The main purpose of a discriminant function analysis is to predict group membership based on a linear combination of the interval variables. The procedure begins with a set of observations where both group membership and the values of the interval variables are known. The end result of the procedure is a model that allows prediction of group membership when only the interval variables are known. A second purpose of discriminant function analysis is an understanding of the data set, as a careful examination of the prediction model that results from the procedure can give insight into the relationship between group membership and the variables used to predict group membership.
Discriminant analysis is a statistical method that is used by researchers to help them understand the relationship between a "dependent variable" and one or more "independent variables." A dependent variable is the variable that a researcher is trying to explain or predict from the values of the independent variables. Discriminant analysis is similar to regression analysis and analysis of variance (ANOVA). The principal difference between discriminant analysis and the other two methods is with regard to the nature of the dependent variable.
Discriminant analysis requires the researcher to have measures of the dependent variable and all of the independent variables for a large number of cases. In regression analysis and ANOVA, the dependent variable must be a "continuous variable." A numeric variable indicates the degree to which a subject possesses some characteristic, so that the higher the value of the variable, the greater the level of the characteristic. A good example of a continuous variable is a person's income.
Discriminant analysis is most often used to help a researcher predict the group or category to which a subject belongs. For example, when individuals are interviewed for a job, managers will 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.
Then the discriminant function has the following form:
where D = discriminant function score,
B = discriminant function coefficient relating independent variable i to the discriminant function score,
X = value of independent variable i.
The equation is quite similar to a regression equation. Conventional regression analysis should not be used in place of discriminant analysis. The dependent variable would have only two values (high performer and low performer) and would thus violate important assumptions of the regression model. Discriminant analysis does not have these limitations with respect to the dependent variable.
Submitted by-
Prashant Vaish
12060
SIBM, Bangalore
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