We discuss and illustrate the method of simulation extrapolation for fitting models with additive measurement error. We present this discussion in terms of generalized linear models (GLMs) following the notation defined in Hardin and Carroll (2003). As in Hardin, Schmiediche, and Carroll (2003), our discussion includes specified measurement error and measurement error estimated by replicate error-prone proxies. In addition, we discuss and illustrate three extrapolant functions.
CarrollR. J., KüchenhoffH., LombardF., and StefanskiL.A.1996. Asymptotics for the SIMEX estimator in structural measurement error models. Journal of the American Statistical Association91(433): 242–250.
2.
CookJ., and StefanskiL.A.1995. A simulation extrapolation method for parametric measurement error models. Journal of the American Statistical Association89: 1314–1328.
3.
HardinJ. W., and CarrollR.J.2003. Measurement error, GLMs, and notational conventions. Stata Journal3(4): 328–340.
4.
HardinJ. W., SchmiedicheH., and CarrollR.J.2003. The regression-calibration method for fitting generalized linear models with additive measurement error. Stata Journal3(4): 360–371.
5.
StefanskiL. A., and CookJ.1995. Simulation extrapolation: The measurement error jackknife. Journal of the American Statistical Association90(432): 1247–1256.