Covariance Generalized Linear Models: An Approach for Quantifying Uncertainty in Tree Stem Taper Modeling

A natural dependence among diameters measured within-tree is expected in taper data due to the hierarchical structure. The aim of this paper was to introduce the covariance generalized linear model (CGLM) framework in the context of forest biometrics for Pinus taeda stem form modeling. The CGLMs are based on marginal specification, which requires a definition of the mean and covariance components. The tree stem mean profiles were modeled by a nonlinear segmented model. The covariance matrix was built considering four strategies of linear combinations of known matrices, which expressed the variance or correlations among observations. The first strategy modeled only the variance of the diameters over the stem as a function of covariates, the second modeled correlation among observations, the third was defined based on a random walk model, the fourth was based on a structure similar to a mixed-effect model with a marginal specification, and the fourth was a traditional mixed-effect model. Mean squared error and bias showed that the approaches were similar for describing the mean profile for fitting and validation dataset. However, uncertainties expressed by confidence intervals of the relative diameters were significant and related to the matrix covariance structures of the CGLMs. Study Implications: We proposed stem taper modeling based on a new class of statistical models. Covariance generalized linear models allow quantification of the stem dynamic by using a nonlinear model. Uncertainty estimates are performed on a covariance matrix given by a linear combination of known matrices. The matrices enable modeling of the nonconstant variance as well as the several correlation patterns, resulting in a framework more flexible and robust than traditional approaches usually applied for stem taper modeling. For practical purposes, uncertainty modeling can improve forest management planning, because the production limits by timber assortments are more reliable due to the confidence intervals derived from an appropriate uncertainty analysis.