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Misspecified Mean Function Regression

Author

Listed:
  • Richard Berk
  • Lawrence Brown
  • Andreas Buja
  • Edward George
  • Emil Pitkin
  • Kai Zhang
  • Linda Zhao

Abstract

There are over three decades of largely unrebutted criticism of regression analysis as practiced in the social sciences. Yet, regression analysis broadly construed remains for many the method of choice for characterizing conditional relationships. One possible explanation is that the existing alternatives sometimes can be seen by researchers as unsatisfying. In this article, we provide a different formulation. We allow the regression model to be incorrect and consider what can be learned nevertheless. To this end, the search for a correct model is abandoned. We offer instead a rigorous way to learn from regression approximations. These approximations, not “the truth,†are the estimation targets. There exist estimators that are asymptotically unbiased and standard errors that are asymptotically correct even when there are important specification errors. Both can be obtained easily from popular statistical packages.

Suggested Citation

  • Richard Berk & Lawrence Brown & Andreas Buja & Edward George & Emil Pitkin & Kai Zhang & Linda Zhao, 2014. "Misspecified Mean Function Regression," Sociological Methods & Research, , vol. 43(3), pages 422-451, August.
    • Handle: RePEc:sae:somere:v:43:y:2014:i:3:p:422-451
    DOI: 10.1177/0049124114526375
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    References listed on IDEAS

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    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
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