Abstract
In multi-level regression, such as small area studies, and in panel data studies, using a fixed effect for each region leads to models that are flexible but that have poor estimation accuracy; they are over-parameterized. We bridge the gap between Fixed Effects Models, Mixed Effects Models and Partial Linear Models by a flexible modeling of area effects. The transition from Mixed Effects Models to Semiparametric Mixed Effects Models and Fixed Effects Models is achieved by progressively relaxing the smoothness assumption on the semiparametric area specific impact. The methodology is illustrated with a complete simulation study and applied for a small area analysis of tourist expenditures in Galicia.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Diggle, P.J., Heagerty, P., Liang, K.-L., Zeger, S.: Analysis of Longitudinal Data, 2nd edn. Oxford Statistical Science Series, vol. 25. Oxford University Press, Oxford (2002)
Elbers, C., Lanjouw, J.O., Lanjouw, P.: Micro-level Estimation of Poverty and Inequality. Econometrica 71, 355–364 (2003)
Fay, R.E., Herriot, R.A.: Estimates of Income for Small Places. An Application of James-Stein Procedures to Census Data. J. Amer. Statist. Assoc. 74, 269–277 (1979)
Ghosh, M., Nangia, N., Kim, D.H.: Estimation of Median Income of Four-Person Families: A Bayesian Time Series Approach. J. Amer. Statist. Assoc. 91, 1423–1431 (1996)
Goldstein, H.: Multilevel Statistical Models, 3rd edn. Edward Arnold, London (2003)
Hamilton, J.D.: A Parametric Approach to Flexible Nonlinear Inference. Econometrica 69, 537–573 (2001)
Jiang, J., Lahiri, P.: Mixed Model Prediction and Small Area Estimation. Test 15, 1–96 (2006)
Lin, X., Carroll, R.: Semiparametric Regression for Clustered Data Using Generalized Estimating Equations. J. Amer. Statist. Assoc. 96, 1045–1056 (2001)
Lombardía, M.J., Sperlich, S.: Semiparametric Inference in Generalized Mixed Effects Models. J. Roy. Statist. Soc. Ser. B 70, 913–930 (2008)
Opsomer, J., Claeskens, G., Ranalli, M.G., Kauermann, G., Breidt, F.J.: Non-parametric Small Area Estimation Using Penalized Spline Regression. J. Roy. Statist. Soc. Ser. B 70, 265–286 (2008)
Prasad, N.G.N., Rao, J.N.K.: The Estimation of the Mean Squared Error of Small-Area Estimators. J. Amer. Statist. Assoc. 85, 163–171 (1990)
Rao, J.N.K.: Small Area Estimation. John Wiley and Sons, Inc., New-York (2003)
Tutz, G.: Generalized Semiparametrically Structured Mixed Models. Comput. Statist. Data Anal. 46, 777–800 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lombardía, M.J., Sperlich, S. (2010). Smooth Transition from Mixed Models to Fixed Models. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_52
Download citation
DOI: https://doi.org/10.1007/978-3-642-14746-3_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14745-6
Online ISBN: 978-3-642-14746-3
eBook Packages: EngineeringEngineering (R0)