On the bias of structural estimation methods in a polynomial regression with measurement error when the distribution of the latent covariate is a mixture of normals

摘要

The structural variant of a regression model with measurement error is characterized by the assumption of an underlying known distribution of the latent covariate. Several estimation methods, like regression calibration or structural quasi score estimation, take this distribution into account. In the case of a polynomial regression, which is studied here, structural quasi score takes the form of structural least squares (SLS). Usually the underlying latent distribution is assumed to be the normal distribution because then the estimation methods take a particularly simple form. SLS is consistent as long as this assumption is true. The purpose of the paper is to investigate the amount of bias that results from violations of the normality assumption for the covariate distribution. Deviations from normality are introduced by switching to a mixture of normal distributions. It turns out that the bias reacts only mildly to slight deviations from normality.