# The Discriminant Analysis and the Logistic Regression

## Introduction

The discriminant analysis and the logistic regression are similar in that both these types of analysis attempt to predict the membership of a case to one of the groups into which the sample is classified by a categorical dependent variable (Warner, 2013). Both of these analyses allow for creating a linear classification model, that is, a model that attempts to predict membership of a case in groups by defining a linear relationship (Pohar, Blas, & Turk, 2004).

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## When should the researcher decide which analysis to perform?

However, these two methods are different in their approach. More specifically, the discriminant analysis requires that several assumptions about the distribution of the independent variables are met, such as the normality of data; on the other hand, the logistic regression does not require such assumptions to be satisfied (Pohar et al., 2004). Also, it should be noted that the logistic regression can only use a dichotomous dependent variable, whereas the discriminant analysis may be run with a dependent variable that has more than 2 levels (University of Exeter, n.d.).

When a researcher needs to decide which analysis to run, the logistic regression is often preferred to the discriminant analysis, due to the relative simplicity of its interpretation in particular (University of Exeter, n.d.). Also, it is recommended to use logistic regression in situations when multiple assumptions of the discriminant analysis are violated (e.g., group sizes are very unequal, there is no multivariate normality, and/or the condition of homogeneity of variance/covariance matrices is not met) (Warner, 2013, p. 1047). On the other hand, the discriminant analysis may permit for obtaining better results when its assumptions are not violated (i.e., it is more powerful), so it may be advised to use the discriminant analysis in this case (Pohar et al., 2004).

## Conclusion

Both the discriminant analysis and the logistic regression can be run on the same data in most cases (but not e.g. when the dependent variable has more than 3 groups). However, care should be taken; one ought to choose the method for which the required assumptions are violated minimally (Warner, 2013).

## References

Pohar, M., Blas, M., & Turk, S. (2004). Comparison of logistic regression and linear discriminant analysis: A simulation study. Metodoloski Zvezki, 1(1), 143-161. Web.

University of Exeter. (n.d.). Topic 4: Logistic regression and discriminant analysis. Web.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

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