Logistic regression and discriminant analysis by ordinary least squares

Gus Haggstrom

Expert InsightsPublished 1982

If the observations for fitting a polytomous logistic regression model satisfy certain normality assumptions, the maximum likelihood estimates of the regression coefficients are the discriminant function estimates. This paper shows that these estimates, their unbiased counterparts, and associated test statistics for variable selection can be calculated using ordinary least squares regression techniques, thereby providing a convenient procedure for performing discriminant analysis and fitting logistic regression models in the normal case. If the normality assumptions are violated, the discriminant function estimates and test statistics afford readily calculated alternatives to other procedures for fitting logistic regression models, such as the conditional maximum likelihood estimates, that present theoretical and computational difficulties. Empirical evidence is provided to show that the results of fitting logistic regression models using the discriminant function approach often agree closely with those obtained by conditional maximum likelihood.

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Haggstrom, Gus, Logistic regression and discriminant analysis by ordinary least squares. Santa Monica, CA: RAND Corporation, 1982. https://www.rand.org/pubs/papers/P6811.html.
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