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Progress Report-2001 |
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FINAL REPORT |
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TITLE: Evaluating the Statistical Characteristics of Bioeconomic Model Parameters and their Impact on Net Returns
PERSONNEL: Bruce D. Maxwell and Marie Jasieniuk
TIME LINE: Initiation date: September 1, 1999 Termination data: September 14, 2002
ORIGINAL HYPOTHESIS: The bootstrap method was originally hypothesized as a means of evaluating the characteristics of the statistics used by the bioeconomic model in order to determine the accuracy of those predictions.
SUMMARY OF PROGRESS: The bioeconomic model uses parameters estimated by fitting demographic and interference equations to data from winter wheat-jointed goatgrass competition experiments to predict the impact of various management options on jointed goatgrass densities and net returns. To date, we have used classical least squares regression to fit model parameters and evaluate the statistical characteristics of the parameter estimates. However, this approach has not been successful because least squares methods have two major weaknesses: (1) the use of point estimates for regression parameters conceals the uncertainty about the parameter estimates and (2) the least squares approach is not based on a precise definition of the error structure in the available data. To evaluate the statistical characteristics of the model predictions, including their accuracy, and to construct confidence intervals around the parameter estimates, clear assumptions about the distributional properties of the error and the source of the error are required. Parameter estimation based on maximum likelihood analysis, in contrast to least squares methods, offers a statistical framework within which models can be fit to data with consideration of error structure. We applied such a maximum likelihood regression approach to the analysis of winter wheat-jointed goatgrass data sets.
OBJECTIVES: To evaluate the statistical characteristics of bioeconomic model parameters and their impact on net returns.
EXPERIMENTAL DESIGN: The analysis consisted of a two step procedure. In the first step, 18 nonlinear crop-weed interference models were fit to the data for each site and year using maximum likelihood regression methods (Proc NLP: SAS V. 8). In this method, the probability of the observed data values arising from the parameter estimates is maximized rather than minimizing the sums of squared deviations of observed from expected, which is characteristic of least squares regression. A lognormal error structure was assumed. The Akaike information criterion for small sample sizes (AICC ) and the Bayesian information criterion (BIC) (Akaike 1973; Hilborn and Mangel 1997; Burnham and Anderson 1998) were then used to select the “best approximating models” (sensu Burnham and Anderson 1998) for inference about crop-weed competition from the data.
The second step of the statistical analysis involved quantifying the uncertainty about the parameter values using the bootstrap method (Efron and Tibshirani 1993). Data from each site and year were resampled with replacement 2000 times. Parameters for the selected models were estimated for each of the 2000 bootstrap samples using maximum likelihood regression. Ninety-five percent confidence intervals were then calculated from the bootstrap distributions using the percentile bootstrap (Dixon 1993) because the bootstrap distributions were generally centered around the observed values.
PROGRESS/CONCLUSIONS: Previously, we used least squares regression methods to fit demographic and interference equations to data from winter wheat-jointed goatgrass competition experiments, estimate model parameters, and evaluate the statistical characteristics of the parameter estimates (Jasieniuk et al. 1999, 2001 listed in the PUBLICATIONS section). However, this approach has been only partially successful because least squares methods have two major weaknesses: (1) the use of point estimates for regression parameters conceals the uncertainty about the parameter estimates and (2) the least squares approach is not based on a precise definition of the error structure in the available data. To determine the accuracy of model predictions, and to construct confidence intervals around the parameter estimates, clear assumptions about the distributional properties of the error and the source of the error are required. Parameter estimation based on maximum likelihood analysis, in contrast to least squares methods, offers a statistical framework within which models can be fit to data with consideration of error structure. We applied such a maximum likelihood regression approach to the winter wheat-jointed goatgrass data sets but insufficient data points in these data sets prevented us from obtaining reasonable parameter estimates. Hence, we have focused our efforts on barley-wild oat data sets from Montana because they have three to five times more data points than the winter wheat-jointed goatgrass data sets. The analysis takes an information-theoretic approach that treats model formulation, model selection, and the estimation of model parameters and their uncertainty in a unified manner under a common framework (Burnham and Anderson 1998). Data analysis is almost complete and a manuscript describing the methodology and results will be submitted for publication in Weed Science by July 2002. The new statistical approach will be applicable to any crop-weed system, including the analysis of winter wheat-jointed goatgrass interference interactions, providing that sufficient data points are available.
PUBLICATIONS: A manuscript on this research will be submitted for publication in Weed Science by July 2002. This will be the third of a series of papers published in Weed Science on crop yield/yield loss-weed density functional relationships to be used in the winter wheat-jointed goatgrass bioeconomic model. The first two publications are listed below.
Jasieniuk, M., B. D. Maxwell, R. L. Anderson, J. O. Evans, D. J. Lyon, S. D. Miller, D. W. Morishita, A. G. Ogg, Jr., S. Seefeldt, P. W. Stahlman, F. E. Northam, P. Westra, Z. Kebede, and G. A. Wicks. 1999. Site-to-site and year-to-year variation in Triticum aestivum - Aegilops cylindrica interference relationships. Weed Sci. 47:529-537.
Jasieniuk, M., B. D. Maxwell, R. L. Anderson, J. O. Evans, D. J. Lyon, S. D. Miller, D. W. Morishita, A. G. Ogg, Jr., S. Seefeldt, P. W. Stahlman, F. E. Northam, P.Westra, Z. Kebede, G. A. Wicks. 2001. Evaluation of models predicting winter wheat yield as a function of winter wheat and jointed goatgrass densities. Weed Sci. 49:48-60.
TECHNOLOGY TRANSFER ACTIVITIES: A manuscript describing the results of the statistical analyses will be submitted for publication in Weed Science by July 2002. This will be the third of a series of papers critically evaluating crop yield/yield loss-weed density functional relationships to be used in the winter wheat-jointed goatgrass bioeconomic model for the prediction of the impact of various management options on jointed goatgrass densities and net returns. Results of the research will also be presented at upcoming WSSA and WSWS annual meetings. |
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