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Title: How the use of properly weighted data can aid in the selection of sorption models

item Bolster, Carl
item TELLINGHUISEN, JOEL - Vanderbilt University

Submitted to: SERA-IEG 17 Bulletin
Publication Type: Abstract Only
Publication Acceptance Date: 6/17/2010
Publication Date: 7/2/2010
Citation: Bolster, C.H., Tellinghuisen, J. 2010. How the use of properly weighted data can aid in the selection of sorption models. SERA-IEG 17 Bulletin.

Interpretive Summary:

Technical Abstract: The use of unweighted least-squares (ULS) regression is the most common method for fitting models to P sorption data; however, recent studies have shown that the assumption of constant variance inherent in ULS is unlikely to be valid for most P sorption studies. Furthermore, in most sorption studies both dependent and independent variables will have uncertainty associated with them, therefore the traditional approach of weighting sorption data solely by the inverse of the variance in the dependent variable is not a suitable regression method and in some cases may actually yield poorer parameter estimates and uncertainties than ULS. In this study we examine the role of proper weighting in the LS analysis of P sorption data when both the dependent (y) and independent (x) variables contain heteroscedastic errors by calculating an effective variance function which specifically accounts for correlated errors in x and y. We show that by using properly weighted data, the value of the weighted sum of squared errors follows an X(squared) distribution and therefore can be used as an objective criterion for assessing model fits. We also show how visual inspection of the weighted residuals can further improve the analyst’s ability to objectively make model comparisons. Using this approach on multiple data sets we show that the Langmuir model is rarely, if ever, the best model to use for assessing P sorption to soils.