A model of the form: 



In (1.0 - Rg^j) = do * diD . ^22) 



was then tried on the remaining data sets to determine the power in the model: 



h/l " ^0 - eiD"'^l (23) 



This was also weighted and proved reasonable for Douglas-fir on the Coconino, Tonto, 

 and Lincoln National Forests. 



Both white pine and white fir on the Lincoln National Forest proved to be particu- 

 larly troublesome, with all previous attempts failing to provide a reasonable model. 

 In order to force a reasonable model on these two data sets, the following model was 

 fitted: 



1.0 - Rg/j = ^oD"^ + 91^'^ , (24) 



This was then transformed to 



Rg/j = 1.0 - ^oD"^ - giD"^ (25) 



Model (25) could not be corrected with a weighted slope because doing so caused the 

 intercept to exceed 1. 



Again, all final models, with the final slope correction multiplied into them, were 

 checked by plotting. The caution given in the section on gross International 1/4-inch 

 board foot volume for unforked trees concerning the interpretation of this approach 

 applies even more strongly here. In this case, if all of the model components were 

 multiplied out, there would be from 23 to 63 independent variables to fit and the result 

 would be even more unreasonable than in the International 1/4-inch board foot volume 

 case. 



IX. Gross Soribner Board Foot Volume — Forked Trees 



The techniques used were the same as for International 1/4-inch board foot volume 

 ■'n forked trees. In this case, however, the basic model for Douglas-fir behaved reason- 

 ably so no special effort was necessary to model it. 



X. Probability of a Tree Being Unsound in Cubic Foot Volume — Unforked and Forked Trees 



By definition, the probability of a tree being unsound must take on a value between 

 and 1. A form that constrains itself between these two values is the logistic 

 function: 



-X 



PrC =1.0/(1.0+6 ^) (26) 



c 



where 



PrC = Predicted probability of a tree being unsound in total stem and in merchant- 

 able cubic foot volume 



X = A function of the tree's measured attributes. 

 c 



Hamilton (1974) developed program RISK to fit this function to a dichotomous dependent 

 variable. The approach basically uses the first degree term of the Taylor Series expan- 

 sion of the function in weighted nonlinear regression. Output, in part, consists of 

 the regression coefficients, an F-statistic that tests the significance of the 



39 



