## Wednesday, 31 August 2011

### Applications of Discriminant Analysis

Applications of Discriminant Analysis

Discriminant analysis is a statistical technique widely used in the business world. Discriminant analysis uses a collection of interval variables to predict a categorical variable that may be a dichotomy or have more than two values.

The technique involves finding a linear combination of independent variables (predictors) – the discriminant function – that creates the maximum difference between group membership in the categorical dependent variable.

Thus, DA is used when:

· the dependent variable is categorical with the predictor independent variables interval level such as age, income, attitudes, perceptions, and years of education.

· there are more than two Dependant Variable categories, unlike logistic regression, which is limited to a dichotomous dependent variable.

Discriminant analysis is used to forecast the outcome of a variety of variables that impact the profitability of a business. Classic examples of the applicantion of discriminant analysis include:

• Performing an default risk evaluation of loan applicants;
• Benchmarking of potential job applicants;
• Forecasting insurance risk
• Predicting academic performance from historical data
• Developing auditing patterns
• Fraud management

Discriminant analysis is most often used to help researchers analyze the group or category to which a subject belongs. Let us look at two examples.

Judging the credit worthiness of a loan-applicant

Discriminant analysis has been used with success in consumer credit and other forms of instalment lending in which various characteristics of an individual are quantitatively rated and a credit decision is made on the basis of the total score. The plastic credit cards many of us carry often are given out on the basis of a credit scoring system that takes into account such things as age, occupation, duration of employment, home ownership, years of residence, telephone, and annual income.

Numerical rating systems also are used by companies extending trade credit. With the overall growth of trade credit, a number of companies are finding it worthwhile to screen out "clear" accept and reject applicants. In other words, routine credit decisions are made on the basis of a numerical score.

Marginal applicants, who fall between "clear" accept or reject signals, can then be analyzed in detail by the credit analyst. In this way, a company is able to achieve greater efficiency in its credit investigation process. It uses trained credit analysts to the best advantage.

Judging the suitability of a candidate for a job.

When individuals are interviewed for a job, managers do not know for sure how job candidates will perform on the job if hired. Suppose, however, that a human resource manager has a list of current employees who have been classified into two groups: "high performers" and "low performers." These individuals have been working for the company for some time, have been evaluated by their supervisors, and are known to fall into one of these two mutually exclusive categories.

The manager also has information on the employees' backgrounds: educational attainment, prior work experience, participation in training programs, work attitude measures, personality characteristics, and so forth. This information was known at the time these employees were hired. The manager wants to be able to predict, with some confidence, which future job candidates are high performers and which are not.

A researcher or consultant can use discriminant analysis, along with existing data, to help in this task.

There are two basic steps in discriminant analysis. The first involves estimating coefficients, or weighting factors, that can be applied to the known characteristics of job candidates (i.e., the independent variables) to calculate some measure of their tendency or propensity to become high performers. This measure is called a "discriminant function." Second, this information can then be used to develop a decision rule that specifies some cut-off value for predicting which job candidates are likely to become high performers.

The tendency of an individual to become a high performer can be written as a linear equation. The values of the various predictors of high performer status (i.e., independent variables) are multiplied by "discriminant function coefficients" and these products are added together to obtain a predicted discriminant function score.

This score is used in the second step to predict the job candidates likelihood of becoming a high performer.

There are more complicated cases, in which the dependent variable has more than two categories. Discriminant analysis allows for such a case, as well as many more categories and this is where it scores over multivariate regression analysis. The interpretation, however, of the discriminant function scores and coefficients becomes more complex

Author: Aniruddha Dasgupta

Group: Finance 3