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Mixed generalized Akaike information criterion for small area models

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  • María José Lombardía
  • Esther López‐Vizcaíno
  • Cristina Rueda

Abstract

A mixed generalized Akaike information criterion xGAIC is introduced and validated. It is derived from a quasi‐log‐likelihood that focuses on the random effect and the variability between the areas, and from a generalized degree‐of‐freedom measure, as a model complexity penalty, which is calculated by the bootstrap. To study the performance of xGAIC, we consider three popular mixed models in small area inference: a Fay–Herriot model, a monotone model and a penalized spline model. A simulation study shows the good performance of xGAIC. Besides, we show its relevance in practice, with two real applications: the estimation of employed people by economic activity and the prevalence of smokers in Galician counties. In the second case, where it is unclear which explanatory variables should be included in the model, the problem of selection between these explanatory variables is solved simultaneously with the problem of the specification of the functional form between the linear, monotone or spline options.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:180:y:2017:i:4:p:1229-1252
    DOI: 10.1111/rssa.12300
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    References listed on IDEAS

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    Cited by:

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    2. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
    3. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2022. "A new approach to the gender pay gap decomposition by economic activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 219-245, January.
    4. 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.
    5. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    6. Pan, Lanfeng & Li, Yehua & He, Kevin & Li, Yanming & Li, Yi, 2020. "Generalized linear mixed models with Gaussian mixture random effects: Inference and application," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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