Simultaneous inference for linear mixed model parameters with an application to small area estimation

Open access financiado por Universite de Geneve (article funding)European Regional Development Fund[Abstract]: Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster-level parameters or subject-specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster-level parameters. We employ a consistent bootstrap approximation of the distribution of max-type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas.Swiss National Science Foundation; 200021-192345,Swiss National Science Foundation; P2GEP2_195898Xunta de Galicia; ED431C 2020/14Ministerio de Ciencia e Innovación; PID2020-113578RB-I00Galician Innovation Agency/ Ministerio de Economía, empleo e industria; COV20/00604Xunta de Galicia; ED431G2019/0

Simultaneous Inference for Empirical Best Predictors With a Poverty Study in Small Areas

[Abstract]: Today, generalized linear mixed models (GLMM) are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under GLMM. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.The authors gratefully acknowledge the support from the Swiss National Science Foundation for the project 200021-192345. In addition, they acknowledge the support from the MINECO grants MTM2017-82724-R and MTM2014-52876-R, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF. The computations were performed at the University of Geneva on the Baobab cluster.Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431G/0

Empirical best prediction under area-level Poisson mixed models

[Abstract] The paper studies the applicability of area-level Poisson mixed models to estimate small area counting indicators. Among the available procedures for fitting generalized linear models, the method of moments (MM) and the penalised quasi-likelihood (PQL) method are employed. The empirical best predictor (EBP) of the area mean is derived using MM and compared with plug-in alternatives using MM and PQL. The plug-in estimator using PQL is computationally faster and provides competitive performance with respect to EBP that involves high complex integrals. An approximation to the mean squared error (MSE) of the EBP is given and three MSE estimators are proposed. The first two MSE estimators are plug-in estimators without and with bias correction to the second order and the third one is based on parametric bootstrap. Several simulation experiments are carried out for analysing the behaviour of the EBP and for comparing the estimators of the MSE of the EBP. A good choice in practice is the bootstrap alternative since it performs similarly to the analytical versions and is computationally faster. The developed methodology and software are applied to data from the 2008 Spanish living condition survey. The target of the application is the estimation of poverty rates at province level.Xunta de Galicia; CN2012/130Ministerio de Ciencia e Innovación; MTM2013-41383-PMinisterio de Ciencia e Innovación; MTM2014-52876-RMinisterio de Ciencia e Innovación; MTM2011-22392Ministerio de Ciencia e Innovación; MTM2008-03010Ministerio de Ciencia e Innovación; MTM2012-37077-C02-0

Small area prediction of proportions and counts under a spatial Poisson mixed model

[Abstract]: This paper introduces an area-level Poisson mixed model with SAR(1) spatially correlated random effects. Small area predictors of proportions and counts are derived from the new model and the corresponding mean squared errors are estimated by parametric bootstrap. The behaviour of the introduced predictors is empirically investigated by running model-based simulation experiments. An application to real data from the Spanish living conditions survey of Galicia (Spain) is given. The target is the estimation of domain proportions of women under the poverty line.Supported by the Instituto Galego de Estatística, by MICINN Grants PID2020-113578RB-I00 and PGC2018-096840-B-I00, by the Generalitat Valenciana Grant PROMETEO/2021/063 and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C 2020/14), and by GAIN (Galician Innovation Agency) and the Regional Ministry of Economy, Employment and Industry Grant COV20/00604 and Centro de Investigación del Sistema Universitario de Galicia ED431G 2019/01, all of them through the ERDF.Generalitat Valenciana; PROMETEO/2021/063Xunta de Galicia; ED431C/2020/14Xunta de Galicia; COV20/00604Xunta de Galicia; ED431G/2019/0

Simultaneous Inference for Empirical Best Predictors with a Poverty Study in Small Areas

Today, generalized linear mixed models are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under generalized linear mixed models. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.Comment: 46 pages, 20 figures; simulations and data analysis expanded, additional remarks adde

Selection model for domains across time: application to labour force survey by economic activities

