Identifiability of logistic regression with homoscedastic error: Berkson model

TL;DR

This paper investigates the conditions under which logistic regression models with Gaussian measurement errors are identifiable, providing criteria based on the distribution of observed regressors and error variance knowledge.

Contribution

It establishes new sufficient conditions for the identifiability of logistic regression parameters in Berkson models with homoscedastic errors, considering both known and unknown error variances.

Findings

Regression parameters are identifiable if observed regressor distribution isn't concentrated at a single point when error variance is known.

Parameters are identifiable if observed regressor distribution isn't concentrated at three or fewer points when error variance is unknown.

Key analytic tools involve relations between the smoothed logistic distribution and its derivatives.

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.