Height-diameter models: a comprehensive review with new insights on relationships to generalized linear models and differential equations

Abstract

Forest scientists use regression models widely, particularly for height-diameter modeling. These models offer several benefits for estimating height in homogeneous or non-homogeneous stands. The original models for height estimation based on diameter at breast height have been extended to include other variables, thanks to technological advancements. The purpose of this article is to provide a literature review using the methodology outlined by Cervo and Bervian (2011), providing helpful information to forest biometricians in selecting a height-diameter model that utilizes historical data. The models can be classified into four main groups and extended to include other covariates besides diameter at breast height. Many of the models used data transformation but results showed that with the exception of one group (nonlinear models), all other models can be considered a generalized linear model, with corresponding linear predictors and link functions. The paper also discusses the generation process of these models, the species to which they are commonly applied, and how they can be created using general ordinary differential equations.