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Title: Confidence interval estimation for an empirical model quantifying the effect of soil moisture and plant development on soybean (Glycine max (L.) Merr.) leaf conductance

Author
item MATTHEWS, JESSICA - National Oceanic & Atmospheric Administration (NOAA)
item SMITH, RALPH - North Carolina State University
item Fiscus, Edwin

Submitted to: International Journal of Pure and Applied Mathematics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/20/2012
Publication Date: 4/1/2013
Citation: Matthews, J., Smith, R., Fiscus, E.L. 2013. Confidence interval estimation for an empirical model quantifying the effect of soil moisture and plant development on soybean (Glycine max (L.) Merr.) leaf conductance. International Journal of Pure and Applied Mathematics. 83(3):439-464.

Interpretive Summary: This paper addresses the uncertainty analysis of a statistical model describing the relationships between soil moisture content and leaf conductance in soybean using a variety of statistical methods. We conclude from these analyses that the wild bootstrap method is the most realistic and reliable in describing the observations.

Technical Abstract: In this work, we address uncertainty analysis for a model, presented in a companion paper, quantifying the effect of soil moisture and plant development on soybean (Glycine max (L.) Merr.) leaf conductance. To achieve this we present several methods for confidence interval estimation. Estimation of confidence intervals for model parameters and predictions is investigated using asymptotic theory, Monte Carlo methods, and bootstrap methods. A computationally feasible solution for estimating confidence intervals for model parameters via asymptotic theory is unattainable. Confidence intervals for model predictions under water-stressed environmental conditions when using asymptotic theory and Monte Carlo methods are artificially large due to underlying false assumptions of normality. For this model, where the residuals exhibit heteroscedasticity, the confidence intervals estimated by the “wild” bootstrap method appear the most realistic of the methods investigated. Of the three methods presented for estimating 95% confidence intervals for model predictions, it is our opinion that the bootstrap method is the most reliable.