A comparison of quadratic versus segmented regression procedures for estimating nutrient requirements

Continued improvements in dietary formulation will require increasingly detailed knowledge of nutrient requirements. The objective of this study was to evaluate bias and precision of estimates of nutrient requirements from quadratic versus segmented regression. One hundred 0-to-3-wk turkey growth experiments were simulated to provide data with known nutrient requirements. Nine diets contained levels of an arbitrary nutrient ranging from 80 to 120% of recommended. The true nutrient requirement was uniformly randomly distributed between 90 and 110% of recommended. The requirements were estimated as the intersection of the segmented regression lines from a two-slope model, and 0.90 and 0.95 of the maximum gain predicted from quadratic regression coefficients. The mean true requirement was 99.42%, and predictions were 102.14+/-0.61, 107.81+/-0.61, and 99.59+/-0.61% for 0.90 of quadratic maximum, 0.95 of quadratic maximum and segmented regression, respectively. The segmented regression resulted in the closest prediction to the true nutrient requirement in 73 of 100 replicates. The average squared deviation of the requirement from their estimates were 15.18 for 0.90 of quadratic maximum, 78.72 for 0.95 of quadratic maximum, and 2.41 for segmented regression. The quadratic regressions yielded overestimates, particularly when the experimental diets were not centered on the requirement, suggesting that a bias can be introduced by experimental design. Segmented regression procedures resulted in more precise estimates of nutrient requirements, were less likely to suffer from bias, and required less a priori knowledge of the true requirement than did quadratic regression procedures.