This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11749-020-00712-4[Abstract]: This paper introduces a small area estimation approach that borrows strength across domains (areas) and time and is efficiently used to obtain labour force estimators by economic activity. Specifically, the data across time are used to select different models for each domain; such selection is done with an aggregated mixed generalized Akaike information criterion statistic which is obtained using data across all time points and then is split into individual component for each domain. The approach makes a selection from different estimators, including the direct estimator, synthetic and mixed estimators derived from different models using auxiliary information. Results from several simulation experiments, some with original designs, show the good performance of the approach against standard small area approaches. In addition, it is shown the important practical advantages in the real application.Supported by the MINECO Grants MTM2017-82724-R, MTM2015-71217-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF.Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431G/0

A New Approach to the Gender Pay Gap Decomposition by Economic Activity

This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of the Royal Statistical Society Series A: Statistics in Society, following peer review. The version of record [M. J. Lombardía, E. López-Vizcaíno, y C. Rueda, «A New Approach to the Gender Pay Gap Decomposition by Economic Activity», Journal of the Royal Statistical Society Series A: Statistics in Society, vol. 185, n.º 1, pp. 219-245, ene. 2022] is available online at: https://doi.org/10.1111/rssa.12742.[Abstract]: 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.Supported by the MINECO grants MTM2017-82724-R, MTM2015-71217-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C 2020/14 and Centro de Investigación del Sistema universitario de Galicia ED431G 2019/01), all of them through the ERDF.Xunta de Galicia; ED431C 2020/14Xunta de Galicia; ED431G 2019/0

Poverty Mapping Under Area-Level Random Regression Coefficient Poisson Models

[Abstract]: 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.This work was supported by the Ministry of Science and Innovation and the State Research Agency of the Spanish Government through the European Regional Development Fund (PID2022-136878NB-I00, PID2020-113578RB-I00 and PRE2021-100857 to Naomi Diz-Rosales funded by MCIN/AEI/10.13039/501100011033); by the Conselleria d’Innovació, Universitats, Ciéncia i Societat Digital of the Generalitat Valenciana (Prometeo/2021/063); by the Consellería de Cultura, Educación, Formación Profesional e Universidades of the Xunta de Galicia through the European Regional Development Fund (Competitive Reference Groups ED431C/2020/14, COV20/00604, and ED431G/2019/01); and by Centro de Investigación en Tecnologías de la Información y las Comunicaciones (CITIC) that is supported by Xunta de Galicia, collaboration agreement between the Consellería de Cultura, Educación, Formación Profesional e Universidades and the Galician universities for the reinforcement of the research centers of the Sistema Universitario de Galicia (CIGUS).Xunta de Galicia; ED431C/2020/14Xunta de Galicia; COV20/00604Xunta de Galicia; ED431G/2019/0

Mapping the Poverty Proportion in Small Areas under Random Regression Coefficient Poisson Models

Cursos e Congresos, C-155[Abstract] In a complex socio-economic context, policy makers need highly disaggregated poverty indicators. In this work, we develop a methodology in small area estimation to derive predictors of poverty proportions under a random regression coefficient Poisson model, introducing bootstrap estimators of mean squared errors. Maximum likelihood estimators of model parameters and random effects mode predictors are calculated using a Laplace approximation algorithm. Simulation experiments are conducted to investigate the behaviour of the fitting algorithm, the predictors and the mean squared error estimator. The new statistical methodology is applied to data from the Spanish survey of living conditions to map poverty proportions by province and sex, developing a tool to support policy decision makingXunta de Galicia; ED431C-2020/14This research is part of the grant PID2020-113578RB-I00, funded by MCIN/AEI/10.13039/501100011033/. It has also been supported by the Spanish grant PID2022-136878NB-I00, the Valencian grant Prometeo/2021/063, by the Xunta de Galicia (Competitive Reference ED431C-2020/14) and by CITIC that is supported by Xunta de Galicia, collaboration agreement between the Consellería de Cultura, Educación, Formación Profesional e Universidades and the Galician universities for the reinforcement of the research centres of the Sistema Universitario de Galicia (CIGUS). The first author was also sponsoredby the Spanish Grant for Predoctoral Research Trainees RD 103/2019 being this work part of grant PRE2021-100857, funded by MCIN/AEI/10.13039/501100011033/ and ESF