Survey Methodology
Bayesian inference for a variance component model using pairwise composite likelihood with survey data

by Mary E. Thompson, Joseph Sedransk, Junhan Fang and Grace Y. YiNote 1

  • Release date: June 21, 2022
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Abstract

We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.

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Thompson, M.E., Sedransk, J., Fang, J. and Yi, G.Y. (2022). Bayesian inference for a variance component model using pairwise composite likelihood with survey data. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 48, No. 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2022001/article/00002-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, 2022

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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