Modeling response curves and testing treatment effects in repeated measures experiments: a multilevel nonlinear mixed-effects model approach

A multilevel nonlinear mixed-effects modeling approach is used to model loblolly pine (Pinus taeda L.) stand volume growth in conjunction with four silvicultural treatments. Comparisons of treatment effects over time are integrated with the model-building process. Three-level random effects are introduced into a modified Richards growth model. Within-plot heterogeneity and correlation still occur, which are described by the exponential variance function and a first-order autoregressive model. The combination of complete vegetation control with fertilization results in the largest growth response; annual fertilization has the next largest growth response, with the exception that at very early stages the response is lower than that of vegetation control only; the control has the lowest growth response. The advantages of the multilevel nonlinear mixed effects model include its ability to handle unbalanced and incomplete repeated measures data, its flexibility to model multiple sources of heterogeneity and complex patterns of correlation, and its higher power to make treatment comparisons. We address in detail a general strategy of multilevel nonlinear mixed effects model building.