Using Weighted Least Squares Regression for Obtaining Langmuir Sorption Constants.

One of the most commonly used models for describing phosphorus (P) sorption to soils is the Langmuir model. To obtain model parameters, the Langmuir model is fit to measured sorption data using least squares regression. Least squares regression is based on several assumptions including normally distributed and constant measurement errors. It is unclear, however, whether the error distribution representative of P sorption studies violates these assumptions. In addition, it is unknown what impact violating these assumptions has on model fits and fitted parameter estimates. Therefore, this study was undertaken to address the issue of measurement uncertainty on model fits and parameter estimates using the Langmuir model on P sorption data. First, the error structure for sorption data for five soils was determined through high replication (n = 10) P sorption studies. Based on this observed error structure, Monte-Carlo simulations were performed to compare parameter estimates between two nonlinear and four linear Langmuir equations to determine which equation provided the best parameter estimates for error structure representative of P sorption studies. Next, Monte-Carlo simulations were performed using weighted data to determine what effect ignoring measurement uncertainty had on parameter estimates. Finally, model fits and parameter estimates obtained for the five soils were compared using four different weighting schemes. Results of this study will provide useful information on the error structure representative of P sorption studies and the importance of accounting for measurement error when obtaining Langmuir constants through least squares regression analysis.