| Abstract: | We study structural measurement error models when the binary reponse Y and true predictor x follow a logistic regression model and the observed proxy X satisfies a conditional independence assumption. Assuming that a structural measurement error model is appropriate, we compare two approaches to estimation. In the first approach no assumptions about the distribution of x are made; in the second approach it is assumed that x has a normal distribution. When the normality assumption holds, the second approach yields a consistent and asymptotically efficient estimator; however, consistency is lost when the normality assumption is violated. The first approach yields consistent estimators irrespective of the distribution of x; however, it sacrifices efficiency when x is normally distributed. In the latter case we examine the loss of efficiency for some parametric specifications of known importance. |
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