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Summary: With the rise in popularity of digital Atlases to communicate spatial variation, there is an increasing need for robust small area estimates. However, current small area estimation methods suffer from various modelling problems when data are very sparse or when estimates are required for areas with very small populations. These issues are particularly heightened when modelling proportions. Additionally, recent work has shown significant benefits in modelling at both the individual and area levels. We propose a two‐stage Bayesian hierarchical small area estimation approach for proportions that can account for survey design, reduce direct estimate instability and generate prevalence estimates for small areas with no survey data. Using a simulation study, we show that, compared with existing Bayesian small area estimation methods, our approach can provide optimal predictive performance (Bayesian mean relative root mean squared error, mean absolute relative bias and coverage) of proportions under a variety of data conditions, including very sparse and unstable data. To assess the model in practice, we compare modelled estimates of current smoking prevalence for 1,630 small areas in Australia using the 2017–2018 National Health Survey data combined with 2016 census data. [ABSTRACT FROM AUTHOR]

This study investigates the trends in chronic malnutrition (stunting) among young children across Bangladesh's 64 districts and 544 sub-districts from 2000 to 2018. We utilized remote-sensed data–nighttime light intensity to indicate urbanization, and environmental factors like precipitation and vegetation levels–to examine patterns of stunting. Our primary data source was the Bangladesh Demographic and Health Survey, conducted six times within the study period. Using Bayesian multilevel time-series models, we integrated cross-sectional, temporal, and spatial data to estimate stunting rates for years not covered by the direct survey information. This approach, enhanced by remote-sensed data, allowed for greater prediction accuracy by incorporating information from neighboring areas. Our findings show a significant reduction in national stunting rates, from nearly 50% in 2000 to about 30% in 2018. Despite this overall progress, some districts have consistently high levels of stunting, while others show fluctuating levels. Our model gives more precise sub-district estimates than previous methods, which were limited by data gaps. The study highlights Bangladesh's advancements in reducing child stunting, highlighting the value of integrating remote-sensed data for more precise and credible analysis. [ABSTRACT FROM AUTHOR]

The National Health and Nutrition Examination Survey (NHANES) is a major program of the National Center for Health Statistics, designed to assess the health and nutritional status of adults and children in the United States. The analysis of NHANES dental caries data faces several challenges, including (1) the data were collected using a complex, multistage, stratified, unequal-probability sampling design; (2) the sample size of some primary sampling units (PSU), e.g., counties, is very small; (3) the measures of dental caries have complicated structure and correlation, and (4) there is a substantial percentage of nonresponses, which are expected not to be missing at random or non-ignorable. We propose a Bayesian hierarchical spatial model to address these analysis challenges. We develop a two-level Potts model that closely resembles the caries evolution process, and captures complicated spatial correlations between teeth and surfaces of the teeth. By adding Bayesian hierarchies to the Potts model, we account for the multistage survey sampling design, while also enabling information borrowing across PSUs for small-area estimation. We incorporate sampling weights by including them as a covariate in the model and adopt flexible B-splines to achieve robust inference. We account for non-ignorable missing outcomes and covariates using the selection model. We use data augmentation coupled with the noisy Monte Carlo algorithm to overcome the numerical difficulty caused by doubly-intractable normalizing constants and sample posteriors. Our analysis results show strong spatial associations between teeth and tooth surfaces, including that dental hygienic factors, such as fluorosis and sealant, reduce dental disease risks. [ABSTRACT FROM AUTHOR]

In this paper we estimate monetary and non-monetary poverty measures at two sub-regional levels in the region of Tuscany (Italy) using data from the ad-hoc Survey on Vulnerability and Poverty held by Regional Institute from Economic Planning of Tuscany (IRPET). We estimate the percentage of households living in poverty conditions and three supplementary fuzzy measures of poverty regarding deprivation in basic needs and lifestyle, children deprivation, and financial insecurity. The key feature of the survey is that it was carried out after the COVID-19 pandemic, therefore, some of the items collected focus on the subjective perception of poverty eighteen months after the beginning of the pandemic. We assess the quality of these estimates either with initial direct estimates along with their sampling variance, and with a secondary small area estimation when the formers are not sufficiently accurate. [ABSTRACT FROM AUTHOR]

In small area estimation, the sample size is so small that direct estimators have seldom enough adequate precision. Therefore, it is common to use auxiliary data via covariates and produce estimators that combine them with direct data. Nevertheless, it is not uncommon for covariates to be measured with error, leading to inconsistent estimators. Area-level models accounting for measurement error (ME) in covariates have been proposed, and they usually assume that the errors are an i.i.d. Gaussian model. However, there might be situations in which this assumption is violated especially when covariates present severe outlying values that cannot be cached by the Gaussian distribution. To overcome this problem, we propose to model the ME through sub-Gaussian α -stable (SG α S) distribution, a flexible distribution that accommodates different types of outlying observations and also Gaussian data as a special case when α = 2 . The SG α S distribution is a generalization of the Gaussian distribution that allows for skewness and heavy tails by adding an extra parameter, α ∈ (0 , 2 ] , to control tail behaviour. The model parameters are estimated in a fully Bayesian framework. The performance of the proposal is illustrated by applying to real data and some simulation studies. [ABSTRACT FROM AUTHOR]

