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A new class of semi-mixed effects models and its application in small area estimation

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  • José Lombardía, María
  • Sperlich, Stefan

Abstract

In multi-level regression, using a fixed effect for each cluster leads to models that are flexible but that have poor estimation accuracy. In small area studies, for example, fixed effects models are typically over-parameterized. Regarding region as a random effect reduces the number of parameters, and hence, the flexibility, but requires crucial assumptions, such as that of independence between covariates and the random effects. A new class of semi-mixed effects models introduced here includes random and fixed effects models as extreme cases. This class of models constitutes a continuum of models, indexed by a “slider”, that determines the position of the model between these two extremes. Thus, the model selected can be close to the parsimonious random effects case, but far enough away from it to filter out unwanted dependences. The methodology is used for a small area analysis of tourist expenditures in Galicia.

Suggested Citation

  • José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2903-2917
    DOI: 10.1016/j.csda.2012.01.015
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    1. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    2. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    3. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    4. Gabriel DEMOMBYNES & Chris ELBERS & Jean O. LANJOUW & Peter LANJOUW, 2008. "How Good is a Map? Putting Small Area Estimation to the Test," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 116(4), pages 465-493.
    5. R. Crouchley & R. B. Davies, 1999. "A comparison of population average and random‐effect models for the analysis of longitudinal count data with base‐line information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 331-347.
    6. María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930, November.
    7. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    8. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    9. Thomas Kneib & Ludwig Fahrmeir, 2006. "Structured Additive Regression for Categorical Space–Time Data: A Mixed Model Approach," Biometrics, The International Biometric Society, vol. 62(1), pages 109-118, March.
    10. Alessandro Tarozzi & Angus Deaton, 2009. "Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 773-792, November.
    11. Wangli Xu & Lixing Zhu, 2009. "Kernel‐based Generalized Cross‐validation in Non‐parametric Mixed‐effect Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 229-247, June.
    12. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    13. Verbeke G. & Spiessens B. & Lesaffre E., 2001. "Conditional Linear Mixed Models," The American Statistician, American Statistical Association, vol. 55, pages 25-34, February.
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    Cited by:

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    2. Tomasz Brodzicki & Katarzyna Sledziewska & Dorota Ciolek & Stanislaw Uminski, 2015. "Extended gravity model of Polish trade. Empirical analysis with panel data methods," Working Papers 1503, Instytut Rozwoju, Institute for Development.
    3. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
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    5. Xuemei Hu & Weiming Yang, 2019. "Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models," Statistical Papers, Springer, vol. 60(4), pages 1039-1058, August.
    6. Reluga, Katarzyna & Lombardía, María-José & Sperlich, Stefan, 2024. "Bootstrap-based statistical inference for linear mixed effects under misspecifications," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).

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