Mixed-effects modeling of shortleaf pine (Pinus echinata Mill.) growth data

Abstract

Scope and Methods of Study: The objective of this study was to develop individual-tree mixed-effects models for basal area growth and the diameter-height relationship of shortleaf pine (Pinus echinata Mill.). Repeated measurements for attributes including diameter at breast height and total height from over 200 permanent plots were available from eastern Oklahoma and western Arkansas. Models with plot random-effects were fitted using the S-Plus nlme library and SAS PROC NLMIXED utilizing a calibration dataset. Models with independently and normally distributed errors were fitted first. Then possible spatially correlated and/or heterogeneous within-plot errors were modeled for basal area growth. The most promising models were tested using an independently selected dataset from the same study.

Results and Conclusions: Though increasingly popular in forestry, mixed-effects modeling technique has never previously been used in shortleaf pine growth modeling. Nonlinear mixed models with plot random-effects were found to fit the data better than the models fitted with a complete random sample assumption (the ordinary least-squares method) as reported in Lynch et al. (1999) for both a basal area growth model and a model for diameter-height relationship. Because data were grouped by plots, a mixed-effects model with plot-level random-effects was a more realistic representation of the data structure than ordinary least squares. Spatial correlation among tree measurements within a plot did not appear to be important in presence of plot random-effects. However, variance modeling using a variance function with tree basal area as a covariate accounted for heterogeneity of within-plot errors better than the modeling approach in which constant variance was assumed.