Logit regressions with continuous dependent variables measured with error

The logit regression model is generally used as a method for estimating relationships in which the dependent variable is binary in nature, though it is also useful for estimation when the dependent variable is continuous but bounded on the unit intervals. Logit parameter estimates in this case are obtained by ordinary least squares regression on a simple transformation on the dependent variable. In such applications, however, measurement error in the dependent variable, rather than being relatively benign as in ordinary linear regressions, is a source of heteroscedasticity, calling into question the efficiency of the OLS estimator in such cases.