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Borrowing information over time in binomial/logit normal models for small area estimation

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  • William R. Bell
  • Carolina Franco

Abstract

Linear area level models for small area estimation, such as the Fay-Herriot model, face challenges when applied to discrete survey data. Such data commonly arise as direct survey estimates of the number of persons possessing some characteristic, such as the number of persons in poverty. For such applications, we examine a binomial/logit normal (BLN) model that assumes a binomial distribution for rescaled survey estimates and a normal distribution with a linear regression mean function for logits of the true proportions. Effective sample sizes are defined so variances given the true proportions equal corresponding sampling variances of the direct survey estimates. We extend the BLN model to bivariate and time series (first order autoregressive) versions to permit borrowing information from past survey estimates, then apply these models to data used by the U.S. Census Bureau’s Small Area Income and Poverty Estimates (SAIPE) program to predict county poverty for school-age children. We compare prediction results from the alternative models to see how much the bivariate and time series models reduce prediction error variances from those of the univariate BLN model. Standard conditional variance calculations for corresponding linear Gaussian models that suggest how much variance reduction will be achieved from borrowing information over time with linear models agree generally with the BLN empirical results.

Suggested Citation

  • William R. Bell & Carolina Franco, 2015. "Borrowing information over time in binomial/logit normal models for small area estimation," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 563-584, December.
  • Handle: RePEc:csb:stintr:v:16:y:2015:i:4:p:563-584
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    References listed on IDEAS

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    1. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
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    1. repec:bla:jorssa:v:180:y:2017:i:4:p:1163-1190 is not listed on IDEAS
    2. Partha Lahiri & Jiraphan Suntornchost, 2020. "A general Bayesian approach to meet different inferential goals in poverty research for small areas," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 237-253, August.
    3. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    4. Sanjoy K. Sinha, 2019. "Robust small area estimation in generalized linear mixed models," METRON, Springer;Sapienza Università di Roma, vol. 77(3), pages 201-225, December.
    5. Lahiri Partha & Suntornchost Jiraphan, 2020. "A general Bayesian approach to meet different inferential goals in poverty research for small areas," Statistics in Transition New Series, Statistics Poland, vol. 21(4), pages 237-253, August.
    6. Jerry J. Maples, 2017. "Improving small area estimates of disability: combining the American Community Survey with the Survey of Income and Program Participation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1211-1227, October.
    7. Karina Acosta & Juliana Jaramillo-Echeverri & Daniel Lasso & Alejandro Sarasti-Sierra, 2024. "Informalidad municipal en Colombia," Documentos de trabajo sobre Economía Regional y Urbana 327, Banco de la Republica de Colombia.

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