Comparing the logarithmic transformation and the Box-Cox transformation for individual tree basal area increment models

Abstract

Individual tree growth models are increasingly being used in silviculture scenario simulation at the stand level or in forecasts of wood supply on a large scale, and there is a correspondingly substantial number of published diameter increment models. In most cases, the relationship between individual tree basal area increment or diameter increment and covariables was described by a linear regression. In doing so, the logarithmic transformation for left-sided variable transformation was used exclusively to meet the assumptions of regression analysis. The Box-Cox transformation is one alternative that has scarcely been used to date in forest growth modeling. The two transformation approaches were compared using a simple individual tree basal area increment model with four tree species. The results were as follows: (1) the Box-Cox transformation yielded a better residual structure of the models by reducing the skew; (2) the transformation bias is smaller using the Box-Cox transformation; (3) the mean squared error of estimation is smaller with the Box-Cox transformation; and (4) the Box-Cox transformation leads to systematically higher estimated values than logarithmic transformation. On the basis of the results presented here, it is recommended that the Box-Cox transformation should be considered as a viable alternative in statistical modeling in forestry and in other fields as well if the transformation of variables is required.