We develop a unit-level one-inflated beta model for the purpose of small area estimation. Our specific interest is in estimation of seat-belt use rates for Iowa counties using data from the Iowa Seat-Belt Use Survey. As a result of small county sample sizes, small area estimation methods are needed. We propose frequentist and Bayesian implementations of a unit-level one-inflated beta model. We compare the Bayesian and frequentist predictors to simpler alternatives through simulation. We apply the proposed Bayesian and frequentist procedures to data from the Iowa Seat-Belt Use Survey. [ABSTRACT FROM AUTHOR]

This article develops model-based predictors for area-level proportions of employed men and women by occupation sectors and for entropies and divergence indexes (DIs) within and between sex groups. Since the direct estimators of the proportions add up to one in the occupational sections, they are compositions that can be imprecise if the sample sizes are small. We fit a multivariate Fay–Herriot model to logratio transformations of the direct estimators of the proportions. Small area estimators of the proportions, entropies, and DIs are derived from the fitted model and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyze the behavior of the introduced model-based predictors are carried out. We give an application to Spanish Labour Force Survey data from 2022. The target is to investigate the state of sex occupational entropies and divergences in Spanish provinces. [ABSTRACT FROM AUTHOR]

Two challenges in small area estimation occur when (i) the sample selection mechanism depends on the outcome variable and (ii) the parameter of interest is a nonlinear function of the response variable in the assumed model. If, given the values of the model covariates, the sample selection mechanism depends on the model response variable, the design is said to be informative for the model. Pfeffermann and Sverchkov (2007) develop a small area estimation procedure for informative sampling, focusing on the prediction of small area means. Molina and Rao (2010) develop a small area estimation procedure for general parameters that are nonlinear functions of the model response variable. The method of Molina and Rao assumes noninformative sampling. We combine these two approaches to develop a procedure for the estimation of general parameters in small areas under informative sampling. We introduce a parametric bootstrap MSE estimator that is appropriate for an informative sample design. We evaluate the validity of the proposed procedures through extensive simulation studies and illustrate the procedures utilizing Mexico's income data. [ABSTRACT FROM AUTHOR]

Small area estimation (SAE) approach has been employed to produce realistic estimates for the variable of interest in cases when the available data are insufficient to produce reliable estimates for the domain. Missing data is a significant issue that affects sample surveys, but in case of SAE, it is particularly vulnerable. To overcome the problem of missing data in case of SAE, this study is a fundamental effort that proposes some general imputation methods for the domain mean estimation under simple random sampling. The mean square error expressions of the proposed imputation methods are determined up to first order approximation. The analytical study is carried out to establish the efficiency conditions. A simulation analysis is performed by utilizing hypothetically created data sets. Further, the simulation analysis is extended with a real data application. In addition, appropriate recommendations for practical applications have been provided to survey experts. [ABSTRACT FROM AUTHOR]

Small area estimation (SAE), which combines a population census and a sample survey, is widely used to estimate poverty and welfare indicators in small areas. A common situation in practice is that a population census is conducted using both short‐ and long‐form questionnaires. The short form is used to collect basic demographic information for the whole population, while the long form is used to collect additional information, such as employment, from a random sample. This study shows that combining both short‐ and long‐form data can improve estimation efficiency. This method is applied to poverty maps for the 2014–2019 period in Vietnam. [ABSTRACT FROM AUTHOR]

Poverty mapping is a powerful tool to study the geography of poverty. The choice of the spatial resolution is central as poverty measures defined at a coarser level may mask their heterogeneity at finer levels. We introduce a small area multi-scale approach integrating survey and remote sensing data that leverages information at different spatial resolutions and accounts for hierarchical dependencies, preserving estimates coherence. We map poverty rates by proposing a Bayesian Beta-based model equipped with a new benchmarking algorithm accounting for the double-bounded support. A simulation study shows the effectiveness of our proposal and an application on Bangladesh is discussed. [ABSTRACT FROM AUTHOR]

County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) are useful for program development and evaluation. Since county sample sizes in the CEAP survey are insufficient to support reliable direct estimators, small area estimation procedures are needed. The quantity of water runoff is a useful covariate but is unavailable for the full population. We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model with sheet and rill erosion as the response. As the runoff and sheet and rill erosion are estimators from the same survey, the measurement error in the covariate is important as is the correlation between the measurement error and the sampling error. We conduct a detailed investigation of small area estimation in the presence of a correlation between the measurement error in the covariate and the sampling error in the response. In simulations, the proposed predictor is superior to small area predictors that assume the response and covariate are uncorrelated or that ignore the measurement error entirely. [ABSTRACT FROM AUTHOR]

