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Research investigating dose-response relationship is common in agricultural science. Animal response to drug dose and plant response to amount of irrigation, pesticide, or fertilizer are familiar examples. This paper is 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 1) to determine lower threshold below which plants show deficiency symptoms and 2) to determine upper point-of-diminishing returns, above which excessive doses are economically and environmentally costly. Landes, at al. (1999 and Olson et al. (2001) did initial work identifying potentially useful models. Paparozzi, et al. (2005) investigated dose (microand macro-nutrient) response (elemental leaf and stem concentration) relationships in Poinsettia. They found that 1) nutrients must be considered as a system, hence multifactor experiments are essential, 2) resources are limited, meaning that experiments must use response-surface principles, and 3) nutrient-response relationships are rarely modeled adequately by 2 order polynomial regression models, so standard response surface methods are inadequate. This paper presents models and designs that address these requirements and a simulation study to assess and compare the small-sample behavior of these models and designs.

A COMPARISON OF MODELS AND DESIGNS FOR EXPERIMENTS WITH NONLINEAR DOSE-RESPONSE RELATIONSHIPS