Bivariate and generalized models for taper stem representation and assortments production of loblolly pine (Pinus taeda L.)

Modeling is an important statistical tool to Forest Science, especially to forest planning by predicting the forest's yield and assortments, for instance. This paper evaluated the accuracy of bivariate and generalized linear mixed modeling in the representation of the Pinus taeda L. trunk taper and the estimation of its assortments. To compose the fitting data, 558 trees from plantations located in the Southern region of Santa Catarina, Brazil, were scaled. Initially, the data's bivariate normality was evaluated, and the bivariate standard normal distribution was fitted. Six generalized linear mixed models were fitted for the bivariate representation of diameter and height in the trunk. Afterwards, some statistical indices were obtained to verify the quality of the fitted models and, in a complementary way, of the bivariate graphs of the residuals. Even with the application of Box-Cox transformation, the results indicate the non-normality of the variables, but the transformation contributed to improve the model fitting in 50%. The ordinal and exponential models obtained the best statistics for height representation, with the Akaike Information Criterion (AIC) value being reduced from 16,430.13 to 5,686.78 when considering normal distribution. When evaluating the assortments prediction, there were high discrepancies in the estimated values (246 logs for sawmill and 120 logs for veneers) versus the observed ones (881 logs for sawmill and 628 logs for veneers), which corresponds to a 75% underestimation of total logs per hectare. Thus, the generalized linear mixed modeling improved the trunk taper representation, and the bivariate modeling was not efficient to predict assortments production.