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On Expressing the Probabilities of Categorical Responses as Linear Functions of Covariates

DOI: 10.4236/am.2013.411200, PP. 1485-1489

Keywords: Logistic Regression, Linear Regression, Maximum Likelihood Estimation, Least-Squares Estimation

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Logistic regression is usually used to model probabilities of categorical responses as functions of covariates. However, the link connecting the probabilities to the covariates is non-linear. We show in this paper that when the cross-classification of all the covariates and the dependent variable have no empty cells, then the probabilities of responses can be expressed as linear functions of the covariates. We demonstrate this for both the dichotmous and polytomous dependent variables.


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[3]  C. R. Rao and H. Toutenburg, “Linear Models: Least Squares and Alternatives,” Springer, New York, 1999.
[4]  J. L. Schafer, “Analysis of Incomplete Multivariate Data,” Chapman & Hall/CRC, Boca Raton, 1999.


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