Discriminant Function Analysis

Discriminant Function Analysis

PURPOSE

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.

EXAMPLES

For example, a graduate admissions committee might divide a set of past graduate students into two groups: students who finished the program in five years or less and those who did not. Discriminant function analysis could be used to predict successful completion of the graduate program based on GRE score and undergraduate grade point average. Examination of the prediction model might provide insights into how each predictor individually and in combination predicted completion or non-completion of a graduate program.

Another example might predict whether patients recovered from a coma or not based on combinations of demographic and treatment variables. The predictor variables might include age, sex, general health, time between incident and arrival at hospital, various interventions, etc. In this case the creation of the prediction model would allow a medical practitioner to assess the chance of recovery based on observed variables. The prediction model might also give insight into how the variables interact in predicting recovery.

The Simplest Case

The simplest case of discriminant function analysis is the prediction of dichotomous group membership based on a single variable. An example of the simplest case is the prediction of successful completion of a graduate program based on the GRE verbal score. In this case, since the prediction model includes only a single variable, it gives little insight into how variables interact with each other in prediction. Thus prediction of group membership will be the major focus of the next section of this chapter.

With respect to the data file and purpose of analysis, this simplest case is identical to the case of linear regression with dichotomous dependent variables. As discussed previously, data of this type may be represented in any number of different forms: scatterplots, tables of means and standard deviations, and overlapping frequency polygons. Because overlapping frequency polygons have such an intuitive appeal, they will be used to describe how discriminant function analysis works.

Prediction Accuracy

A single interval variable might discriminate between groups in an almost perfect fashion, not at all, or somewhere in between. For example, if one wished to differentiate adult males and females, one could collect information on how many bras the person owned, score on the last statistics test, and height. In the case of the number of bras, the discrimination would be very good, but not perfect (some women don't own any bras, some men do). In the case of the score on the last statistics test, little discrimination would be possible because males and females generally score about the same. In the case of height, some discrimination between adult males and females would be possible, but it would be far from perfect.

In general, the larger the difference between the means of the two groups relative to the within groups variability, the better the discrimination between the groups. The following program allows the student to explore data sets with different degrees of discrimination ability.

Navneet Kumar

MBA -operations Group 11