Nonlinear Mixed Modeling Approach – An Application to Tree Growth Data

Nonlinear mixed-effects modeling approach was used to model the individual tree height-age relationship in Mongolian pine (Pinus sylvestris L.var.mongolica Litv.). A set of 345 pairs of height-age measurements was used to fit the model. These were taken at 30 temporary plots from natural stands. Ten nonlinear growth equations were evaluated to find a local model, which only includes the ages of the tree as explanatory variables. After selecting the local model, a nonlinear mixed model technique was applied to fit the local model. The model building process involved the estimation of fixed and random parameters and autoregressive correlation structures. The second-order moving average model MA (2) was incorporated into the mixed-effects model. The MA (2) correlation structure can explain the dependency among repeated measurements within the tree. By calibrating the model it is possible to predict random parameters of the mixed model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.