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The estimation of poverty indicators using mixed effects random forests: case study for the Mexican state of Veracruz
Krennmair, P.; Schmid, T.; Tzavidis, N.
Abstract: Mapping and analysing the spatial concentration of poverty is imperative for evidence-based policies to translate into inclusive and sustainable actions. The use of national sample surveys to obtain detailed and reliable estimates for poverty indicators on disaggregated geographical and other domains (e.g. demographic groups) imposes a methodological challenge. Small Area Estimation is a collective term for (model-based) procedures, which combine survey data with existing auxiliary information (e.g. census or administrative data) using predictive models to estimate domain-specific statistical indicators. We propose the use of mixed effects random forests as flexible, robust, and reliable method to produce domain-specific cumulative distribution functions from which (non-linear) poverty estimators can be obtained. This paper is driven by our aim to inform a transparent and steady discussion on current methodological improvements for Small Area Estimation, such as the use of (tree-based) machine learning methods and their contribution to recent requirements for poverty assessment. We evaluate proposed point and uncertainty estimators in a design-based simulation and focus on a case study uncovering spatial patterns of poverty for the Mexican state of Veracruz.
Analysing opportunity cost of care work using mixed effects random forests under aggregated census data
Krennmair, P.; Würz, N.; Schmid, T.
Abstract: Reliable estimators of the spatial distribution of socio-economic indicators are essential for evidence-based policy-making. As sample sizes are small for highly disaggregated domains, the accuracy of the direct estimates is reduced. To overcome this problem small area estimation approaches are promising. In this work we propose a small area methodology using machine learning methods. The semi-parametric framework of mixed effects random forest combines the advantages of random forests (robustness against outliers and implicit model-selection) with the ability to model hierarchical dependencies. Existing random forest-based methods require access to auxiliary information on population-level. We present a methodology that deals with the lack of population micro-data. Our strategy adaptively incorporates aggregated auxiliary information through calibration-weights - based on empirical likelihood - for the estimation of area-level means. In addition to our point estimator, we provide a non-parametric bootstrap estimator measuring its uncertainty. The performance of the proposed point estimator and its uncertainty measure is studied in model-based simulations. Finally, the proposed methodology is applied to the 2011 Socio-Economic Panel and aggregate census information from the same year to estimate the average opportunity cost of care work for 96 regional planning regions in Germany.
The R package saeTrafo for estimating unit-level small area models under transformations
Abstract: The R package saeTrafo provides new statistical methodology for the estimation of small area means using unit-level models under transformations. The method of Würz et al. (2022, JRSSA) enables the use of unit-level models dealing with both limited auxiliary data (often the only source of data due to confidentiality agreements) and skewed distributed dependent variables like income (by using transformations such as the log or data-driven log-shift). In addition to the implementation of the new methodology, saeTrafo provides established methods for unitlevel models under transformations, allowing further applications and comparisons. It is of advantage that the most suitable method is automatically selected and uncertainty estimates are easily offered. In addition, tools for creating plots (model validation and estimator evaluation), visualisation on maps and exporting to Excel and OpenDocument Spreadsheets are provided. The functionalities of the package are demonstrated with exemplary data based on Austrian income and living conditions.
- Releasing Survey Microdata with Exact Cluster Locations and Additional Privacy Safeguards
Koebe, T.; Arias-Salazar, A.; Schmid, T.
Abstract: Household survey programs around the world publish fine-granular georeferenced microdata to support research on the interdependence of human livelihoods and their surrounding environment. To safeguard the respondents’ privacy, micro-level survey data is usually (pseudo)-anonymised through deletion or perturbation procedures such as obfuscating the true location of data collection. This, however, poses a challenge to emerging approaches that augment survey data with auxiliary information on a local level. Here, we propose an alternative microdata dissemination strategy that leverages the utility of the original microdata with additional privacy safeguards through synthetically generated data using generative models. We back our proposal with experiments using data from the 2011 Costa Rican census and satellite-derived auxiliary information. Our strategy reduces the respondents’ re-identification risk for any number of disclosed attributes by 60-80% even under re-identification attempts.
- A framework for producing small area estimates based on area-level models in R
Harmening, S.; Kreutzmann, A.-K.; Pannier, S.; Salvati, N.; Schmid, T.
