Use of discriminant analysis to predict arson-prone structures

Abstract

The technique of discriminant analysis is widely used for discriminating arson from nonarson structures. Since in this particular case only two groups are involved viz., the arson and the match groups, the computations required for obtaining a discriminant function are relatively simple. Because of this, it is possible to delete a variable by examining the value of a sub i d sub i where a sub i is the coefficient for the i-th variable in the discriminant function and d sub i is the difference between the means for the arson and the match groups for the i th variable (i=1, 2, ... , p). Thus, if a sub i d sub i is less than 0 then we delete the i th variable from consideration because inclusion of such a varable, increases the probability of misclassification. A prior knowledge of a i d i is particularly useful when we have large numbers of variables to be considered. This will help to reduce the number of discriminant functions one needs to consider in order to arrive at the discriminant function which minimizes the misclassification probability. Frequently, in developing a discriminant function one strives to increase the probability of correct classification. However, this probability reflects two components, viz., the probability of correct classification of known arson structures and the probability of correct classification of known nonarson structures. Even if the overall probability of correct classification is high, it does not necessarily imply, as the illustrations of Boston and New York City indicate, that the resulting discriminant function is also efficient in the sense that more arson cases are correctly classified than the nonarson cases. To this end, a procedure has been suggested to compute the cost of the wrong decision for a discriminant function which can be used to compare the cost of two similar types of discriminant functions. Using the relative cost efficiency criterion, it has been shown that the discriminant function for Newark is more efficient than the discriminant function for either Boston or New York City.