Discriminant Function Analysis

by G. David V. Garson

DISCRIMINANT FUNCTION ANALYSIS Discriminant function analysis, also known as discriminant analysis or simply DA, is used to classify cases into the values of a categorical dependent, usually a dichotomy. If discriminant function analysis is effective for a set of data, the classification table of correct and incorrect estimates will yield a high percentage correct. Discriminant function analysis is found in SPSS under Analyze>Classify>Discriminant. If the specified grouping variable has two categories, the procedure is considered "discriminant analysis" (DA). If there are more than two categories the procedure is considered "multiple discriminant analysis" (MDA). The full content is now available from Statistical Associates Publishers. is the unformatted table of contents. Table of ContentsOverview6Key Terms and Concepts7Variables7Discriminant functions7Pairwise group comparisons8Output statistics8Examples9SPSS user interface9The "Statistics" button10The "Classify" button10The "Save" button13The "Bootstrap" button13The "Method" button14 SPSS Statistical output for two-group DA16The "Analysis Case Processing Summary" table16The "Group Statistics" table16The "Tests of Equality of Group Means" table16The "Pooled Within-Group Matrices" and "Covariance Matrices" tables.18The "Box's Test of Equality of Covariance Matrices" tables18The "Eigenvalues" table19The "Wilks' Lambda" table21The "Standardized Canonical Discriminant Function Coefficients" table21The "Structure Matrix" table23The "Canonical Discriminant Functions Coefficients" table23The "Functions at Group Centroids" table24The "Classification Processing Summary" table24The "Prior Probabilities for Groups" table25The "Classification Function Coefficients" table25The "Casewise Statistics" table26Separate-groups graphs of canonical discriminant functions27The "Classification Results" table27SPSS Statistical output for three-group MDA28Overview and example28MDA and DA similarities28The "Eigenvalues" table29The "Wilks' Lambda" table29The "Structure Matrix" table30The "Territorial Map"31Combined-groups plot34Separate-groups plots34SPSS Statistical output for stepwise discriminant analysis35Overview35Example35Stepwise discriminant analysis in SPSS36Assumptions41Proper specification41True categorical dependent variables41Independence41No lopsided splits41Adequate sample size41Interval data42Variance42Random error42Homogeneity of variances (homoscedasticity)42Homogeneity of covariances/correlations42Absence of perfect multicollinearity43Low multicollinearity of the independents43Linearity43Additivity43Multivariate normality43Frequently Asked Questions44Isn't discriminant analysis the same as cluster analysis?44When does the discriminant function have no constant term?44How important is it that the assumptions of homogeneity of variances and of multivariate normal distribution be met?44In DA, how can you assess the relative importance of

70 pages, Kindle Edition

First published September 2, 2012