TITLE:
On Expressing the Probabilities of Categorical Responses as Linear Functions of Covariates
AUTHORS:
Tejas A. Desai
KEYWORDS:
Logistic Regression; Linear Regression; Maximum Likelihood Estimation; Least-Squares Estimation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11,
November
5,
2013
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 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.