Southern Research Station

Title: Modeling Multiplicative Error Variance: An Example Predicting Tree Diameter from Stump Dimensions in Baldcypress

Author: Parresol, Bernard R.

Date: 1993

Source: Forest Science, Vol. 39, No. 4, pp. 670-679

Station ID: --

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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Citation

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