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

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.