Comparison of a modified log-logistic distribution with established models for tree height prediction

Abstract

The complexity of data structure from different forest stands across the world has necessitated the continuous introduction of new models in forestry. No single model is expected to provide accurate fit to all data sets. Therefore, in this study, the cumulative distribution function (cdf) of the Log-Logistic distribution was modified to construct a new height-diameter (h-d) model for Gmelina arborea Roxb plantation in Omo Forest Reserve, Nigeria. A total of 60 sample plots of 0.04 ha were used in this study. Tree diameters and heights measurement were taken on 1,189 trees. The new h-d model was termed M. LogL and its performance was compared with five established traditional h-d models that have been used in quantitative forestry study. These include: Logistic h-d, Chapman-Richards (C-R) h-d, Weibull h-d, Näslund h-d and Curtis h-d. Model assessment was based on adjusted R², root mean squared error (RMSE), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC). The result showed that the performance of the new M. LogL h-d was comparable to other traditional h-d models used in forestry. The adjusted R2, RMSE, AIC, BIC and HQC were 0.629, 3.343, 2555.599, 2565.527 and 2555.480, respectively. However, the Logistic h-d model had the overall best fit to the data set. The order of ranking was: Logistic > M. LogL > Curtis > C-R > Weibull > Näslund. Therefore, the M. LogL model can be used to predict tree height for the Gmelina arborea plantation.

Keywords: Modified Log-Logistic, height-diameter, Gmelina arborea, Omo forest reserve