAL and BIC correctly identified the true LP order for additive genetic and permanent environmental effects with 100% probability in simulations.
• AIC tended to select overly complex models (over-parameterization).
• When the true model was unknown, PAL selected the best model more frequently than AIC, while BIC failed to select the best model.

Conclusions:

• The penalizing adaptively the likelihood (PAL) method is a reliable criterion for selecting Legendre polynomial order in random regression models.
• PAL demonstrates superior performance compared to AIC and BIC, particularly in scenarios where model uncertainty exists.
• PAL offers a robust approach to model order selection in genetic and environmental effect modeling.