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Improving survey‐weighted least squares regression

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  • Lonnie Magee

Abstract

The weighted least squares (WLS) estimator is often employed in linear regression using complex survey data to deal with the bias in ordinary least squares (OLS) arising from informative sampling. In this paper a ‘quasi‐Aitken WLS’ (QWLS) estimator is proposed. QWLS modifies WLS in the same way that Cragg’s quasi‐Aitken estimator modifies OLS. It weights by the usual inverse sample inclusion probability weights multiplied by a parameterized function of covariates, where the parameters are chosen to minimize a variance criterion. The resulting estimator is consistent for the superpopulation regression coefficient under fairly mild conditions and has a smaller asymptotic variance than WLS.

Suggested Citation

  • Lonnie Magee, 1998. "Improving survey‐weighted least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 115-126.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:115-126
    DOI: 10.1111/1467-9868.00112
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    Cited by:

    1. Goodwin, Roger L, 2015. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.3," MPRA Paper 64863, University Library of Munich, Germany, revised 07 Jun 2015.
    2. Miriam Kesselmeier & Norbert Benda & André Scherag, 2020. "Effect size estimates from umbrella designs: Handling patients with a positive test result for multiple biomarkers using random or pragmatic subtrial allocation," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    3. Goodwin, Roger L, 2014. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0," MPRA Paper 64391, University Library of Munich, Germany, revised 15 May 2015.

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