The 31st Morris Hansen Lecture gave a broad overview of some fundamental issues regarding the roles of statistical models in surveys, with an emphasis on a method of model selection known as the fence. This discussion provides some general lecture remarks and expands on the possible applicability of the fence methods in small area estimation. Unit-level and area-level small area estimation modeling illustrations are provided. A general variable selection framework for small area estimation is presented, along with recent application studies and ideas for expansion to include the fence methods. [ABSTRACT FROM AUTHOR]

This paper introduces a new statistical methodology for estimating Duncan dissimilarity indexes of occupational segregation by sex in administrative areas and time periods. Given that direct estimators of the proportion of men (or women) in the group of employed people for each occupational sector are not accurate enough in the considered estimation domains, we fit to them a three-fold Fay–Herriot model with random effects at three hierarchical levels. Based on the fitted area-level model, empirical best predictors of the cited proportions and Duncan segregation indexes are derived. A parametric bootstrap algorithm is implemented to estimate the mean squared error. Some simulation studies are included to show how the proposed predictors have a good balance between bias and mean squared error. Data from the Spanish Labour Force Survey are used to illustrate the performance of the new statistical methodology and to give some light about the current state of sex occupational segregation by province in Spain. Research claims that there is a sex gap that persists despite advances in the inclusion of women in the labour market in recent years and that is related to the unequal sharing of family responsabilities and the stigmas still present in modern societies. [ABSTRACT FROM AUTHOR]

In literature, several researchers have discovered that the reviews written about Airbnb accommodation tend to be extremely positive than those published on other famous platforms, consequently, many negative experiences remain untracked. Leaving negative experiences underrepresented hampers hosts' ability to improve their services. To overcome this gap, we employ Small Area Estimation to quantify negative sentiment in Airbnb reviews and the relative critical topics that characterize them. Our methodology involves a two-step process: first, we employ sentiment analysis and topic modeling to identify negative sentiment and critical issues, followed by the application of a mixed effect random forest model to provide a granular analysis of Airbnb reviews in small sub-populations in the context of small area estimation. We focus on domains of the city of Rome defined by geographical areas and the presence of hosts and Superhosts. Our findings reveal nuanced sentiment variations and critical topic proportions that traditional methods often overlook. [ABSTRACT FROM AUTHOR]

Estimating economic poverty indicators at the local level is essential for well-targeted data-driven welfare policies. However, Italy is a country characterized by strong geographical heterogeneity represented by unequal price levels among different areas, and computing poverty indicators with a national monetary poverty threshold can be misleading. This work proposes a novel approach to estimate monetary poverty incidence at the provincial level in Italy considering the different price levels within national boundaries. To account for local price variation, Spatial Price Indices (SPIs) are computed using scanner data on retail prices. The SPIs are estimated in two ways, referring to the mean local prices and using the 20th percentile of the prices. These two kinds of SPIs are used to adjust the national poverty line when computing the poverty incidence at the provincial level using Small Area Estimation (SAE) models. Our findings suggest that adjusting the national poverty line using the SPIs to compute a monetary poverty index can modify the poverty mapping results from the map produced with the traditional national poverty line that ignores price differences. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In low- and middle-income countries, household surveys are the most reliable data source to examine health and demographic indicators at the subnational level, an exercise in small area estimation. Model-based unit-level models are favoured for producing the subnational estimates at fine scale, such as the admin-2 level. Typically, the surveys employ stratified 2-stage cluster sampling with strata consisting of an urban/rural designation crossed with administrative regions. To avoid bias and increase predictive precision, the stratification should be acknowledged in the analysis. To move from the cluster to the area requires an aggregation step in which the prevalence surface is averaged with respect to population density. This requires estimating a partition of the study area into its urban and rural components, and to do this we experiment with a variety of classification algorithms, including logistic regression, Bayesian additive regression trees, and gradient boosted trees. Pixel-level covariate surfaces are used to improve prediction. We estimate spatial HIV prevalence in women of age 15–49 in Malawi using the stratification/aggregation method we propose. [ABSTRACT FROM AUTHOR]

Background An extensive literature documents substantial variations in life expectancy (LE) between countries and at various levels of subnational geography. These variations in LE are significantly correlated with socioeconomic covariates, though no analyses have been produced at the finest feasible census tract (CT) level of geographic disaggregation in Canada or designed to compare Canada with the United States. Data and methods Abridged life tables for each CT where robust estimates were feasible were estimated comparably with U.S. data. Cross-tabulations and graphical visualizations are used to explore patterns of LE across Canada, for Canada's 15 largest cities, and for the 6 largest U.S. cities. Results LE varies by as much as two decades across CTs in both countries' largest cities. There are notable differences in the strength of associations with socioeconomic status (SES) factors across Canada's largest cities, though these associations with income-poverty rates are noticeably weaker for Canada's largest cities than for the United States' largest cities. Interpretation Small area geographic variations in LE signal major health inequalities. The association of CT-level LE with SES factors supports and extends similar findings across many studies. The variability in these associations within Canada and compared with those in the United States reinforces the importance for population health of better understanding differences in social structures and public policies not only at the national and provincial or state levels, but also within municipalities to better inform interventions to ameliorate health inequalities. [ABSTRACT FROM AUTHOR]

