Abstract
In this paper we focus on small area models with measurement error in covariates. Based on data from the Measuring Morality study, a nationally representative survey of United States residents, that contains a validated behavioural measure of generosity (the dictator game) along with the household income of respondents, we define a measurement error model suitable to obtain area-level estimates of generosity at the district level. We investigate the effect of introducing the measurement error in this model, focusing on fully Bayesian as well as Empirical Bayesian (EB) estimation proposed in the recent literature. We discuss the characteristics of each of the two approaches and analyze the impact of the measurement error on the resulting estimates based on real data and a simulation study.
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References
Alvares, D., Armero, C., Forte, A.: What does objective mean in a Dirichlet multinomial process? Int. Stat. Rev. 106–118 (2017)
Arima, S., Polettini, S.: A unit-level small area model with misclassified covariates. J. R. Stat. Soc. A. (2019). https://doi.org/10.1111/rssa.12468
Arima, S., Datta, G.S., Liseo, B.: Objective Bayesian analysis of a measurement error small area model. Bayesian Anal. 72(2), 363–384 (2012)
Arima, S., Datta, G.S., Liseo, B.: Models in small area estimation when covariates are measured with error. In: Pratesi, M. (ed.) Analysis of Poverty Data by Small Area Estimation, pp. 151–170. Wiley, New York (2016)
Carroll, R.J., Ruppert, D., Stefanski, L., Crainiceanu, C.: Measurement Error in Nonlinear Models: A Modern Perspective, 2nd edn. Chapman & Hall, CRC, Boca Raton (2006)
Côtè, S., House, J., Willer, R.: High economic inequality leads higher-income individuals to be less generous. Ann. PNAS 112(52), 15838–15843 (2015)
Datta, G.S., Day, B., Maiti, T.: Multivariate Bayesian small area estimation: an application to survey and satellite data. Sankhyā: Indian J. Stat. Ser. A 60(3), 344–362 (1998)
Engel, C.: Dictator games: a meta study. Exp. Econ. 14(4), 583–610 (2011)
Ghosh, M., Sinha, K.: Empirical Bayes estimation in finite population sampling under functional measurement error models. J. Stat. Plan. Inference 137, 2759–2773 (2007)
Ghosh, M., Sinha, K., Kim, D.: Empirical and hierarchical Bayesian estimation in finite population sampling under structural measurement error model. Scand. J. Stat. 33(3) (2006)
Rao, J.N.K., Molina, I.: Small Area Estimation, 2nd edn. Wiley, Hoboken (2015)
Torabi, M., Datta, G.S., Rao, J.N.K.: Empirical Bayes estimation of small area means under nested error linear regression model with measurement error in the covariates. Scand. J. Stat. 36, 355–368 (2009)
Trautmann, S.T., van de Kuilen, G., Zeckhauser, R.J.: Social class and (un)ethical behavior: a framework, with evidence from a large population sample. Perspect. Psychol. Sci. 8(5), 487–497 (2013)
Ybarra, L.M.R., Lohr, S.L.: Small area estimation when auxiliary information is measured with error. Biometrika 95(4), 919–931 (2008)
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Polettini, S., Arima, S. (2019). An Investigation of Hierarchical and Empirical Bayesian Small Area Predictors Under Measurement Error. In: Petrucci, A., Racioppi, F., Verde, R. (eds) New Statistical Developments in Data Science. SIS 2017. Springer Proceedings in Mathematics & Statistics, vol 288. Springer, Cham. https://doi.org/10.1007/978-3-030-21158-5_17
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DOI: https://doi.org/10.1007/978-3-030-21158-5_17
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