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Under an area-level random regression coefficient Poisson model, this article derives small area predictors of counts and proportions and introduces bootstrap estimators of the mean squared errors (MSEs). The maximum likelihood estimators of the model parameters and the mode predictors of the random effects are calculated by a Laplace approximation algorithm. Simulation experiments are implemented to investigate the behavior of the fitting algorithm, the predictors, and the MSE estimators with and without bias correction. The new statistical methodology is applied to data from the Spanish Living Conditions Survey. The target is to estimate the proportions of women and men under the poverty line by province. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present an original approach to estimate the gender pay gap (GPG). We propose a model‐based decomposition, similar to the most popular approaches, where the first component measures differences in group characteristics and the second component measures the unexplained effect; the latter being the real gap. The novel approach incorporates model selection and bias correction. The pay gap problem in a small area context is considered in this paper, although the approach is flexible to be applied to other contexts. Specifically, the methodology is validated for analysing wage differentials by economic activities in the region of Galicia (Spain) and by analysing simulated data from an experimental design that imitates the generation of real data. The good performance of the proposed estimators is shown in both cases, specifically when compared with those obtained from the widely used Oaxaca–Blinder approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The aim of the paper is the estimation of small area labour force indicators like totals of employed and unemployed people and unemployment rates. Small area estimators of these quantities are derived from four multinomial logit mixed models, including a model with correlated time and area random effects. Mean-squared errors are used to measure the accuracy of the estimators proposed and they are estimated by analytic and bootstrap methods. The methodology introduced is applied to real data from the Spanish Labour Force Survey of Galicia. [ABSTRACT FROM AUTHOR]