Domain prediction with grouped income data

One popular small area estimation method for estimating poverty and inequality indicators is the empirical best predictor under the unit-level nested error regression model with a continuous dependent variable. However, parameter estimation is more challenging when the response variable is grouped due to data confidentiality concerns or concerns about survey response burden. The work in this paper proposes methodology that enables fitting a nested error regression model when the dependent variable is grouped. Model parameters are then used for small area prediction of finite population parameters of interest. Model fitting in the case of a grouped response variable is based on the use of a stochastic expectation–maximization algorithm. Since the stochastic expectation–maximization algorithm relies on the Gaussian assumptions of the unit-level error terms, adaptive transformations are incorporated for handling departures from normality. The estimation of the mean squared error of the small area parameters is facilitated by a parametric bootstrap that captures the additional uncertainty due to the grouping mechanism and the possible use of adaptive transformations. The empirical properties of the proposed methodology are assessed by using model-based simulations and its relevance is illustrated by estimating deprivation indicators for municipalities in the Mexican state of Chiapas.

data confidentiality, interval-censored data, nested error regression model, small area estimation, survey response burden

10.1111/rssa.12736

0964-1998

1501-1523

Walter, Paul

86b72b53-a20e-4bfd-ab91-fe9b37fd2c37

Gross, Marcus

cc6bc9e3-dbfb-4d64-b9d9-915a81b48a9b

Schmid, Timo

6f0ac270-0f64-4f86-ad3c-77a722cb14a4

Tzavidis, Nikolaos

431ec55d-c147-466d-9c65-0f377b0c1f6a

October 2021

Walter, Paul

86b72b53-a20e-4bfd-ab91-fe9b37fd2c37

Gross, Marcus

cc6bc9e3-dbfb-4d64-b9d9-915a81b48a9b

Schmid, Timo

6f0ac270-0f64-4f86-ad3c-77a722cb14a4

Tzavidis, Nikolaos

431ec55d-c147-466d-9c65-0f377b0c1f6a

Walter, Paul, Gross, Marcus, Schmid, Timo and Tzavidis, Nikolaos (2021) Domain prediction with grouped income data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 184 (4), 1501-1523. (doi:10.1111/rssa.12736).

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Accepted/In Press date: 25 June 2021

e-pub ahead of print date: 3 August 2021

Published date: October 2021

Additional Information: Funding Information: The research has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 730998, InGRID-2, Integrating Research Infrastructure for European expertise on Inclusive Growth from data to policy. Furthermore, Schmid and Tzavidis gratefully acknowledge support by grant ES/N011619/1 - Innovations in Small Area Estimation Methodologies from the UK Economic and Social Research Council and funding under the Data and Evidence to End Extreme Poverty (DEEP) research programme. DEEP is a consortium of the Universities of Cornell, Copenhagen, and Southampton led by Oxford Policy Management, in partnership with the World Bank's Development Data Group and funded by the UK Foreign, Commonwealth & Development Office. The authors are grateful to the National Council for the Evaluation of Social Development Policy (CONEVAL, Consejo Nacional de Evaluaci?n de la Pol?tica de Desarrollo Social) for providing the data used in empirical work. The views set out in this paper are those of the authors and do not reflect the official opinion of CONEVAL. The numerical results are not official estimates and are only produced for illustrating the methods. Finally, the authors are indebted to the Joint Editor, Associate Editor and two referees for comments that significantly improved the paper. Funding Information: The research has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 730998, InGRID‐2, Integrating Research Infrastructure for European expertise on Inclusive Growth from data to policy. Furthermore, Schmid and Tzavidis gratefully acknowledge support by grant ES/N011619/1 ‐ Innovations in Small Area Estimation Methodologies from the UK Economic and Social Research Council and funding under the Data and Evidence to End Extreme Poverty (DEEP) research programme. DEEP is a consortium of the Universities of Cornell, Copenhagen, and Southampton led by Oxford Policy Management, in partnership with the World Bank's Development Data Group and funded by the UK Foreign, Commonwealth & Development Office. The authors are grateful to the National Council for the Evaluation of Social Development Policy (CONEVAL, Consejo Nacional de Evaluación de la Política de Desarrollo Social) for providing the data used in empirical work. The views set out in this paper are those of the authors and do not reflect the official opinion of CONEVAL. The numerical results are not official estimates and are only produced for illustrating the methods. Finally, the authors are indebted to the Joint Editor, Associate Editor and two referees for comments that significantly improved the paper. Publisher Copyright: © 2021 The Authors. Journal of the Royal Statistical Society: Series A (Statistics in Society) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society.

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