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Logistic regression compared with the Discriminant Function
  • Binary logistic regression
    • This term is used in SPSS for regression analysis using the log odds of a dichotomous variable.
    • Others refer to the method as dichotomous logistic regression.
  • Multinomial logistic regression
    • SPSS uses this term for regression analysis using a polychotomous variable.
    • Other refer to it as polychotomous logistic regression.
    • SPSS says
      • Multinomial Logistic Regression is useful for situations in which you want to be able to classify subjects based on values of a set of predictor variables. This type of regression is similar to logistic regression, but it is more general because the dependent variable is not restricted to two categories.
  • Discriminant Analysis
    • This term usually embraces both the case of dichotomous and polychotomous dependent variables.
    • That is the practice in SPSS, which offers discriminant analysis as an option under Classify.
    • Discriminant analysis approaches the classification of cases in two or more groups as a problem in multiple analysis of variance of differences between and within group means.

Figure from Marasculio and Levin, Multivriate Statistics in the Social Sciences (1983), p. 269, showing Fisher's discriminant function: a linear combination of two variables that maximizes the distances between the center of two populations.