# Multiple Discriminant Analysis

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WEB EXTENSION 22A Multiple Discriminant Analysis s we have seen, bankruptcy—or even the possibility of bankruptcy—can cause significant trauma for a firm’s managers, investors, suppliers, customers, and community. Thus, it would be beneficial to be able to predict the likelihood of bankruptcy so that steps could be taken to avoid it or at least to reduce its impact. One approach to bankruptcy prediction is multiple discriminant analysis (MDA), a statistical technique similar to regression analysis. In this extension, we discuss MDA in detail and illustrate its application to bankruptcy prediction.1 Suppose a bank loan officer wants to segregate corporate loan applications into those likely to default and those unlikely to default.…show more content…
1. The discriminant function is fitted (that is, the values of a, b1, and b2 are obtained) using historical data for a sample of firms that either went bankrupt or did not go bankrupt during some past period. When the data in the lower part of Figure 22A-1 were fed into a “canned” discriminant analysis program (the computing centers of most universities and large corporations have such programs), the following discriminant function was obtained: Web Extension 22A: Multiple Discriminant Analysis 3 Z ¼ −0:3877 − 1:0736ðCurrent ratioÞ þ 0:0579ðDebt ratioÞ 2. This equation was plotted on Figure 22A-1 as the locus of points for which Z = 0. All combinations of current ratios and debt ratios shown on the line result in Z = 0.2 Companies that lie to the left of the line (and also have Z < 0) are unlikely to go bankrupt; those that lie to the right (and have Z > 0) are likely to go bankrupt. It can be seen from the graph that one X (indicating a failing company) lies to the left of the line and that two dots (indicating nonbankrupt companies) lie to the right of the line. Thus, the discriminant analysis failed to properly classify three companies: Z Po s i t i v e : M D A Pr e d i c t s B a n k r up t c y Did subsequently go bankrupt Remained solvent 8 2 Z Ne g a t i v e : M DA Pre d i ct s S o l v e ncy 1 8 The model did not perform perfectly, since two predicted bankruptcies remained solvent and one firm that was expected to remain