A Comparative Assessment of Alternative Approaches to Tree Diameter Increment Modelling

Tree diameter increment data are often characterized by skewness and heteroscedasticity. Increments can also be so small that null values are recorded in the field. Several modelling approaches exist to tackle these issues. We compared four approaches to diameter at breast height (DBH) increment modelling: (i) traditional linear regression of log-transformed shifted DBH increments, (ii) the truncated standard Tobit model applied to the same response, and two generalized linear models (GLM) based on the (iii) Gamma and (iv) inverse Gaussian distributions. We fitted a simple model with each approach to black spruce (Picea mariana (Mill.) BSP) DBH increments measured in permanent sample plots in Quebec, Canada. The comparison relied on biases per decile of predicted values and the generalized Pearson χ² statistic. The truncated standard Tobit model showed the smallest biases, followed by the Gamma GLM and traditional linear regression. The inverse Gaussian GLM yielded the worst fit. Although the logarithmic transformation of response variables has been criticized in the literature, coupling it with a truncated standard Tobit model can yield a statistically sound model. We conclude that this novel approach should be regarded as an effective tool, not dismissed solely because the response variable is log-transformed.