Abstract:

Variable selection and transformation selection are widely studied problems in the linear and mixed regression models. [1] states "The selection of a transformation may be properly viewed as model selection". The working model always depends on which procedure is done first, variable or transformation selection. The strategy for selecting the working model under different transformations for small area estimation methods based in particular on mixed regression models, is still under discussion [2]. In this paper we propose a simultaneous variable and transformation selection algorithm, which takes into account data-driven transformations and a model selection methodoly based on a mixed generalized Akaike information criterion (xAIC). The objective of the present work is twofold. First, we extended the xAIC of model selection, proposed in [3], in case unit-level data are used. Second, we incorporate this criterion into the selection of data-driven transformations methodology [4] under the same context. The same procedure is also provided in case area-level data are used. Our work involves extensive model-based simulations under different scenarios. Finally, the conclusions from the empirical studies are used for analyzing the spatial distribution of poverty in Mexico by using real survey and census data.

References:

[1] R. M. Sakia, (1992) The Box-Cox transformation technique: A review, Journal of the Royal Statistical Society. Series D, 41, 169-178.

[2] J.N.K. Rao, (2003) Small area estimation, John Wiley & Sons.

[3] M.J. Lombardía, E. López-Vizcaíno, C. Rueda, (2017) Mixed generalized Akaike information criterion for small area models, Journal of the Royal Statistical Society. Series A, 4, 1229-1252.

[4] N. Rojas-Perilla, S. Pannier, T. Schmid, N. Tzavidis, (2017) Data-driven transformations in small area estimation, Discussion Paper 30/20177, School of Business and Economics, Freie Universitat Berlin: Berlin, 26, 211-252.