Regression model checking with Berkson measurement errors

This paper discusses asymptotically distribution free tests for the lack-of-fit of a parametric regression model in the Berkson measurement error model. These tests are based on a martingale transform of a certain marked empirical process of calibrated residuals. A simulation study is included to assess the effect of measurement error on the proposed test. It is observed that empirical level is more stable across the chosen measurement error variances when fitting a linear model compared to when fitting a nonlinear model, while, in both cases, the empirical power decreases as this error variance increases, against all chosen alternatives.