Identifiability of logistic regression with homoscedastic error: Berkson model
Volume 2, Issue 2 (2015), pp. 131–146
Pub. online: 7 July 2015
Type: Research Article
Open Access
Open Access
Received
20 May 2015
20 May 2015
Revised
19 June 2015
19 June 2015
Accepted
20 June 2015
20 June 2015
Published
7 July 2015
7 July 2015
Abstract
We consider the Berkson model of logistic regression with Gaussian and homoscedastic error in regressor. The measurement error variance can be either known or unknown. We deal with both functional and structural cases. Sufficient conditions for identifiability of regression coefficients are presented.
Conditions for identifiability of the model are studied. In the case where the error variance is known, the regression parameters are identifiable if the distribution of the observed regressor is not concentrated at a single point. In the case where the error variance is not known, the regression parameters are identifiable if the distribution of the observed regressor is not concentrated at three (or less) points.
The key analytic tools are relations between the smoothed logistic distribution function and its derivatives.
References
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