Gate 4: Necessary engineering, logging, and environ- 

 mental cost information is gathered. Timber value is set, 

 the appraisal is prepared, and the total sale package is 

 reviewed. 



Gate 5: Bids are accepted and the successful bidder is 

 determined. The output is the bid report. 



Gate 6: The winning bidder is evaluated with respect to 

 financial qualifications, Equal Emplojmient Opportunity 

 clearance, and so on. The timber sale passes through gate 

 6 when all requirements are met; the award of the con- 

 tract is the output. 



The "gates" are important to this study because they 

 not only progress temporally toward the actual implemen- 

 tation of the timber sale, but they also depict increasing 

 quantity and quality of information that can be utilized by 

 statistical classification models. Because gates 5 and 6 

 occur after the sale is sold (or not sold) they are of no use 

 in predicting salability and will not be considered further. 



At gate 1 an area is brought into the planning process 

 through development of a position statement — a docu- 

 ment that is a prerequisite to listing a proposed timber 

 sale on the timber sale action plan (USDA FS 1985, 

 2414.27). At this point, 10 years from the auction date, 

 very little site-specific information is known. Examples 

 of information known at this gate are slope, elevation, and 

 acreage within the proposed sale area. Over the long time 

 span of sale development many external influences may 

 alter salability. 



Gates 2 and 3 are closely related and will be treated as 

 a single, composite gate. They deal with developing a sale 

 area design and preparing for sale plan implementation. 

 At these gates specific sale characteristics are developed. 

 Sale characteristics include number and size of the cut- 

 ting units, the volume-per-acre harvested, the miles of 

 road construction, the silvicultural systems needed, the 

 logging method required, and so forth. Gates 2 and 3 

 occur about 1 to 3 years before the auction date. 



Gate 4, the final gate for predicting salability, com- 

 pletes the package by generating the appraisal. At this 

 gate, the planner's sale design decisions are converted 

 into appraisal information — dollars per thousand board 

 feet. Information generated at this gate includes stump- 

 to-mill costs and the advertised selling rate. Gate 4 oc- 

 curs about 3 months before the auction. 



Classification Methods 



The major factor affecting selection of statistical classi- 

 fication methods is the dichotomous nature of the depend- 

 ent variable. In this problem, the dependent variable 

 takes on two values (0 = unsold, 1 = sold) and identifies 

 group membership. For this class of problem, potentially 

 useful methods are limited to regression analysis, dis- 

 criminant analysis, and logistic regression. The method 

 of regression analysis was discarded because of the poten- 

 tial violations of certain key assumptions, principally the 

 variance of the error term is not constant for all observa- 

 tions, and the predicted values are not guaranteed to lie 

 in the (0, 1) interval (see Pindyck and Rubinfeld 1981). 

 The methods of logistic regression and discriminant 



analysis seem well suited to the problem of predicting 

 salability. 



LOGISTIC REGRESSION 



Logistic regression relates a qualitative dependent vari- 

 able, such as "sold" or "unsold" timber sales, to independ- 

 ent predictor variables through a cumulative logistic 

 probability function (see Maddala 1983; Pindyck and 

 Rubinfeld 1981). Parameter estimation is based on maxi- 

 mum likelihood estimation. These estimates have several 

 desirable properties, such as all parameters being consis- 

 tent and efficient asymptotically (Pindyck and Rubinfeld 

 1981). All parameter estimators are known to be normal, 

 therefore the ^-test can be applied to test for significance. 

 Also, research has shown that if certain discriminant func- 

 tion assumptions are violated, the logistic regression pro- 

 vides better prediction results (Press and Wilson 1978). 



The logistic regression predicts a probability of an event 

 occurring. The general model is specified as: 



Probability. = (1) 



Probability, is the probability of an event occurring (sale 

 selling), e is the base of natural logarithms (approximately 

 2.718), and 7 is estimated: 



y = B<, + 5,X, + S^2+... ^BX.^E, (2) 



Equation 2 above is presented in this research. To predict 

 a probability that an event will occur, you must first calcu- 

 late a y and then substitute that value into equation (1). 



Given the predicted probability that an offering will sell, 

 a decision rule needs to be adopted to perform classifica- 

 tion. The common decision rule is based on a probability 

 of one-half. If the probability is greater than or equal to 

 0.50, the sale is predicted to be a sold sale. If the probabil- 

 ity is less than 0.50, the sale is predicted to be an unsold 

 sale. This specific decision rule will generate a specific 

 classification result. 



Most of the following results are based on the 50 percent 

 decision rule discussed above. The effect of changing this 

 rule is also explored. 



DISCRIMINANT ANALYSIS 



Discriminant analysis is the traditional classification 

 technique. The basic strategy in discriminant analysis is 

 to form an equation (discriminant function) that uses inde- 

 pendent variables to classify observations into designated 

 groups (sold and unsold timber sales). The discriminant 

 function (equation) has the following form: 



L = 5,X,+S^3+... + BX (3) 



where L is the dependent variable (sold and unsold sales) 

 and Xj through X. are independent variables. The com- 

 mon expectation is the production of a discriminant func- 

 tion (equation) that optimally separates the designated 

 groups. 



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