A recent application in machine learning has introduced a novel approach, complemented by big data sources, aimed at providing precise estimates for small geographical areas. This method employs a dual strategy: (a) hybrid estimation, involving the integration of big data sources with imputed values derived from K nearest neighbours (KNN) to address missing target variable values from the big data source; and (b) calibration of the collective sum of small area estimates to an independent yet efficient national total. Evaluating its efficacy using simulated data from the 2016 Australian population census, the calibrated KNN (CKNN) method demonstrated superior performance compared to the Fay-Herriot method based on area-level covariates. This paper enhances the comparative analysis by contrasting the CKNN method with a hierarchical Bayes method using the logit-normal model (LN) relevant for binary data. Broadly speaking, the LN method can be viewed as the Bayesian equivalent of Battese-Harter-Fuller (BHF) method, which incorporates unit-level covariates. Our results demonstrate the CKNN method's superiority over the LN method. However, the application of hybrid estimation to the LN method significantly diminishes this superiority. Although CKNN estimates maintain better precision, they are not as accurate as the estimates from the hybridized LN method. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved Nested Error Regression model in which the random effects for each area are given a prior distribution using the Poisson–Dirichlet Process. Based on this model, we mainly investigate the construction of the parameter estimation using the Empirical Bayesian(EB) estimation method, and we adopt various methods such as the Maximum Likelihood Estimation(MLE) method and the Markov chain Monte Carlo algorithm to solve the model parameter estimation jointly. The viability of the model is verified using numerical simulation, and the proposed model is applied to an actual small area estimation problem. Compared to the conventional normal random effects linear model, the proposed model is more accurate for the estimation of complex real-world application data, which makes it suitable for a broader range of application contexts. [ABSTRACT FROM AUTHOR]

Supplemental Digital Content is Available in the Text. County-level prevalences of arthritis and arthritis-attributable pain outcomes have significant spatial clustering patterns, and factors shaping these patterns are different for different outcomes. Research on the geographic distribution of pain and arthritis outcomes, especially at the county level, is limited. This is a high-priority topic, however, given the heterogeneity of subnational and substate regions and the importance of county-level governments in shaping population health. Our study provides the most fine-grained picture to date of the geography of pain in the United States. Combining 2011 Behavioral Risk Factor Surveillance System data with county-level data from the Census and other sources, we examined arthritis and arthritis-attributable joint pain, severe joint pain, and activity limitations in US counties. We used small area estimation to estimate county-level prevalences and spatial analyses to visualize and model these outcomes. Models considering spatial structures show superiority over nonspatial models. Counties with higher prevalences of arthritis and arthritis-related outcomes are mostly clustered in the Deep South and Appalachia, while severe consequences of arthritis are particularly common in counties in the Southwest, Pacific Northwest, Georgia, Florida, and Maine. Net of arthritis, county-level percentages of racial/ethnic minority groups are negatively associated with joint pain prevalence, but positively associated with severe joint pain prevalence. Severe joint pain is also more common in counties with more female individuals, separated or divorced residents, more high school noncompleters, fewer chiropractors, and higher opioid prescribing rates. Activity limitations are more common in counties with higher percentages of uninsured people. Our findings show that different spatial processes shape the distribution of different arthritis-related pain outcomes, which may inform local policies and programs to reduce the risk of arthritis and its consequences. [ABSTRACT FROM AUTHOR]

This article introduces bayesian spatial smoothing models for disease mapping—a specific application of small area estimation where the full universe of data is known—to a wider audience of public health professionals using firearm suicide as a motivating example. Besag, York, and Mollié (BYM) Poisson spatial and space–time smoothing models were fitted to firearm suicide counts for the years 2014-2018. County raw death rates in 2018 ranged from 0 to 24.81 deaths per 10 000 people. However, the highest mortality rate was highly unstable, based on only 2 deaths in a population of approximately 800, and 80.5% of contiguous US counties experienced fewer than 10 firearm suicide deaths and were thus suppressed. Spatially smoothed county firearm suicide mortality estimates ranged from 0.06 to 4.05 deaths per 10 000 people and could be reported for all counties. The space–time smoothing model produced similar estimates with narrower credible intervals as it allowed counties to gain precision from adjacent neighbors and their own counts in adjacent years. bayesian spatial smoothing methods are a useful tool for evaluating spatial health disparities in small geographies where small numbers can result in highly variable rate estimates, and new estimation techniques in R software have made fitting these models more accessible to researchers. [ABSTRACT FROM AUTHOR]

