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Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

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  • Schneeweiss, Hans
  • Cheng, Chi-Lun

Abstract

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.

Suggested Citation

  • Schneeweiss, Hans & Cheng, Chi-Lun, 2006. "Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 455-473, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:455-473
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    References listed on IDEAS

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    1. Chi‐Lun Cheng & Hans Schneeweiss & Markus Thamerus, 2000. "A small sample estimator for a polynomial regression with errors in the variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 699-709.
    2. Alexander Kukush & Hans Schneeweis & Roland Wolf, 2004. "Three estimators for the poisson regression model with measurement errors," Statistical Papers, Springer, vol. 45(3), pages 351-368, July.
    3. Chi‐Lung Cheng & Hans Schneeweiss, 1998. "Polynomial regression with errors in the variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 189-199.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    1. Kukush Alexander & Shklyar Sergiy & Masiuk Sergii & Likhtarov Illya & Kovgan Lina & Carroll Raymond J & Bouville Andre, 2011. "Methods for Estimation of Radiation Risk in Epidemiological Studies Accounting for Classical and Berkson Errors in Doses," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-30, February.
    2. Erik Meijer & Susann Rohwedder & Tom Wansbeek, 2008. "Prediction of Latent Variables in a Mixture of Structural Equation Models, with an Application to the Discrepancy Between Survey and Register Data," Working Papers WR-584, RAND Corporation.
    3. Erik Meijer & Susann Rohwedder & Tom Wansbeek, 2008. "Prediction of Latent Variables in a Mixture of Structural Equation Models, with an Application to the Discrepancy Between Survey and Register Data," Working Papers 584, RAND Corporation.
    4. Hans Schneeweiss & Thomas Augustin, 2006. "Some recent advances in measurement error models and methods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 183-197, March.

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