Abstract

Research investigating dose-response relationships is common in agricultural science. This paper is an expansion on previous work by Guo, et al. (2006) motivated by plant nutrition research in horticulture. Plant response to level of nutrient applied is typically sigmoidal, i.e. no response at very low levels, observable response at mid-levels, point-of-diminishing returns and plateau at high levels. Plant scientists need accurate estimates of these response relationships for many reasons, including determining the lower threshold below which plants show deficiency symptoms and the point of diminishing returns, above which excessive doses are economically and environmentally costly. Guo et al. presented models and designs that address these requirements and a simulation study to assess and compare the small-sample behavior of these models and designs. This paper expands on that simulation study. In addition, a simulation study based procedure for exploring designs for experimental scenarios fitting this description is presented. This simulation study approach utilizes simulation based fit statistics in conjunction with various lack-of-fit plots to produce a design robust to multiple candidate models.

Keywords

response surface, nonlinear regression, Central Composite Design, face centered cube design, Hoerl model, Gompertz model, Mitscherlich model, Logistic model

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Apr 25th, 2:00 PM

AFTER FURTHER REVIEW: AN UPDATE ON MODELING AND DESIGN STRATEGIES FOR AGRICULTURAL DOSE-RESPONSE EXPERIMENTS

Research investigating dose-response relationships is common in agricultural science. This paper is an expansion on previous work by Guo, et al. (2006) motivated by plant nutrition research in horticulture. Plant response to level of nutrient applied is typically sigmoidal, i.e. no response at very low levels, observable response at mid-levels, point-of-diminishing returns and plateau at high levels. Plant scientists need accurate estimates of these response relationships for many reasons, including determining the lower threshold below which plants show deficiency symptoms and the point of diminishing returns, above which excessive doses are economically and environmentally costly. Guo et al. presented models and designs that address these requirements and a simulation study to assess and compare the small-sample behavior of these models and designs. This paper expands on that simulation study. In addition, a simulation study based procedure for exploring designs for experimental scenarios fitting this description is presented. This simulation study approach utilizes simulation based fit statistics in conjunction with various lack-of-fit plots to produce a design robust to multiple candidate models.