A random coefficient model for chlorophyll-nutrient relationships in lakes


Journal Article

Statistical models of nutrient-phytoplankton relationships in lakes are usually fitted on cross-sectional data sets and thus describe multi-lake behavior using a single set of global model parameters. As a result, prediction of individual lake response reflects behavior among lakes, increasing prediction error by the among-lake variance. Alternatively, a random coefficient model may be applied to the same cross-sectional data set to yield lake-specific parameters as opposed to a single set of global parameters. The random coefficients are based on classical estimators that reflect both global behavior and lake-specific response. Under normality, known variance, and a noninformative prior, the mean of the posterior Bayesian distribution on the lake-specific parameters is equivalent to the estimated random coefficients. In this study, the random coefficient model was applied to a cross-sectional data set on chlorophyll a, nitrogen, and phosphorus in North Carolina lakes. Both global and lake-specific parameters were estimated for these data. A second data set representing different years of observations for the same lakes was used to compare the two modeling approaches on the basis of prediction variance; the result was a 12.7% reduction in mean squared prediction error for the random coefficient model. Other applications of the random coefficient model in empirical and mechanistic modeling are suggested in a concluding discussion. © 1993.

Full Text

Duke Authors

Cited Authors

  • Reckhow, KH

Published Date

  • January 1, 1993

Published In

Volume / Issue

  • 70 / 1-2

Start / End Page

  • 35 - 50

International Standard Serial Number (ISSN)

  • 0304-3800

Digital Object Identifier (DOI)

  • 10.1016/0304-3800(93)90071-Y

Citation Source

  • Scopus