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.

Soybean [Glycine max (L.) Merr.] is a versatile crop due to its multitude of uses as a high protein meal and vegetable oil. Soybean seed traits such as seed protein and oil concentration and seed size are important quantitative traits. The objective of this study was to identify representative protein, oil, and seed size quantitative trait loci (QTL) in soybean. A recombinant inbred line (RIL) population consisting of 131 F6-derived lines was created from two prominent ancestors of North American soybeans ('Essex' and 'Williams') and the RILs were grown in six environments. One hundred simple sequence repeat (SSR) markers spaced throughout the genome were mapped in this population. There were a total of four protein, six oil, and seven seed size QTL found in this population. The QTL found in this study may assist breeders in marker-assisted selection (MAS) to retain current positive QTL in modern soybeans while simultaneously pyramiding additional QTL from new germplasm.

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Repeated measures data occur in a wide variety of experimental situations and are often analyzed without full consideration of the statistical issues involved. In this paper, a discussion of model construction, univariate versus multivariate solutions, and statistical assumptions is motivated by examples from a tree physiology experiment. In addition, several examples from the forestry literature are reviewed. It is hoped that this discussion will help scientists with little statistical training to become aware of the different analyses available and perhaps to recognize the associated models in their own research. The examples range from a simple repeated measures design with one within-subject factor and no between-subjects factors to a more complex design involving multiple within-subject and between-subjects factors. The modelling approach used here permits a straightforward comparison between the univariate and multivariate solutions. Although no single approach is consistently best, the multivariate approach is always appropriate and provides the same interpretations as the univariate approach. However, when appropriate assumptions such as sphericity are met, power considerations tend to favor the more traditional univariate analysis.