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

Abstract

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. For. Sci. 39(4):670-679.

Heteroscedasticity, consistency, estimated generalized least squares, prediction confidence intervals