The next step was modeling the change in model parameters across time-since-last-cutting 

 and stand structure. To model the effect of stand structure, two new variables were intro- 

 duced: RMBA. and RUBA . , which were computed by dividing MBA. (or UBA.) by total stand basal 

 area. These variables are based on the hypothesis that an even-aged"^ stand would exhibit more 

 basal area in the middle basal area class (or less of its total basal area in the upper basal 

 area class) than would an uneven-aged stand. 



Utilizing the time-since-last-cutting and two of the "stand structure" variables (RUBA3 

 and RMBA2) as independent variables themselves or as multipliers with the other variables, a 

 second set of "screening" runs was made on three data sets: blackjack pine with the even-aged 

 data, blackjack pine without the even-aged data, and yellow pine. From these runs, the two 

 most promising models from each data set were selected for more detailed analysis. The 

 independent variables for these models are found in table 27. Both blackjack pine growth 

 equations were used in each of the two blackjack pine data sets because no choice has been 

 made as to which blackjack pine growth equations will be final. 



Table 27 . --independent variables in mortality models selected from each data set for final 



analysis 



Data set 



Model number 



Independent variables 



Blackjack pine with 



1 



BJBAGl, RMBA2 



even-aged data 









2 



BJBAGl, RUBA3 





3 



BJBAG2, RMBA2 





4 



BJBAG2, RUBA 3 



Blackjack pine without 



1 



BJBAGl, A2*BJBAG1 



even-aged data 









2 



Ai*BJBAGl, 





3 



BJBAG2, Ai*BJBAG2 





4 



Ai*BJBAG2, d2 



Yellow pine 



1 



YPBAG, Ai*YPBAG 





2 



YPBAG, Ai*YPBAG, 



Up to this point, the selection of the "best" model has been made by jointly considering 

 four factors: (1) reasonableness of signs on the independent variables; (2) overall signifi- 

 cance of the model as indicated by an "F" statistic in RISK; (3) maximization of "t" values on 

 each parameter, as computed by RISK; and (4) minimization of a chi-square "goodness-of-f it" 

 value also computed by RISK. Of the three measures of fit computed in RISK (R, t, and chi- 

 square), Hamilton (1974) preferred the chi-square. Unfortunately, the chi-square tables in 

 RISK used predicted event classes too wide for the mortality data used in this study. As a 

 result, the observations fell in very few of the classes. To correct for this, a program was 

 written to compute the chi-square statistic over a reasonable range of predicted mortality 

 classes and also over diameter classes. 



Using this program, chi-square values were determined for the models selected for final 

 analysis. Analysis of the results indicated that both yellow pine equations appear to perform 

 well. Because model 2 (the model with YPBAG, A;l*YPBAG and D^) has slightly better chi-square 

 values, it was chosen as the best yellow pine mortality model. The goodness-of-fit test 

 across diameter classes is found in table 10. 



70 



