Non‐parametric generalized linear mixed models in small area estimation

Torabi, Mahmoud; Shokoohi, Farhad

doi:10.1002/cjs.11236

Cited by 11 publications

(16 citation statements)

References 30 publications

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“…(), Salvati et al . (), Sperlich and Lombardía (), Rueda and Lombardía () or Torabi and Shokoohi (), among others). In fact, analytical values for GDF are known only when the fitted model is linear (Han () and references therein).…”

Section: Introductionmentioning

confidence: 97%

Mixed Generalized Akaike Information Criterion for Small Area Models

Lombardía

López-Vizcaíno²,

Rueda

2017

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary 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.

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Section: Introductionmentioning

confidence: 97%

Mixed Generalized Akaike Information Criterion for Small Area Models

Lombardía

López-Vizcaíno²,

Rueda

2017

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…Tsutakawa, Shoop & Marienfield (1985), Clayton & Kaldor (1987), Nandram, Sedransk & Pickle (1999), Langford et al (1999), Datta, Ghosh & Waller (2000), Dean & MacNab (2001), among others, used Poisson mixed models to study rates of different diseases in small areas. Ghosh et al (1998) and Torabi & Shokoohi (2015) proposed generalized linear models (GLMs) with random area effects to predict small area statistics. Ghosh et al (1999) and Torabi (2019) extended the GLMs to handle spatial data and applied the model to disease mapping.…”

Section: Introductionmentioning

confidence: 99%

“…Ghosh et al. (1998) and Torabi & Shokoohi (2015) proposed generalized linear models (GLMs) with random area effects to predict small area statistics. Ghosh et al.…”

Section: Introductionmentioning

confidence: 99%

Copula‐based predictions in small area estimation

2020

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Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall's tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application.

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“…() extended the linear mixed model approach in the context of small‐area estimation to the case in which a linear relationship may not hold, using penalised spline (P‐spline) regression. Torabi & Shokoohi () proposed generalised linear mixed models (GLMMs) using P‐spline regression to unify the analysis of normal and non‐normal responses. From a very different perspective, Chambers & Tzavidis () studied an approach for small‐area estimation that is based on M‐quantile regression which allows for models that are robust to the distributional assumptions on the errors and area effects.…”

Section: Introductionmentioning

confidence: 99%

Semi‐parametric small‐area estimation by combining time‐series and cross‐sectional data methods

Shokoohi¹,

Torabi

2018

Aus NZ J of Statistics

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In survey sampling, policymaking regarding the allocation of resources to subgroups (called small areas) or the determination of subgroups with specific properties in a population should be based on reliable estimates. Information, however, is often collected at a different scale than that of these subgroups; hence, the estimation can only be obtained on finer scale data. Parametric mixed models are commonly used in small-area estimation. The relationship between predictors and response, however, may not be linear in some real situations. Recently, small-area estimation using a generalised linear mixed model (GLMM) with a penalised spline (P-spline) regression model, for the fixed part of the model, has been proposed to analyse cross-sectional responses, both normal and non-normal. However, there are many situations in which the responses in small areas are serially dependent over time. Such a situation is exemplified by a data set on the annual number of visits to physicians by patients seeking treatment for asthma, in different areas of Manitoba, Canada. In cases where covariates that can possibly predict physician visits by asthma patients (e.g. age and genetic and environmental factors) may not have a linear relationship with the response, new models for analysing such data sets are required. In the current work, using both time-series and cross-sectional data methods, we propose P-spline regression models for small-area estimation under GLMMs. Our proposed model covers both normal and non-normal responses. In particular, the empirical best predictors of small-area parameters and their corresponding prediction intervals are studied with the maximum likelihood estimation approach being used to estimate the model parameters. The performance of the proposed approach is evaluated using some simulations and also by analysing two real data sets (precipitation and asthma).

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Non‐parametric generalized linear mixed models in small area estimation

Cited by 11 publications

References 30 publications

Mixed Generalized Akaike Information Criterion for Small Area Models

Mixed Generalized Akaike Information Criterion for Small Area Models

Copula‐based predictions in small area estimation

Semi‐parametric small‐area estimation by combining time‐series and cross‐sectional data methods

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