Transformation strategies for variables in modeling stands and natural forests

Abstract

Linear regression has been widely used in several areas of knowledge due to its practicality. In forest science, this tool is essential for modeling tree variables and relationships. However, for proper application, some assumptions must be met, among which are the normality of residuals and homogeneity of variances, which are often violated. In this perspective, variable transformation strategies represent promising alternatives for correct statistical inferences. Therefore, this study aimed to evaluate different transformation strategies in linear regression models for predicting tree height and volume in stands and natural forests. To model the height-diameter relationship, data from Pinus oocarpa stands that were 5 and 19 years-old were used. For volume modeling, natural forest databases from Amazon and Atlantic Forests were used, as well as P. oocarpa stands. Different variable transformation strategies were tested: Log, reciprocal, Box-Cox, Manly, Bickel-Doksum, Yeo-Johnson, Glog, Dual power, G power, Log shift, shifted square root, and square root. Modeling with transformed variables that simultaneously corrected the assumptions of normality of residuals and homoscedasticity were statistically evaluated to select the most appropriate strategies. Thus, transformation is indicated in situations in which at least one of the assumptions is violated. On these occasions, in studies of height-diameter relationship, Manly and Box-Cox strategies are recommended, while in volume modeling, log and Box-Cox are indicated.