Kith the inherent difficulty of predicting mortality, I decided to include an independent 

 variable that incorporated all of the above independent variables into one. The obvious 

 choice for independent variable is predicted basal area growth. The probability of mortality 

 would decrease as basal area growth increased. Predicted basal area growth was used instead 

 of actual basal area growth because all independent variables must be observable when the 

 model is actually applied in the stand simulator (Monserud 1976) . The use of actual basal 

 area growth in equation development and then predicted basal area growth in application of 

 the equation would introduce a random variable as an independent variable, which violates one 

 of the assumptions of least squares regression. To clarify this last point, consider the 

 following example: 



Suppose you wanted to obtain an estimator of Y as a function of X (the predicted value 

 of X) because once the estimator of Y is determined, the only value available to activate the 



estimator is X. However, the observed values (Y, X) do exist prior to the development of the 



estimator. Now if Y and X are related by 



Y = Bo + BiX + El (1) 

 and if 



X - \ + e2 or (2) 



X - e2 = X, (3) 



then, if X (the observed value) is used instead of X (the predicted value) to develop equation 

 (1), the effect is to model: 



Y - 3o + 3i(X-e2) + El (3) into (1) 



= 3o + 6iX-6ie2 + El 



and Kmenta (1971) has shorn that the effect of this is to make the estimators of Sq and 

 inconsistent . 



The three predicted basal area grovrths used were: blackjack pine with the even-aged data 

 (BJBAGl), blackjack pine without the even-aged data (BJBAG2) , and yellow pine (YPBAG) . 



"Screening" Independent Variables 



Program RISK helped determine which of the independent variables best predicted mortality. 

 To do this, a run was created to fit 14 equations for the three blackjack pine data sets and 

 11 equations for the two yellow pine data sets. The three blackjack pine data sets were (1) 

 virgin uneven-aged data, (2) managed uneven-aged data, and (3) managed even-aged data; and the 

 two yellow pine data sets were (1) virgin uneven-aged data, and (2) managed uneven-aged data. 

 These preliminary data sets were chosen to both reduce the expense of running RISK on large 

 data sets, and to allow an examination and subsequent modeling of the trends in model param- 

 eters across the various data sets as functions of stand structure and time-since-last-cutting, 

 if necessary. 



For both blackjack pine and yellow pine, the results of this "screening" run indicated 

 that the only independent variables with predictive strength were D, D^, and the basal area 

 growth equations. Because the variable D2 proved to be better than D, it was used in 

 the remainder of the analysis. 



69 