This article provides a review of the work carried out in Colombia on small area estimation. It considers initiatives of an academic nature, mainly originating from universities, as well as initiatives focused on generating offcial statistics from public offices and private companies in the country. The objective of the work is to update the interested reader on the progress of this methodology in the country and to encourage the community to deepen into the analysis and publication of content on small area estimation. Additionally, a summary of the main models used in small area estimation is presented. [ABSTRACT FROM AUTHOR]

Information about some poverty indicators is important not only for the large administrative level but also for lower administrative level. This information can be obtained from many surveys. Unfortunately, many surveys are usually designed to satisfy accuracy for large populations. As a result, it is often encountered that the sample size from some sub-populations which can be obtained from a survey is too small to produce a reliable direct estimator. The sub-population which the selected sample from it is not large enough to produce a reliable direct estimator is also called a small area. In this paper, we propose the spatial empirical best predictor (SEBP) for some poverty indicators in some small areas. The SEBP is derived under a unit-level spatial lognormal mixed model which incorporates spatial dependence into the covariance structure. The mean square prediction error (MSPE) of the SEBP is estimated by the parametric bootstrap method. A simulation study was conducted to evaluate the performance of the SEBP compared to the direct estimates as well as the empirical best predictor (EBP). Further, the SEBP was also applied to obtain the estimates of some poverty indicators for some sub-districts in Bogor, Indonesia. The results showed that there is a substantial reduction in MSPE of the SEBP over the direct estimates and the EBP for almost all sub-districts. [ABSTRACT FROM AUTHOR]

In-work poverty has risen to become a key feature of European societies. In 2017, the percentage of workers at risk of low pay in Italy reached an estimated 25% and the issue rose to the forefront of the public and political debate. Yet, due to data limitations, few studies analysed the local distribution of this phenomenon and investigated the macro-determinants associated with its rise. By applying Small Area Estimates (SAE) to EU-SILC data we obtain a novel map of the distribution of in-work poverty in Italy, defined as the share of workers at risk of low pay (AROLP) between 2008 and 2017. The unit of analysis of Local Labour Systems, a non-administrative unit based on commuter flows, highlights the deepening of Italian dualism between Northern and Southern areas, as well as rising within-region wage inequality. By means of a panel fixed-effects model linking estimates of AROLP with data on local sectoral employment, we observe that growth in low-skill sectors such as agriculture is associated with increases in AROLP incidence. On the contrary trends of low pay are negatively associated with the growth of manufacturing and construction sectors, and jobs in non-market services, such as public sector jobs. In addition, variations in overall employment represent the strongest predictor for dynamics of low-pay incidence. [ABSTRACT FROM AUTHOR]

Abstract Sample surveys are extensively used to provide reliable direct estimates for large areas or domains with enough sample sizes at national and regional levels. However, zones are unplanned domains by the Demographic and Health Survey (DHS) program and need more sample sizes to produce direct survey estimates with adequate precision. Conducting surveys in small areas (like zones) is too expensive and time-consuming, making it unfeasible for developing countries like Ethiopia. Therefore, this study aims to use the Hierarchical Bayes (HB) Small Area Estimation (SAE) model to estimate the Community-Based Health Insurance (CBHI) coverage at the zone levels in Ethiopia. To achieve this, we combined the 2019 Ethiopia Mini-Demographic and Health Survey (EMDHS) data with the 2007 population census data. SAE has addressed the challenge of producing reliable parameter estimates for small or even zero sample sizes across Ethiopian zones by utilizing auxiliary information from the population census. The results show that model-based estimates generated by the SAE approach are more accurate than direct survey estimates of CBHI. A map of CBHI scheme coverage was also used to visualize the spatial variation in the distribution of CBHI scheme coverage. From the CBHI scheme coverage map, we noticed notable variations in CBHI scheme coverage across Ethiopian zones. Additionally, this research identified areas with high and low CBHI scheme coverage to improve decision-making and increase coverage in Ethiopia. One of the novelties of this paper is estimating the non-sampled zones; therefore, the policymakers will give equal attention similar to the sampled zones.

Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains and performing small area estimation at the area level. We propose a bias correction framework for a large class of inequality measures comprising the Gini Index, the Generalized Entropy, and the Atkinson index families by accounting for complex survey designs. The proposed methodology does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using EU-SILC data, their results show a noticeable bias reduction for all the measures. Lastly, an illustrative example of application in small area estimation confirms that ignoring ex-ante bias correction determines model misspecification. [ABSTRACT FROM AUTHOR]

In small area estimation, it is sometimes necessary to use model-based methods to produce estimates in areas with little or no data. In official statistics, we often require that aggregates of small area estimates agree with national estimates for internal consistency purposes. Enforcing this agreement is referred to as benchmarking, and while methods currently exist to perform benchmarking, few are ideal for applications with non-normal outcomes and benchmarks with uncertainty. Fully Bayesian benchmarking is a theoretically appealing approach insofar as we can obtain posterior distributions conditional on a benchmarking constraint. However, existing implementations may be computationally prohibitive. In this paper, we critically review benchmarking methods in the context of small area estimation in low- and middle-income countries with binary outcomes and uncertain benchmarks, and propose a novel approach in which posterior samples of small area characteristics from an unbenchmarked model can be combined with a rejection sampler or Metropolis-Hastings algorithm to produce benchmarked posterior distributions in a computationally efficient way. To illustrate the flexibility and efficiency of our approach, we provide comparisons to an existing benchmarking approach in a simulation, and applications to HIV prevalence and under-5 mortality estimation. Code implementing our methodology is available in the R package stbench. [ABSTRACT FROM AUTHOR]

