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Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method

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  • Song Cai

    (School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada)

  • J.N.K. Rao

    (School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada)

Abstract

Model-based estimation of small area means can lead to reliable estimates when the area sample sizes are small. This is accomplished by borrowing strength across related areas using models linking area means to related covariates and random area effects. The effective selection of variables to be included in the linking model is important in small area estimation. The main purpose of this paper is to extend the earlier work on variable selection for area level and two-fold subarea level models to three-fold sub-subarea models linking sub-subarea means to related covariates and random effects at the area, sub-area, and sub-subarea levels. The proposed variable selection method transforms the sub-subarea means to reduce the linking model to a standard regression model and applies commonly used criteria for variable selection, such as AIC and BIC, to the reduced model. The resulting criteria depend on the unknown sub-subarea means, which are then estimated using the sample sub-subarea means. Then, the estimated selection criteria are used for variable selection. Simulation results on the performance of the proposed variable selection method relative to methods based on area level and two-fold subarea level models are also presented.

Suggested Citation

  • Song Cai & J.N.K. Rao, 2022. "Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method," Stats, MDPI, vol. 5(1), pages 1-11, February.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:1:p:9-138:d:742708
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    References listed on IDEAS

    as
    1. Yan Li & Partha Lahiri, 2019. "A Simple Adaptation of Variable Selection Software for Regression Models to Select Variables in Nested Error Regression Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 302-317, December.
    2. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    3. Song Cai & J. N. K. Rao & Laura Dumitrescu & Golshid Chatrchi, 2020. "Effective transformation-based variable selection under two-fold subarea models in small area estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 68-83, August.
    4. Torabi, Mahmoud & Rao, J.N.K., 2014. "On small area estimation under a sub-area level model," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 36-55.
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