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On Expressing the Probabilities of Categorical Responses as Linear Functions of Covariates
The Adani Institute of Infrastructure Management, Ahmedabad, India
- 1 The Adani Institute of Infrastructure Management, Ahmedabad, India
Applied Mathematics·Volume 04 (2013)·Pages 1485–1489·Published 15 October 2013·DOI10.4236/am.2013.411200
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Abstract
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 ha ve 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.
KeywordsLogistic RegressionLinear RegressionMaximum Likelihood EstimationLeast-Squares Estimation
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