Abstract: 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 which may be challenging due to confidentiality constraints. In contrast, area-level models are less demanding with respect to (a) data requirements, as only aggregates are needed for estimating regional indicators, and (b) computational resources, and enable the incorporation of design-based properties. Therefore, the area-level model (Fay and Herriot 1979) and various extensions have been added to version 2.0.2 of the package emdi. These extensions include amongst others (a) transformed 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 function, model diagnostics, benchmarking options, high quality maps and export options of the results enable the user a complete analysis procedure - from model building to diagnostics. The functionality of the package is demonstrated by illustrative examples based on synthetic data for Austrian districts.
- Estimating regional unemployment with mobile network data for functional urban areas in Germany
Hadam, S.; N. Würz; Kreutzmann, A.-K.; Schmid, T.
Abstract: The ongoing growth of cities due to better job opportunities is leading to increased labour-related commuter flows in several countries. On the one hand, an increasing number of people commute and move to the cities, but on the other hand, the labour market indicates higher unemployment rates in urban areas than in the surrounding areas. We investigate this phenomenon on regional level by an alternative definition of unemployment rates in which commuting behaviour is integrated. We combine data from the labour force survey with dynamic mobile network data by small area models for the federal state North Rhine-Westphalia in Germany. From a methodical perspective, we use a transformed Fay-Herriot model with bias correction for the estimation of unemployment rates and propose a parametric bootstrap for the mean squared error estimation that includes the bias correction. The performance of the proposed methodology is evaluated in a case study based on official data and in model-based simulations. The results in the application show that unemployment rates (adjusted by commuters) in German cities are lower than traditional official unemployment rates indicate.
- Small area estimation with multiple imputed survey data
Runge, M.; Schmid, T.
Abstract: Many statistical surveys suffer from a) high non-response rates due to sensitive questions and response burden and b) too small sample sizes to allow for reliable estimates on disaggregated levels due to budget constraints. One way to deal with missing values is to replace them by several plausible values based on a model. Small area estimation is used to estimate regionally disaggregated indicators when direct estimates are imprecise due to small sample sizes. In this paper we propose a framework that tackles both problems at the same time. In particular, we extend the general class of transformed Fay-Herriot models to account for the additional uncertainty from multiple imputation. We derive three subcases of the Fay-Herriot model with particular transformations and provide point and mean squared error estimators. Depending on the subcase, the mean squared error is estimated by analytic solutions or resampling methods. Comprehensive model-based simulations in a controlled environment and design-based simulations based on European income and wealth data show that the proposed methodology leads to reliable and precise results in terms of bias and mean squared error.
- Scale estimation and data-driven tuning constant selection for M-quantile regression
Dwaber, J.; Salvati, N.; Schmid, T.; Tzavidis, N.
Abstract: M-quantile regression is a general form of quantile-like regression which usually utilises the Huber inﬂuence function and corresponding tuning constant. Estimation requires a nuisance scale parameter to ensure the M-quantile estimates are scale invariant, with several scale estimators having previously been proposed. In this paper we assess these scale estimators and evaluate their suitability, as well as proposing a new scale estimator based on the method of moments. Further, we present two approaches for estimating data-driven tuning constant selection for M-quantile regression. The tuning constants are obtained by i) minimising the estimated asymptotic variance of the regression parameters and ii) utilising an inverse M-quantile function to reduce the eﬀect of outlying observations. We investigate whether data-driven tuning constants, as opposed to the usual ﬁxed constant, for instance, at c=1.345, can improve the eﬃciency of the estimators of M-quantile regression parameters. The performance of the data-driven tuning constant is investigated in diﬀerent scenarios using model-based simulations. Finally, we illustrate the proposed methods using a European Union Statistics on Income and Living Conditions data set.
- Asymptotic distribution of regression quantiles in a mixed effects model
Hensel, S.; Pannier, S.; Schmid, T.; Tzavidis, N.
Abstract: Linear quantile models allow for a robust analysis of the conditional distribution of the variable of interest. The introduction of a random effects term extended their range of application to data with complex dependency structures, as they occur in many studies. This paper proposes a higher theoretical understanding of linear quantile mixed models by analysing the asymptotic behaviour of the corresponding maximum likelihood estimator. We will proof the estimators to be consistent and show that it is asymptotically normally distributed. Additionally, a plug-in variance estimator is derived, and its finite sample behaviour is demonstrated in a simulation study.