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

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DOI: 10.4236/am.2013.411200    2,895 Downloads   3,968 Views  
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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 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.

Cite this paper

Desai, T. (2013) On Expressing the Probabilities of Categorical Responses as Linear Functions of Covariates. Applied Mathematics, 4, 1485-1489. doi: 10.4236/am.2013.411200.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] M. E. Stokes, C. S. Davis and G. G. Koch, “Categorical Data Analysis Using the SAS System,” SAS Institute and Wiley, Cary, 2001.
[2] C. R. Rao, “Linear Statistical Inference and Its Application,” Wiley, New York, 1973.
http://dx.doi.org/10.1002/9780470316436
[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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