In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model‐based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often ignore the survey design, while traditional small area estimation approaches may not incorporate both unit‐level covariate information and spatial smoothing in a design consistent way. We propose a smoothed model‐assisted estimator that accounts for survey design and leverages both unit‐level covariates and spatial smoothing. Under certain regularity assumptions, this estimator is both design consistent and model consistent. We compare it with existing design‐based and model‐based estimators using real and simulated data. [ABSTRACT FROM AUTHOR]

Since the beginning of the 21st Century obesity has become a major public health concern in Mexico. Survey data have been key to tracking the evolution of the national and regional prevalence of obesity over time. However, these data are insufficient for policymakers and researchers interested in obesity from a more local and spatial perspective. This paper uses two secondary data sources: the Mexican National Health and Nutrition Survey 2021 and the Mexican National Population Census 2020. This paper implements a Bayesian hierarchical approach to model survey and census data to produce municipal-level estimates for Mexico in 2020. The results indicate that obesity has inter and intra-regional variability. Obesity is more prevalent in the north and in the Yucatan peninsula and tends to be lower in the state of Chiapas. However, within these regions there is some degree of variability in obesity rates. The results provide a more detailed geographical picture of obesity across Mexico and raise the possibility of using the resulting estimates for further statistical and policy-relevant research. [ABSTRACT FROM AUTHOR]

Sample surveys are extensively used to provide reliable direct estimates for large areas or domains with enough sample sizes at national and regional levels. However, zones are unplanned domains by the Demographic and Health Survey (DHS) program and need more sample sizes to produce direct survey estimates with adequate precision. Conducting surveys in small areas (like zones) is too expensive and time-consuming, making it unfeasible for developing countries like Ethiopia. Therefore, this study aims to use the Hierarchical Bayes (HB) Small Area Estimation (SAE) model to estimate the Community-Based Health Insurance (CBHI) coverage at the zone levels in Ethiopia. To achieve this, we combined the 2019 Ethiopia Mini-Demographic and Health Survey (EMDHS) data with the 2007 population census data. SAE has addressed the challenge of producing reliable parameter estimates for small or even zero sample sizes across Ethiopian zones by utilizing auxiliary information from the population census. The results show that model-based estimates generated by the SAE approach are more accurate than direct survey estimates of CBHI. A map of CBHI scheme coverage was also used to visualize the spatial variation in the distribution of CBHI scheme coverage. From the CBHI scheme coverage map, we noticed notable variations in CBHI scheme coverage across Ethiopian zones. Additionally, this research identified areas with high and low CBHI scheme coverage to improve decision-making and increase coverage in Ethiopia. One of the novelties of this paper is estimating the non-sampled zones; therefore, the policymakers will give equal attention similar to the sampled zones. [ABSTRACT FROM AUTHOR]

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]

Many surveys collect information on discrete characteristics and continuous variables, that is, mixed-type variables. Small-area statistics of interest include means or proportions of the response variables as well as their domain means, which are the mean values at each level of a different categorical variable. However, item nonresponse in survey data increases the complexity of small-area estimation. To address this issue, we propose a multivariate mixed-effects model for mixed-type response variables subject to item nonresponse. We apply this method to two data structures where the data are missing completely at random by design. We use empirical data from two separate studies: a survey of pet owners and a dataset from the National Resources Inventory. In these applications, our proposed method leads to improvements relative to a direct estimator and a predictor based on a univariate model. [ABSTRACT FROM AUTHOR]

Objective: The aim of this paper is to present bootstrap algorithms for measuring the accuracy of estimation and prediction in design-based and model-based approaches in survey sampling and small area estimation. Three proposals of prediction-mean squared error estimators are also examined. Research Design & Methods: Various bootstrap procedures are shown and used to estimate the design- and prediction-mean squared errors based on real data. Computations are supported by two R packages. Findings: Three prediction-mean squared error estimators are proposed. Implications / Recommendations: The bootstrap algorithms used in the design-based approach give similar results for the considered data for the variance estimates of the considered estimator, implying that the speed of the algorithms may be important for practitioners in cases of similar properties. The proposed estimators of the prediction mean squared error produce higher estimates than other estimators in the model-based approach, indicating a positive bias that can be interpreted as a pessimistic accuracy estimate. Contribution: All the presented bootstrap algorithms are easily applicable using two R packages available at R CRAN and GitHub. Three double bootstrap prediction-MSE estimators are proposed and analysed in the real-data application. Article type: original article. [ABSTRACT FROM AUTHOR]

