| Abstract: | Summary 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
i
d
i
where a
i
is the coefficient for the i
th
variable in the discriminant function and d
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
i
d
i
<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.
Reference: Shiledar Baxi, H., “Use of Discriminant Analysis to Predict Arson-Prone Structures,” Fire Technology, Vol. 20,
No. 4, November 1984, p. 17 |
