Comparison of Fixed- and Mixed-effects Approaches to Taper Modeling for Scots Pine in West Poland

Abstract

Diameter measurements along the stem, which are the basis for taper models, usually have a hierarchical structure. Mixed-effects models, where fixed and random effects are distinguished, are a possible solution for this type of data. However, in order to fully absorb the potential of this method, random effects prediction, which requires additional measurements (diameter along stem), is recommended. This article presents a comparison of various fitting methods (mixed- and fixed-effects model approaches) of the variable-exponent taper model created by Kozak for determining the outside bark diameter along the stem and predicting the tree volume of Scots pine trees in west Poland. During the analysis, it was assumed that no additional measured data were available for practical use; therefore, for the mixed-effects model approach, fixed effects prediction without random effects was applied. Both fitting strategies were compared based on modeling and an independent validation data set. The comparison of mixed- and fixed-effects fitting strategies for the diameter along the stem indicated that the taper model fitted using the mixed-effects model approach better fit the data. Moreover, the error rate for the total tree volume prediction for the independent data set was lower for the mixed-effects model solution than for the fixed-effects one.