Survey Methodology
Authors’ response to comments on “Handling non‑probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”:

Some new developments on likelihood approaches to estimation of participation probabilities for non‑probability samples

by Jean-François Beaumont, Keven Bosa, Andrew Brennan, Joanne Charlebois and Kenneth ChuNote 1

  • Release date: June 25, 2024
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Abstract

Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.

Key Words:    Best linear unbiased estimation; Best linear unbiased prediction; Estimating equation; Population likelihood; Pseudo likelihood; Sample likelihood.

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How to cite

Beaumont, J.-F., Bosa, K., Brennan, A., Charlebois, J. and Chu, K. (2024). Authors’ response to comments on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”: Some new developments on likelihood approaches to estimation of participation probabilities for non probability samples. Survey Methodology, Statistique Canada, n° 12‑001‑X au catalogue, vol. 50, n° 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2024001/article/00001-eng.htm.

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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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