The linear discriminant function and its classification 

 rule depend on several statistical assumptions (Maddala 

 1983). If the assumptions are violated, corrective proce- 

 dures are recommended (Johnson and Wichem 1982; 

 Meddala 1983; Press and Wilson 1978). The linear dis- 

 criminant functions were tested for compliance with the 

 statistical assumptions and corrective procedures applied 

 when necessary. 



Classification can be achieved using either Fisher's 

 linear discriminant function (equation presented above) 

 or classification functions (see Morrison 1976 for a discus- 

 sion on classification functions — classification functions 

 presented in tables 10 through 15, appendix B). Classifi- 

 cation depends on the calculated discriminant score and 

 a critical value. If the calculated discriminant score is 

 greater than zero (the critical value) it is assigned to the 

 sold sales category, and if less than zero to the unsold 

 sales category. 



Study Design 



The Gates timber sale planning process provided the 

 fi-amework for this analysis. As the sale progresses fi^om 

 gate 1 to gate 4, site, sale, appraisal, and economic infor- 

 mation is generated. This information was used to de- 

 velop the equations. The gate 1 equation is based on the 

 general site characteristics known at that time in the 

 planning process. The gate 2-3 equation is based on infor- 

 mation fi-om gate 1 (site characteristics) plus information 

 fi*om gates 2 and 3 (sale characteristics). The third equa- 

 tion, based at gate 4, uses all prior information plus the 

 appraisal information generated at this gate. If one 

 chooses to use measures of economic expectations as inde- 

 pendent variables, gate 4 would be the appropriate gate. 

 Estimates of economic expectations were not used. 



I analyzed timber sales auctioned during January 1980 

 through December 1985 on National Forests in the North- 

 em Region of the Forest Service. All timber sales were 

 competitively auctioned and were of at least $2,000 mini- 

 mum value. The sampling period consisted of the high 

 markets of the early 1980's, a major recession in 1982 and 

 1983, and a recovery during 1984 and 1985. Given that 

 the major thrust of this research was the development 

 and comparison of methods that quantify salability, the 

 sample diversity was not a hindrance. But the equations 

 should be used only to predict salability for sales that will 

 be competitively auctioned. 



I randomly sampled 389 sold and unsold timber sales 

 fi"om the 13 National Forests in the Northern Region. 

 Of the 389 sales, 349 timber sales were sampled on the 

 "westside" National Forests (Bitterroot, Lolo, Flathead, 

 Kootenai, Idaho Panhandle, Clearwater, Eind Nez Perce). 

 Of the 349 westside timber sales, 204 were sold timber 

 sales; the remaining 145 timber sales were unsold. I 

 sampled 40 timber sales on the "eastside" National For- 

 ests (Custer, Gallatin, Beaverhead, Helena, Lewis & 

 Clark, and Deerlodge). They were composed of 26 sold 

 and 14 unsold sales. 



Analytical Procedures 



MODEL CONSTRUCTION 



The equations were checked for violations of the as- 

 sumptions and were corrected if appropriate. Given the 

 empirical nature of equation development, Wilk's lambda 

 (stepwise procedure) was used to generate the final 

 discriminant functions. For logistic regression, an "all- 

 possibles" regression subroutine based on ordinary least 

 squares was used to develop preliminary equations. Of 

 course, the timber sale and economic characteristics used 

 were considered logical variables in determining sold and 

 unsold timber sales. 



Both statistical classification methods were developed 

 using SPSSX (Nie 1983) and BMDP (Dixon 1981) statisti- 

 cal software on a Vax 8600 computer. 



EVALUATION CRITERIA 



Using either the classification functions or Fisher's 

 linear discriminant function, I produced a classification 

 matrix that presents the predicted classification results. 

 The classification matrix is a tabular method used to 

 present the percentage correctly and incorrectly classified. 

 Another method used to measure goodness of fit is the 

 Holdout method (Lachenbruch 1975), also known as the 

 Jackknife method. This method predicts the group to 

 which a sale belongs when the sale is not involved in the 

 model -building process. This technique generates a better 

 estimate of the error variance than the classification 

 method described above. Both of these methods are used 

 to produce classification results for the discriminant 

 functions. 



The logistic regression equation predicts the probability 

 of a sale being sold given sale attributes and market infor- 

 mation. Since it predicts a probability, we must adopt a 

 rule that aggregates these probabilities into groups. The 

 decision rule adopted aggregated sales with predicted 

 probabilities greater than or equal to 0.50 into the sold 

 sales group. If the predicted probability is less than 0.50, 

 the sale is predicted to be an unsold timber sale. Once the 

 decision rule was implemented, a classification matrix 

 was constructed, indicating how well the equation pre- 

 dicted sold and unsold timber sales. 



CUTOFF POINTS 



Particularly important is the link between probability 

 levels, classification results, and the cost of making a 

 decision error. The decision rule of 0.50 probability im- 

 plies the costs of misclassifying sold and unsold sales is 

 equal. But it may be more costly ft"om a managerial 

 standpoint to classify a sale as salable, when actually it 

 will not sell. 



Analysts and decision makers are fi'ee to adopt any 

 decision rule. A different decision rule will lead to 

 different classification results. Decision rules imply an 

 underlying cost of making a decision error. These costs 

 are not consistent from user to user. A particular land 

 manager may view misclassification of a predicted sold 

 sale more costly than misclassification of a predicted un- 

 sold sale. The land manager's cost of misclassification 

 will lead to a particular decision rule, and thus, different 

 classification results. 



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