The Fay–Herriot model for multiply imputed data with an application to regional wealth estimation in Germany

Kreutzmann, Ann-Kristin; Marek, Philipp; Runge, Marina; Salvati, Nicola; Schmid, Timo

doi:10.1080/02664763.2021.1941805

Cited by 3 publications

(7 citation statements)

References 41 publications

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“…For future research, the methodology could be extended to the use of survey data where the data have been imputed multiple times by the data provider due to item non-response. The approach of Kreutzmann et al (2022), which uses multiply imputed data from the Household Finance and Consumption Survey to estimate wealth averages, could therefore be extended to nonlinear indicators and appropriate transformations to allow Rubin's pooling rules (Rubin 1987) for multiply imputed data to be applied. Esteban et al (2012) study area-level time models for nonlinear indicators such as poverty incidence and poverty gap.…”

Section: Discussionmentioning

confidence: 99%

Estimating Intra-Regional Inequality with an Application to German Spatial Planning Regions

Runge

2023

Journal of Official Statistics

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Income inequality is a persistent topic of public and political debate. In this context, the focus often shifts from the national level to a more detailed geographical level. In particular, inequality between or within local communities can be assessed. In this article, the estimation of inequality within regions, that is, between households, is considered at a regionally disaggregated level. From a methodological point of view, a small area estimation of the Gini coefficient is carried out using an area-level model linking survey data with related administrative data. Specifically, the Fay-Herriot model is applied using a logit-transformation followed by a bias-corrected back-transformation. The uncertainty of the point estimate is assessed using a parametric bootstrap procedure to estimate the mean squared error. The validity of the methodology is shown in a model-based simulation for the point estimator as well as for the uncertainty measure. The proposed methodology is illustrated by estimating model-based Gini coefficients for spatial planning regions in Germany, using survey data from the Socio-Economic Panel and aggregate data from the 2011 Census. The results show that intra-regional inequality is more diverse than a consideration only between East and West suggests.

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Section: Discussionmentioning

confidence: 99%

Estimating Intra-Regional Inequality with an Application to German Spatial Planning Regions

Runge

2023

Journal of Official Statistics

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“…An approach to modeling the non-missing at random mechanism in SAE under informative sampling and nonresponse can be found in Sverchkov and Pfeffermann (2018). Kreutzmann et al (2022) and Bijlsma et al (2020) use a Fay-Herriot model with pooled direct estimators after multiple imputation and take into account the additional uncertainty due to the missing values in the sampling variance. However, both ignore the additional uncertainty in the regressionsynthetic part of the model.…”

Section: Motivationmentioning

confidence: 99%

“…Therefore, the M direct estimators û Dir * d;m and their variances s 2 * e d;m are pooled on the transformed scale and substituted in Equations ( 8) and (9). Kreutzmann et al (2022) present a Fay-Herriot estimator which uses pooled direct components on the original scale, which are substituted in the (log transformed) Fay-Herriot model. We extend this approach and transform the direct components of each imputed data set to estimate the regression-synthetic components.…”

Section: Component Poolingmentioning

confidence: 99%

“…The simulation setup and data models are chosen to be consistent with those of Kreutzmann et al (2022). For the simulations, finite populations of size N ¼ 60,000 with D ¼ 100 domains are generated so that in each domain the population size N d is between 200 and 1,000 for d ¼ 1,..., D. The samples were drawn via stratified random sampling, where the strata represent the domains.…”

Section: Data Generationmentioning

confidence: 99%

“…The FH estimator before deletion serves as the gold standard in this simulation. In addition, we compare the performance of the proposed FH.MI estimators with the pooled Fay-Herriot estimator (FH.RR) mentioned in Section 3 and with the estimator proposed by Kreutzmann et al (2022) denoted by FH.DirectRR. They consider the estimator under a normal and log-normal setting for a mean value, and so we also examine this estimator only under these settings.…”

Section: Performance Of Point Estimatorsmentioning

confidence: 99%

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Small Area with Multiply Imputed Survey Data

Runge,

Schmid

2023

Journal of Official Statistics

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In this article, we propose a framework for small area estimation with multiply imputed survey data. Many statistical surveys suffer from (a) high nonresponse rates due to sensitive questions and response burden and (b) too small sample sizes to allow for reliable estimates on (unplanned) disaggregated levels due to budget constraints. One way to deal with missing values is to replace them by several plausible/imputed values based on a model. Small area estimation, such as the model by Fay and Herriot, is applied to estimate regionally disaggregated indicators when direct estimates are imprecise. The framework presented tackles simultaneously multiply imputed values and imprecise direct estimates. In particular, we extend the general class of transformed Fay-Herriot models to account for the additional uncertainty from multiple imputation. We derive three special cases of the Fay-Herriot model with particular transformations and provide point and mean squared error estimators. Depending on the case, the mean squared error is estimated by analytic solutions or resampling methods. Comprehensive simulations in a controlled environment show that the proposed methodology leads to reliable and precise results in terms of bias and mean squared error. The methodology is illustrated by a real data example using European wealth data.

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A Framework for Producing Small Area Estimates Based on Area-Level Models in R

Harmening,

Kreutzmann,

Schmidt

et al. 2023

The R Journal

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The R package emdi facilitates the estimation of regionally disaggregated indicators using small area estimation methods and provides tools for model building, diagnostics, presenting, and exporting the results. The package version 1.1.7 includes unit-level small area models that rely on access to micro data. The area-level model by Fay and Herriot (1979) and various extensions have been added to the package since the release of version 2.0.0. These extensions include (a) area-level models with back-transformations, (b) spatial and robust extensions, (c) adjusted variance estimation methods, and (d) area-level models that account for measurement errors. Corresponding mean squared error estimators are implemented for assessing the uncertainty. User-friendly tools like a stepwise variable selection, model diagnostics, benchmarking options, high quality maps and results exportation options enable a complete analysis procedure. The functionality of the package is illustrated by examples based on synthetic data for Austrian districts.

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The Fay–Herriot model for multiply imputed data with an application to regional wealth estimation in Germany

Cited by 3 publications

References 41 publications

Estimating Intra-Regional Inequality with an Application to German Spatial Planning Regions

Estimating Intra-Regional Inequality with an Application to German Spatial Planning Regions

Small Area with Multiply Imputed Survey Data

A Framework for Producing Small Area Estimates Based on Area-Level Models in R

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