Objective: The aim of this paper is to present bootstrap algorithms for measuring the accuracy of estimation and prediction in design-based and model-based approaches in survey sampling and small area estimation. Three proposals of prediction-mean squared error estimators are also examined. Research Design & Methods: Various bootstrap procedures are shown and used to estimate the design- and prediction-mean squared errors based on real data. Computations are supported by two R packages. Findings: Three prediction-mean squared error estimators are proposed. Implications / Recommendations: The bootstrap algorithms used in the design-based approach give similar results for the considered data for the variance estimates of the considered estimator, implying that the speed of the algorithms may be important for practitioners in cases of similar properties. The proposed estimators of the prediction mean squared error produce higher estimates than other estimators in the model-based approach, indicating a positive bias that can be interpreted as a pessimistic accuracy estimate. Contribution: All the presented bootstrap algorithms are easily applicable using two R packages available at R CRAN and GitHub. Three double bootstrap prediction-MSE estimators are proposed and analysed in the real-data application.

In this article, we propose some direct and synthetic logarithmic estimators for estimating the domain mean of small area based on a simple random sampling design. The mean square error expressions of the proposed direct and synthetic estimators are obtained to first order approximation. The efficiency conditions are obtained under which the proposed direct and synthetic estimators dominate their conventional aspirants. The performances of the suggested direct and synthetic logarithmic estimators are examined by a comprehensive simulation study carried out on some artificially drawn symmetric and asymmetric populations. Furthermore, a real data application of the suggested methods is also provided as a case study using the paddy crop acreage data for small domains, where small domains are the revenue inspector circles (RIC) in Mohanlalganj tehsil, Uttar Pradesh, India.

BackgroundThe global prevalence of crimes against women has made it an enduring public health challenge that has persisted over time. The achievement of the 2030 Sustainable Development Goal (SDG) is intricately tied to the actions taken to prevent these crimes as their repercussions directly affect progress across various SDGs. This study aimed to provide a comprehensive examination of the prevalence of crimes against women across districts and states in India, analyzing changes from 2020 to 2022, and subsequently identifying associated factors.MethodsThe study is an ecological analysis conducted across all districts of India using the data on crimes against women for the period 2020 and 2022 obtained from the National Crime Records Bureau (NCRB) of India. A small area estimation method was used to obtain district-level relative risks of crime against women for both periods. Hotspot analysis was carried out to identify the current hotspots and coldspots. Further spatial regression was used to identify the factors associated with crimes against women in the year 2022.ResultsThe results indicated a rise in the reported crime against women cases between 2020 and 2022. The rate of crimes against women at the national level was found to be 57 in the year 2020, whereas, in 2022, it increased to 67. The highest crime rate in the year 2022 was found to be 145 in Delhi, while Nagaland had the lowest crime rate of 5. The relative risk of crime against women varied from 0.046 to 4.68 in 2020, while in 2022, it spanned from 0.02 to 6.10. Significant hotspots were found in parts of Rajasthan, Madhya Pradesh, Haryana, Telangana, and Odisha. The results of the spatial error regression model showed that the sex ratio and the population density of the district have significant associations with the occurrence of crimes against women.ConclusionThe rise in the incidence of crime against women emphasizes the importance of tackling the spatial inequality in relative risk across Indian districts. By thoughtfully addressing this variation and conducting targeted studies in high-risk areas, we can enhance our understanding of the obstacles to implementing effective measures against violence targeting women.

This article considers the issue of domain mean estimation utilizing bivariate auxiliary information based enhanced direct and synthetic logarithmic type estimators under simple random sampling (SRS). The expressions of mean square error (MSE) of the proposed estimators are provided to the 1st order approximation. The efficiency criteria are derived to exhibit the dominance of the proposed estimators. To exemplify the theoretical results, a simulation study is conducted on a hypothetically drawn trivariate normal population from R programming language. Some applications of the suggested methods are also provided by analyzing the actual data from the municipalities of Sweden and acreage of paddy crop in the Mohanlal Ganj tehsil of the Indian state of Uttar Pradesh. The findings of the simulation and real data application exhibit that the proposed direct and synthetic logarithmic estimators dominate the conventional direct and synthetic mean, ratio, and logarithmic estimators in terms of least MSE and highest percent relative efficiency.

