Nonlinear multilevel seemingly unrelated height-diameter and crown length mixed-effects models for the southern Transylvanian forests, Romania

In this study, we used an extensive sampling network established in central Romania to develop tree height and crown length models. Our analysis included more than 18 000 tree measurements from five different species. Instead of building univariate models for each response variable, we employed a multivariate approach using seemingly unrelated mixed-effects models. These models incorporated variables related to species mixture, tree and stand size, competition, and stand structure. With the inclusion of additional variables in the multivariate seemingly unrelated mixed-effects models, the accuracy of the height prediction models improved by over 10% for all species, whereas the improvement in the crown length models was considerably smaller. Our findings indicate that trees in mixed stands tend to have shorter heights but longer crowns than those in pure stands. We also observed that trees in homogeneous stand structures have shorter crown lengths than those in heterogeneous stands. By employing a multivariate mixed-effects modelling framework, we were able to perform cross-model random-effect predictions, leading to a significant increase in accuracy when both responses were used to calibrate the model. In contrast, the improvement in accuracy was marginal when only height was used for calibration. We demonstrate how multivariate mixed-effects models can be effectively used to develop multi-response allometric models that can be easily calibrated with a limited number of observations while simultaneously achieving better-aligned projections.