Model Building in Multi-Factor Plant Nutrition Experiments

Abstract

Often, the goal of plant science experiments is to model plant response as a function of quantitative treatment factors, such as the amount of nutrient applied. As the number of factors increases, modeling the response becomes increasingly challenging, especially since the resources available for such experiments are usually severely limited. Typical methods of analysis, notably second-order response surface regression, often fail to accurately explain the data. Alternatives such as non-linear models and segmented regression have been used successfully with two-factor experiments (Landes, et. aI, 1999). This paper extends previous work to three-and-more factor experiments. Models are assessed to explain the relationship between the levels of nutrients applied and leaf, root, and shoot responses of Poinsettias from an experiment conducted by horticultural researchers at the University of Nebraska-Lincoln. These data illustrate problems that are representative of those that plant researchers typically face. Multiple regression using the Hoed function proved to be especially useful. These analyses suggest a feasible approach to design of experiments suitable for a wide variety of plant science applications with multiple factors and limited resources.

After Further Review: An Update on Modeling and Design Strategies for Agricultural Dose-Response Experiments

“…One such model is the linearized Hoerl model, suggested by Olson, et al (2001). For a single factor the deterministic component of the Hoerl model is…”

A Comparison of Models and Designs for Experiments With Nonlinear Dose-Response Relationships

“…Nonlinear models offer an alternative. In previous Applied Statistics in Agriculture conferences, Landes, et al (1999) and Olson, et al (2001) presented the foundations of this paper's approach. Landes, et al (1999) presented adaptations of Gompertz and Mitscherlich nonlinear models to fit plant nutrition data from Macz et al (1997).…”

“…Running a succession of small experiments to search the experimental region is usually not an option. Olson, et al (2001) proposed a design approach for such experiments. The basic idea is that standard response surface designs -e.g.…”

“…One can easily see that the accuracy of the model fit is vastly improved. Olson, et al (2001) β β β denote main effect, 2-way interaction, 3-way interaction, etc. coefficients associated with the log levels, ln(X i ), of the i th factor.…”

“…Landes, at al. (1999 andOlson et al (2001) did initial work identifying potentially useful models. Paparozzi, et al (2005) investigated dose (micro-and macro-nutrient) response (elemental leaf and stem concentration) relationships in Poinsettia.…”