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Title: Modeling Multiplicative Error Variance: An Example Predicting Tree Diameter from Stump Dimensions in Baldcypress
Author: Parresol, Bernard R.;
Source: Forest Science, Vol. 39, No. 4, pp. 670-679
Publication Series: Miscellaneous Publication
Description: In the context of forest modeling, it is often reasonable to assume a multiplicative heteroscedastic error structure to the data. Under such circumstances ordinary least squares no longer provides minimum variance estimates of the model parameters. Through study of the error structure, a suitable error variance model can be specified and its parameters estimated. This error model is used to construct a covariance matrix which in turn is used to form an estimated generalized least squares estimator of the forest model parameters. The theory is illustrated with data on baldcypress (Taxodium distichum [L.] Rich.). A multiple linear regression equation is developed for predicting diameter at 3 m from solid-wood stump diameter (i.e., diameter inside the fluting) and stump height. By modeling the error structure, standard errors on three of the four coefficients from the tree diameter-stump dimensions regression were reduced by 13 to 50%. The effect on prediction confidence intervals is graphically illustrated.
Keywords: Heteroscedasticity, consistency, estimated generalized least squares, prediction confidence intervals.
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Parresol, Bernard R. 1993. Modeling Multiplicative Error Variance: An Example Predicting Tree Diameter from Stump Dimensions in Baldcypress. Forest Science, Vol. 39, No. 4, pp. 670-679
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