The 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. Another 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 used when:
• The dependent is categorical with the predictor IV’s at interval level such as age, income, attitudes, perceptions, and years of education, although dummy variables can be used as predictors as in multiple regression. Logistic regression IV’s can be of any level of measurement.
• There are more than two DV categories, unlike logistic regression, which is limited to a dichotomous dependent variable.
Discriminant analysis involves the determination of a linear equation like regression that will predict which group the case belongs to. The form of the equation or function is:
D=v1XI + v2X2 + v3X3.....
=viXi + a
Where D = discriminate function
v = the discriminant coefficient or weight for that variable
X = respondent’s score for that variable
a = a constant
i = the number of predictor variables
Purpose of Discriminant analysis:
• To investigate differences between groups on the basis of the attributes of the cases, indicating which attributes contribute most to group separation. The descriptive technique successively identifies the linear combination of attributes known as canonical discriminant functions (equations) which contribute maximally to group separation.
• Predictive DA addresses the question of how to assign new cases to groups. The DA function uses a person’s scores on the predictor variables to predict the category to which the individual belongs.
• To determine the most parsimonious way to distinguish between groups.
• To classify cases into groups. Statistical significance tests using chi square enable you to see how well the function separates the groups.
• To test theory whether cases are classified as predicted
The aim of the statistical analysis in DA is to combine (weight) the variable scores in some way so that a single new composite variable, the discriminant score, is produced.