Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments

ABSTRACT. A modified Richard's extension model with nonlinear mixed results is developed for modeling slash pine (Pinus elliottii Engelm) dominant height expansion in conjunction with different silvicultural treatments. All three parameters in the pattern turn out to have the two fixed and random individual piece of ground or silvicultural treatments effects. Moving average correlation with 2 was identified as within-plot error arrangement The advantages of the mixed consequences model in prediction for of recent origin responses are demonstrated in detail through formulations and examples. The modified Richards type has a form that combines dominant height extension and site index into individual model form, so the incompatibility between height increase and site index model can be avoided. The general methodologies of nonlinear mixed consequences model building, such as which parameters in the protoplast should be considered to be random and which should be genuinely fixed, howto determine appropriate within-plot variance covariance form and how to specify between-plot variation via appropriate covariate modeling, are addressed in detail. Likelihood ratio proof and Akaike information criterion (AIC) are used in pattern performance evaluation. Some useful graphical archetype diagnosis tools are also not awayed FOR. Sci. 47(3):287-300.

Key Words: Random issues site index model, base age invariant, prediction variance, repeated measurements.

PERMANENT SAMPLE plats measured repeatedly over a fixed extent of time, are often used for evaluating forest development and yield and are especially effective as a sampling rule to evaluate changes in forest conditions (Avery and Burkhart 1994 p 208) In the practice of intensive forest management, more [i]or[/i] less new attributes are added into the usual permanent plat sampling method. For example, to accelerate stand expansion and development and to increase financial turn backs silvicultural treatments such as mechanical and chemical site preparation and herbicide or fertilization applications are true common. To monitor and predict the changes of forest stands with different silvicultural treatments or factors, the permanent piece of grounds are usually established in a more careful way: they are actually built up from more [i]or[/i] less standard experimental design. For example, a split-plot design is frequently used in the southeastern United States. In individual such designed study, soil mark serves as the whole-plot factor and silvicultural treatment as the split-plot factor (Shiver et al. 1994) A split-plot design with repeated measurements naturally forms a split-split piece of ground design with the time factor as the within-plot consequence (Gumpertz and Brownie 1993).

In the forestry literature, a for the use of all approach to modeling such split-plot repeated measurement data from permanent piece of grounds is to only "adjust" the fixed part of the design with some additional fixed bourns that partially explain the "gains" from the silvicultural treatments (Pienaar and Rheney 1995 Martin et al. 1999 Castleberry 1998) The advantage of this approach is its simplicity. It allows any treatment results on forest growth and yield to be explicitly squeeze outed in the model. However, the special properties of split-plot repeatedmeasurement data as discussed above are partially or totally ignored by dint of this approach. For example, the variability of individual plats or within-plot correlation is rarely taken into account in of the like kind an approach. Consequently, different plats no matter how different their piece of ground attributes, will obtain exactly the same "gains" as lengthy as they are treated by means of the same silvicultural treatments. This is usually not realistic, however. Also, any information contained in past observations for a piece of ground or stand is only partially applicable in this approach when predictions are desired for wait fored future values for a specified piece of ground

Gregoire et al (1995) not long ago presented a linear mixed consequences model based on data from permanent piece of grounds and justified the necessity of an appropriate variance-covariance for the modeling of like data. While linear models can be made robust to assumptions about the correlation, especially when the number of observations by plot are small relative to the number of plats (Diggle et al. 1994, p 79) this is not always pure for nonlinear models. The expectation of an individual mean answer usually does not coincide with the marginal mean of the population for a nonlinear pattern (Zeger et al. 1988, Vonesh and Chinchilli 1997 p 295) Thus it is obviously inappropriate to use a population mean rejoinder as the prediction for an individual whose former information is available.

The idea of a random consequences model is not new in forestry. Conceptually it goe back as early as Dr JL Clutter's Duke University PhD dissertation, which is single of the earliest recognitions of the uniqueness of repeated measurements in a forestry connection (Clutter 1961). Clutter noted that the independent randomness assumption in regression analysis is violated by means of the repeated sampling nature of data from permanent plats and a corresponding adjustment in regression analysis may be necessary. His original assumption that observations from a particular plat may reflect an underlying pattern which is particular to that plat and a function of time as well is broadly implemented today through a random effects model the two in statistics and in widespread applied fields, including forestry. Bailey and Clutter's (1974) article, in which the conception of varying parameters uniquely identified with sites (plot-specific parameters) was introduced, can be considered the pioneering work in forestry. Thereafter, other prototypes with varying or random coefficients were introduced in forestry (Garcia 1983 Borders and Bailey and confused noise 1984, Biging 1985, Lappi and Bailey, 1988 McDill and Amateis 1992 Lappi and Malinen 1994)