Modeling of the tree and stand parameters using mixed-effects models

Regression analysis is one of the most popular statistical modeling tools, which can define linear or nonlinear relationships between individual trees and stands parameters. Mixed−effects models are one of the contemporary trends of those regression methods. These models can be applied to describe such features as: height, biomass, taper, site index or volume both at the level of a single tree and whole forest ecosystems. The aim of this work is to present the characteristics of the mixed−effects model, the applicability of linear and nonlinear mixed−effects models in forest studies, and the example of a linear mixed−effects model defining the relationship between bark thickness and diameter at breast height for Scots pine (Pinus sylvestris L.) in comparison to the linear fixed−effect model. Goodness−of−fit for the obtained linear mixed−effect model indicate its better fit to the pine bark thickness than in the case of the mixed−effects model. Moreover, most of the published research results indicate the predominance of both linear and nonlinear mixed−effects models according to fixed−effect ones. These studies indicate the wide possibilities of using mixed−effect models in forestry. However, there are also results pointing to the disadvantages of these models and put into question the legitimacy of their use in forest research. This fact to some extent confirms the results (residuals behavior) obtained in this study. Therefore, it seems necessary to conduct further research, which on the one hand will allow the potential of this solution to be used, and on the other hand will help to clarify emerging doubts