Survey Methodology
Inference from sampling with response probabilities estimated via calibration

by Caren HaslerNote 1

  • Release date: December 20, 2024
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Abstract

A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we highlight problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We present the results of a simulation study in order to illustrate these elements.

Key Words:    Maximum likelihood estimation; Nonresponse; Two-phase estimation; Weighting adjustment.

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How to cite

Hasler, C. (2024). Inference from sampling with response probabilities estimated via calibration. Survey Methodology, 50(2), 235-259. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2024002/article/00013-eng.pdf.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© His Majesty the King in Right of Canada, as represented by the Minister of Industry, 2024

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Catalogue No. 12-001-X

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