Stage (1973) described an alternative method, which could be termed a "Monte Carlo swindle," 

 of introducing a stochastic element into his individual tree log of basal area growth equations 

 while maintaining the relative simplicity of a deterministic model. Because it was expected 

 that individual tree growth within a diameter class would be quite variable, elements from 

 Stage's (1973) "Monte Carlo swindle" were adapted and used in this study. 



The resulting process consists of dividing the number of trees in each diameter class into 

 thirds (one each to represent the fast, slow, and "moderate" growers), predicting the expected 

 residual for each third, and adding or subtracting this to the predicted average log of basal 

 area growth value for the diameter class. In this fashion, estimates of basal area growth are 

 obtained for each third of the diameter class. Upgrowth is then calculated separately for each 

 third, which allows the trees in a diameter class to move into a wider range of larger diameter 

 classes. More realistic predictions should result. 



The final decision before parameter estimation could begin was the choice of appropriate 

 transformations necessary to create those independent variables most likely to be highly corre- 

 lated to the dependent variable. Information used in selecting the independent variables 

 included the silvicultural literature on diameter growth factors for southwestern ponderosa 

 pine and prior general "growth and yield" knowledge reported in the mensurational literature. 

 From this work, 43 potentially useful independent variables were identified and examined in the 

 next phase of the diameter growth modeling process. 



Development of Equations 



Ordinary, least squares regression techniques were used to develop separate equations for 

 both blackjack and yellow pine. I initially separated these two vigor classes because evidence 

 from prior studies suggest significant growth differences between blackjack and yellow pine. 

 The analysis process to determine the form and parameters of the finished models required six 

 phases : 



Phase 1. An all-combinations screening run was made on each individual plot 



data set to eliminate those independent variables not highly corre- 

 lated to the dependent variable. 



Phase 2. The separate plot data were then combined into three sets: virgin, 



uneven-aged data; managed, uneven-aged data; and managed, even- and 

 uneven-aged data. A second set of all combination screening runs 

 was then made for each data set and for yellow and blackjack pine. 

 From these runs, a common set of independent variables exhibiting 

 behavior both reasonable and consistent with mensurational and 

 silvicultural expectations was selected for both yellow and black- 

 jack pine. Because the basic model forms and the size of the 

 parameter estimates differed so greatly between yellow and black- 

 jack pine, I decided that at this phase of the analysis any 

 attempt to combine the two vigor classes through use of dummy 

 variables would be futile. Therefore, separate equations were 

 maintained throughout the rest of the analysis. 



Phase 3. The combined data sets were further collapsed into two sets: uneven- 



aged and even- and uneven-aged. The reason for maintaining separate 

 sets was to allow comparison of the effect upon predictive capability 

 of adding the even-aged data to the uneven-aged. To do this merging, 

 the differences between the model coefficients for the managed and 

 the virgin data sets were handled as functions of time-since-last- 

 cutting. Sigmoidal transformations of time-since-last-cutting 

 were used because the effect of cutting was expected to asymptotically 

 approach the virgin growth rate as time-since-last-cutting increased. 

 Combining these new variables with those already selected, another 

 set of screening runs was made from which the most promising equations 

 were selected and the regression coefficients determined. Examination 

 of these coefficients showed the signs on several of the transform- 

 ations were not reasonable (including the site index transformations), 

 and that a high degree of-multicol linearity existed. 



6 



