Estimation of nutrient requirements using broken-line regression analysis1

Abstract

We evaluated and compared various broken-line regression models and SAS (SAS Inst. Inc., Cary, NC) procedures for estimating nutrient requirements from nutrient dose response data. We used the SAS (Version 9) procedures NLIN and NLMixed and the response data of Parr et al. (2003), who evaluated the isoleucine requirement of growing swine. The SAS NLIN was used to fit 2 different broken-line regression models: a simple 2 straight-line, one-breakpoint model and a quadratic broken-line model in which the response below the single breakpoint was quadratic; there was a plateau above the breakpoint. The latter was fit using 2 different approaches in NLIN. We also used SAS NLMixed to fit 3 different broken-line models: the 2 straight-line, one-breakpoint model that included a random component for the plateau; the quadratic broken-line model that included a random component for the plateau; and the quadratic broken-line model that included random components for both the plateau and the slope of the curve below the requirement. The best fit (greater adjusted R2; least log likelihood) was achieved using SAS NLMixed and the quadratic model with a random component for asymptote included in the model. Model descriptions, SAS code, and output are presented and discussed. Additionally, we provide other examples of possible models and discuss approaches to handling difficult-to-fit data.