Modeling response curves and testing treatment effects in repeated measures experiments: a multilevel nonlinear mixed-effects model approach
Dehai Zhao, Machelle Wilson, and Bruce E. Borders
Abstract: 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.
SREL Reprint #2824
Zhao, D., M. Wilson and B. E. Borders. 2005. Modeling response curves and testing treatment effects in repeated measures experiments: a multilevel nonlinear mixed-effects model approach. Canadian Journal for Research 35:122-132.
