Abstract
The structural variant of a regression model with measurement error is characterized by the assumption of an underlying known distribution type 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 result from violations of the normality assumption in 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Armstrong, B. (1985). Measurement error in the generalized linear model. Comm. in Stat. — Simul. and Comp. 14, 529–544.
Augustin, T. (2002). Some basic results on the extension of quasi-likelihood based measurement error correction to multivariate and flexible structural models. In W. Gaul and G. Ritter(eds.): Classification, Automation, and New Media. Springer, Heidelberg, 29–36.
Card, D. (1999). The causal effect of education on earnings. In O. Ashenfelter and D. Card(Eds.): Handbook of Labor Economics, Elsevier, Amsterdam, 1801–1863.
Carroll, R.J., Ruppert, D. and Stefanski, L.A. (1995). Measurement Error in Nonlinear Models. Chapman and Hall, London.
Cheng, C.-L. and Schneeweiss, H.(1998). Polynomial regression with errors in the variables. J.R. Statist. Soc. B60, 189–199.
Cheng, C.-L. and Schneeweiss, H.(2002). On the Polynomial Measurement Error Model. In S. van Huffel and R Lemmerling (Eds.): Total Least Squares and Errors-in-Variables Modeling. Kluwer, Dordrecht, 131–143.
Cheng, C.-L. and Van Ness, J.W. (1999). Statistical Regression with Measurement Error. London: Arnold.
Cheng, C.-L., Schneeweiss, H. and Thamerus, M. (2000). A small sample estimator for a polynomial regression with errors in the variables. J.R. Statist. Soc. B 62, 699–709.
Fuller, W.A. (1987). Measurment Error Models. New York: Wiley.
Kuha, J.T. and Temple, J. (1999). Covariate measurement error in quadratic regression. Discussion Paper 1999-W2, Nuffield College Oxford.
Kukush, A. und Schneeweiss, H. (2000). A Comparison of Asymptotic Covariance Matrices of Adjusted Least Squares and Structural Least Squares in Error Ridden Polynomial Regression. Discussion Paper 218, Sonderforschungsbereich 386, University of Munich.
Kukush, A., Schneeweiss, H. and Wolf, R. (2001). Relative Efficiency of Three Estimators in a Polynomial Regression with Measurement Errors. Discussion Paper 233, Sonderforschungsbereich 386, University of Munich.
Kukush, A., Schneeweiss, H. and Wolf, R. (2001). Comparing Different Estimators in a Nonlinear Measurement Error Model. Discussion Paper 244, Sonderforschungsbereich 386, University of Munich.
Schneeweiss, H. and Mittag, H.J. (1986). Lineare Modelle mit fehlerbehafteten Daten. Heidelberg: Physica-Verlag.
Schneeweiss, H. and Nittner, T. (2001). Estimating a polynomial regression with measurement errors in the structural and in the functional case — a comparison. In M. Sadeh(Ed.): Data Analysis from Statistical Foundations, A Festschrift in Honour of the 75th Birthday of D.A.S. Fraser, Nova Science, New York, 195–205.
Thamerus, M. (1998). Nichtlineare Regressionsmodelle mit heteroskedastischen Messfehlern. Logos Verlag, Berlin.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Schneeweiss, H., Cheng, CL., Wolf, R. (2002). On the Bias of Structural Estimation Methods in a Polynomial Regression with Measurement Error When the Distribution of the Latent Covariate is Misspecified. In: Klein, I., Mittnik, S. (eds) Contributions to Modern Econometrics. Dynamic Modeling and Econometrics in Economics and Finance, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3602-1_14
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3602-1_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5331-5
Online ISBN: 978-1-4757-3602-1
eBook Packages: Springer Book Archive