APPENDIX F 

 DEVELOPMENT OF A CONVERSION MODEL 



I h)'pothesized that the following independent variables might prove useful for predicting 

 the conversion rate: diameter class size (D) , site index (S) , total number of trees 7.6 inches 

 and larger (TT8) , total basal area in trees 7.6 inches and larger (BA8) , total number of trees 

 in the diameter class (TTDC) , and total basal area in the diameter class (BADC) . Except for 

 site index, I expected that as each of these independent variables increased, the conversion 

 rate would increase. The opposite would hold true for site index. 



The expected relationships between the proposed independent variables and the conversion 

 rate were based upon how changes in these independent variables would affect growth. Growth 

 and vigor are intimately related, and it was expected that a decrease in growth rate would 

 cause an increase in the conversion rate. Therefore, any of the proposed independent variables 

 that would reduce the growth rate as they increased in value would also be expected to increase 

 the conversion rate. 



Based on the same reasoning as discussed in the mortality rate section, 1 decided to 

 express the conversion rate as a proportion. To model this, program RISK was again used. The 

 dichotomous dependent variable was defined as 1.0 if the tree converted to a yellow pine, and 

 a value of 0.0 if it did not. 



Twenty-two regression runs were then made using the data reserved for modeling. These 

 runs were selected to cover most, if not all, reasonable combinations of the independent 

 variables. The runs allowed decisionmaking at various points during the analysis on what 

 combinations of independent variables to examine next. Chi-square values across diameter 

 classes and across predicted conversion classes for the three best models were then examined. 

 In all cases, the predicted values were significantly different from the actual values at the 

 99 percent testing level. An analysis of the chi-square values for the best model indicated 

 the primary area of misfit was in the 12-inch diameter class. A review of the basic data also 

 revealed that all of the conversions in the 11-, 12-, and 13-inch diameter classes and two of 

 the three conversions in the 14-inch diameter class occurred on subplot 13 of plot 61. 



I then decided to circumvent the problem of lack of fit by strengthening the data base. 

 This was done by adding to the conversion data base those subplots originally eliminated 

 because of a highway running through them. Using this expanded data set, the 25 new runs were 

 made using the same procedures as described for the first set of runs. Again, the chi-square 

 values for the three best models indicated a significant difference between predicted and 

 actual values. As before, the lack of fit was due to the high number of conversions on subplot 

 13 in the 11-, 12-, 13-, and 14-inch diameter classes. 



I eliminated subplot 13 from the data base as being atypical of the conversion process, 

 then made the 10 runs listed in table 31. This time, the chi-square values of the three best 

 models (5, 9, and 10) indicated no significant difference at the 99 percent testing level 

 between predicted and actual conversion values across predicted conversion classes. Across 

 diameter classes, only model 9 did not differ significantly from the actual data (table 16) 

 and was therefore chosen as the final model fitted to this data set. 



To test model 9 further, the model was checked against validation data. Across predicted 

 conversion classes, the chi-square value for the validation data was 140.9 with 6 d.f., while 

 across diameter classes it was 178.8 with 7 d.f. In both cases, the difference between predicted 

 and actual conversion was significant at the 99 percent testing level. An examination of the 

 validation data showed that, like subplot 13 of the original data, subplot 16 exhibited a 

 large number of conversions in the 12-inch diameter class. Wny this peculiarity exists in 

 this diameter class on these two subplots is unkno\m, but 1 eliminated subplot 16 from the 

 validation data also. The resulting chi-square fit for this modified validation data set was 

 3.4 with 7 d.f. across diameter classes (table 32) and 3.4 with 6 d.f. across predicted con- 

 version classes. Both of these chi-square statistics were insignificant, indicating a good 

 fit to the modified validation data set. 



75 



