Survey Methodology
Measurement error in small area estimation: Functional versus structural versus naïve models

Warning View the most recent version.

Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please "contact us" to request a format other than those available.

Archived

This page has been archived on the Web.

by William R. Bell, Hee Cheol Chung, Gauri S. Datta and Carolina FrancoNote 1

  • Release date: May 7, 2019
More information PDF version

Abstract

Small area estimation using area-level models can sometimes benefit from covariates that are observed subject to random errors, such as covariates that are themselves estimates drawn from another survey. Given estimates of the variances of these measurement (sampling) errors for each small area, one can account for the uncertainty in such covariates using measurement error models (e.g., Ybarra and Lohr, 2008). Two types of area-level measurement error models have been examined in the small area estimation literature. The functional measurement error model assumes that the underlying true values of the covariates with measurement error are fixed but unknown quantities. The structural measurement error model assumes that these true values follow a model, leading to a multivariate model for the covariates observed with error and the original dependent variable. We compare and contrast these two models with the alternative of simply ignoring measurement error when it is present (naïve model), exploring the consequences for prediction mean squared errors of use of an incorrect model under different underlying assumptions about the true model. Comparisons done using analytic formulas for the mean squared errors assuming model parameters are known yield some surprising results. We also illustrate results with a model fitted to data from the U.S. Census Bureau’s Small Area Income and Poverty Estimates (SAIPE) Program.

Key Words:      Sample survey; Area level model; Covariate; Prediction.

Table of contents

How to cite

Bell, W.R., Chung, H.C., Datta, G.S. and Franco, C. (2019). Measurement error in small area estimation: Functional versus structural versus naïve models. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019001/article/00005-eng.htm.

Note

More information

ISSN : 1492-0921

Editorial policy

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.

Submission of Manuscripts

Survey Methodology is published twice a year in electronic format. Authors are invited to submit their articles in English or French in electronic form, preferably in Word to the Editor, (statcan.smj-rte.statcan@canada.ca, Statistics Canada, 150 Tunney’s Pasture Driveway, Ottawa, Ontario, Canada, K1A 0T6). For formatting instructions, please see the guidelines provided in the journal and on the web site (www.statcan.gc.ca/SurveyMethodology).

Note of appreciation

Canada owes the success of its statistical system to a long-standing partnership between Statistics Canada, the citizens of Canada, its businesses, governments and other institutions. Accurate and timely statistical information could not be produced without their continued co-operation and goodwill.

Standards of service to the public

Statistics Canada is committed to serving its clients in a prompt, reliable and courteous manner. To this end, the Agency has developed standards of service which its employees observe in serving its clients.

Copyright

Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

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

Catalogue No. 12-001-X

Frequency: Semi-annual

Ottawa

close


Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Theoretical results
Section 3. Comparing MSEs for the alternative predictors
Section 4. SAIPE illustration
Section 5. Conclusions
Acknowledgements
Appendix
References

close
Date modified: