Discriminant Analysis

Discriminant analysis is a multivariate statistical technique that can be used to predict group membership from a set of predictor variables. The goal of discriminant analysis is to find optimal combinations of predictor variables, called discriminant functions, to maximally separate previously defined groups and make the best possible predictions about group membership. Discriminant analysis has become a valuable tool in social sciences as discriminant functions provide a means to classify a case into the group that it mostly resembles and help investigators understand the nature of differences between groups. For example, a college admissions officer might be interested in predicting whether an applicant, if admitted, is more likely to succeed (graduate from the college) or fail (drop out or fail) based on a set of predictor variables such as high school grade point average, scores on the Scholastic Aptitude Test, age, and so forth. A sample of students whose college outcomes are known can be used to create a discriminant function by finding a linear combination of predictor variables that best separates Groups 1 (students who succeed) and 2 (students who fail). This discriminant function can be used to predict the college outcome of a new applicant whose actual group membership is unknown. In addition, discriminant functions can be used to study the nature of group differences by examining which predictor variables best predict group membership. For example, which variables are the most powerful predictors of group membership? Or what pattern of scores on the predictor variables best describes the differences between groups? This entry discusses the data considerations involved in discriminant analysis, the derivation and interpretation of discriminant functions, and the process of classifying a case into a group.