Mixed-effects generalized height–diameter model for young silver birch stands on post-agricultural lands

Abstract The purpose of creating regression equations is often to predict unmeasured features based upon more easily obtainable ones. Species-specific height–diameter (H–D) models of trees are an example of this situation and can be defined as either simple or generalized. Simple H–D models express height as a function of tree diameter at the breast height. They are easily applicable without additional measurement but do not take properly into account the variability in H-D relationship between stands. Meanwhile, generalized models also include stand-level predictors. The H-D data sets are often characterized by a grouped structure. The mixed-effects modeling approach is a mainstream method employed for these types of forestry data. In this study, we created a mixed-effects generalized H–D model for young silver birch stands on post-agricultural lands in central Poland. This model was chosen from among 11 simple nonlinear models based on the goodness of fit and residual behavior. We accounted for two stand-level predictors that did not require additional measurements beyond tree diameter at the breast height: quadratic mean diameter at the breast height and basal area. Fixed- and random-effect predictions were then calculated to illustrate that increases in the number of measured trees improves height predictions. Moreover, the gain in predictive power is the largest if extreme trees (i.e., from the extrema of the diameter range) are used for random-effect prediction.