Abstract
Discriminant analysis is a multivariate procedure for the analysis of group differences. It allows examining the difference between two or more groups with respect to a variety of variables in order to answer questions such as: Do the considered groups differ significantly from each other with respect to the variables? Which variables are suitable or unsuitable for distinguishing between the groups? While the analysis of group differences serves primarily scientific purposes, the determination or prediction of the group membership of new elements (classification) is of direct practical relevance. The question then is: Which group does a ‘new’ observation belong to based on its describing variables? The chapter describes discriminant analysis for cases with two or more groups.
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Notes
- 1.
If we are interested in the question whether two groups differ significantly with respect to just one variable, we can use an independent samples t-test. For more than two groups, we can use the univariate analysis of variance (see Sect. 3.2.1).
- 2.
On the website www.multivariate-methods.info, we provide supplementary material (e.g., Excel files) to deepen the reader’s understanding of the methodology.
- 3.
See Sect. 3.2.1.2 for a more detailed discussion of the explained and unexplained variation.
- 4.
- 5.
See Sect. 1.3 for a brief introduction to the basics of statistical testing.
- 6.
For example, if you had a describing variable ‘price’ and changed its unit of measurement from EUR to Cent, the corresponding discriminant coefficient would decrease by a factor of 100. Yet the transformation of the scale has no influence on the discriminatory power of the variable.
- 7.
Visit www.multivariate-methods.info for more information on how to compute the conditional probability with Excel.
- 8.
We use the same data set as for logistic regression (cf. Sect. 5.4) in order to better illustrate similarities and differences between the two methods.
- 9.
Missing values are a frequent and unfortunately unavoidable problem when conducting surveys (e.g. because people cannot or do not want to answer some question(s), or as a result of mistakes by the interviewer). The handling of missing values in empirical studies is discussed in Sect. 1.5.2.
References
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Further reading
Breiman, L., Friedman, J., Olshen, R., & Stone, C. (1984). Classification and regression trees. New York: Chapman & Hall.
Fisher, R. A. (1936). The use of multiple measurement in taxonomic problems. Annals of Eugenics, 7(2), 179–188.
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Huberty, C. J., & Olejnik, S. (2006). Applied MANOVA and discriminant analysis, 2nd edition. Hoboken (N. J.): Wiley-Interscience.
IBM SPSS Inc. (2020). IBM SPSS Statistics 27 documentation. https://www.ibm.com/support/pages/ibm-spss-statistics-27-documentation#en. Accessed March 25, 2021.
Klecka, W. (1993). Discriminant analysis (15th ed.). Beverly Hills: Sage.
Lachenbruch, P. (1975). Discriminant analysis. London: Springer.
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Backhaus, K., Erichson, B., Gensler, S., Weiber, R., Weiber, T. (2021). Discriminant Analysis. In: Multivariate Analysis. Springer Gabler, Wiesbaden. https://doi.org/10.1007/978-3-658-32589-3_4
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DOI: https://doi.org/10.1007/978-3-658-32589-3_4
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