Introduction Despite that the smoking prevalence has considerably declined in Australia after successful public health strategies over many decades, smoking is still the leading cause of preventable diseases and death in Australia. These declines have not occurred consistently across all geographical–demographic domains. In order to provide an evidence base for monitoring the trend towards the goal of reducing smoking across all domains in Australia, this study aims to estimate trends of smoking prevalence for small domains cross-classified by seven age groups (18–24, 25–29, 30–39, 40–49, 50–59, 60–69, and ≥70 years), two genders, and eight states and territories over twenty years (2001–2021). Methods Direct estimates of smoking prevalence for the target small domains were calculated from the micro-data of the Australian National Health Surveys conducted in seven rounds during 2001–2021. The obtained direct estimates were then used as input for developing time-series models expressed in a hierarchical Bayesian structure as a form of small-area estimation. The developed models borrow cross-sectional, temporal, and spatial strength in such a way that they can interpolate smoking levels in the non-survey years for all detailed level small domains. Smoothed trends of smoking prevalence for higher aggregation levels are obtained by aggregation of the detailed level trend predictions. Results Model-based small area estimators provide consistent and reasonable smoothed trends at both detailed and higher aggregation levels. Results show that the national-level trend exhibits a steeper linear decline over the study period, from 24% in 2001 to 12% in 2021, with a considerable gender difference of around 5% over the period, with males reporting a higher prevalence. Improved model-based estimates at the state level and by age also show steady declines in trends except for the Northern Territory (still above 20%) and older age groups 60–69 and ≥70 years (declining trends remain stable after 2012). Conclusions The findings of the study identify the geographical–demographic groups that had poor improvement over the period 2001–2021, and are still behind the target of achieving lower smoking prevalence. These, in turn, will help health researchers and policymakers deliver targeted programs to the most vulnerable, enabling the nation to meet its health goals in a timely way.

Abstract In real life, situations may arise when the available data are insufficient to provide accurate estimates for the domain, the small area estimation (SAE) technique has been used to get accurate estimates for the variable under study. The problem of missing data is a serious problem that has an impact on sample surveys, but small area estimates are especially prone to it. This paper is a basic effort that suggests design based synthetic imputation methods for the domain mean estimation using simple random sampling in order to address the issue of missing data under SAE. The expression of the mean square error for the proposed imputation methods are obtained up to first order approximation. The efficiency conditions are determined and a thorough simulation study is carried out using artificially generated data sets. An application is included with real data that further supports this study.

Local statistics are in high demand in almost all countries due to their relevance for public policy monitoring and evaluation, decision-making, and strategic planning. However, traditional sources of local statistics, such as general censuses, administrative statistics, and national and local surveys, have limitations. This has led to the development of several techniques for estimating parameters over small areas. In this article, we use both spatial and non-spatial estimators for small domains to estimate the local employment rate of women in Algeria. We find that the empirical spatial estimator is the most appropriate and efficient estimator as more spatial correlations are considered. We also find that an approach based on the combination of spatial and non-spatial small area estimators is very beneficial because it allows for obtaining efficient estimates with lower Root Mean Squared Errors (RMSEs). This finding is significant for Algeria and similar countries, where traditional sources of local statistics are limited. The combination of spatial and non-spatial estimators can provide more accurate and reliable estimates of local statistics, which can be used to inform public policy and decision-making. [ABSTRACT FROM AUTHOR]

Chronic childhood undernutrition, known as stunting, is an important population health problem with short- and long-term adverse outcomes. Bangladesh has made strides to reduce chronic childhood undernutrition, yet progress is falling short of the 2030 Sustainable Development Goals targets. This study estimates trends in age-specific chronic childhood undernutrition in Bangladesh's 64 districts during 1997–2018, using underlying direct estimates extracted from seven Demographic and Health Surveys in the development of small area time-series models. These models combine cross-sectional, temporal, and spatial data to predict in all districts in both survey and non-survey years. Nationally, there has been a steep decline in stunting from about three in five to one in three children. However, our results highlight significant inequalities in chronic undernutrition, with several districts experiencing less pronounced declines. These differences are more nuanced at the district-by-age level, with only districts in more socio-economically advantaged areas of Bangladesh consistently reporting declines in stunting across all age groups. [ABSTRACT FROM AUTHOR]

Preterm birth (PTB) remains a key public health issue that disproportionately affects Black individuals. Since spontaneous PTB (sPTB) and medically indicated PTB (mPTB) may have different causes and interventions, we quantified racial disparities for sPTB and mPTB, and we characterized the geographic patterning of these phenotypes, overall and according to race/ethnicity. We examined a pregnancy cohort of 83,952 singleton births at 2 Philadelphia hospitals from 2008–2020, and classified each PTB as sPTB or mPTB. We used binomial regression to quantify the magnitude of racial disparities between non-Hispanic Black and non-Hispanic White individuals, then generated small area estimates by applying a Bayesian model that accounts for small numbers and smooths estimates of PTB risk by borrowing information from neighboring areas. Racial disparities in both sPTB and mPTB were significant (relative risk of sPTB = 1.83, 95% confidence interval: 1.70, 1.98; relative risk of mPTB = 2.20, 95% confidence interval: 2.00, 2.42). The disparity was 20% greater in mPTB than sPTB. There was substantial geographic variation in PTB, sPTB, and mPTB risks and racial disparity. Our findings underscore the importance of distinguishing PTB phenotypes within the context of public health and preventive medicine. Future work should consider social and environmental exposures that may explain geographic differences in PTB risk and disparities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]