Estimation of small area counts with the benchmarking property

Ranalli, Maria Giovanna; Montanari, Giorgio Eduardo; Vicarelli, Cecilia

doi:10.1007/s40300-018-0146-2

Cited by 5 publications

(4 citation statements)

References 34 publications

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“…When the model is misspecified, the effects of internal benchmarking on model performance are uncertain. Previous simulation studies suggest that, depending on the details of the data and model, internal benchmarking can sometimes improve performance (Pfeffermann and Tiller 2006;Pfeffermann 2013;Vesper 2013;Ranalli et al 2018).…”

Section: The Effects Of External and Internal Benchmarking On Model P...mentioning

confidence: 99%

“…Some methods treat benchmarks as constraints on the underlying small area parameters and estimate the small area models under these constraints (Pfeffermann and Barnard 1991;Pfeffermann and Tiller 2006;Fabrizi et al 2012;Pfeffermann et al 2014). Some methods estimate the small area models in a way that the benchmarking constraints are satisfied for point estimators of the small area parameters Rao 2002, 2003;Wang et al 2008;You et al 2013;Bell et al 2013;Ranalli et al 2018).…”

Section: Introductionmentioning

confidence: 99%

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Fully Bayesian Benchmarking of Small Area Estimation Models

Zhang

Bryant²

2020

Journal of Official Statistics

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Estimates for small areas defined by social, demographic, and geographic variables are increasingly important for official statistics. To overcome problems of small sample sizes, statisticians usually derive model-based estimates. When aggregated, however, the model- based estimates typically do not agree with aggregate estimates (benchmarks) obtained through more direct methods. This lack of agreement between estimates can be problematic for users of small area estimates. Benchmarking methods have been widely used to enforce agreement. Fully Bayesian benchmarking methods, in the sense of yielding full posterior distributions after benchmarking, can provide coherent measures of uncertainty for all quantities of interest, but research on fully Bayesian benchmarking methods is limited. We present a flexible fully Bayesian approach to benchmarking that allows for a wide range of models and benchmarks. We revise the likelihood by multiplying it by a probability distribution that measures agreement with the benchmarks. We outline Markov chain Monte Carlo methods to generate samples from benchmarked posterior distributions. We present two simulations, and an application to English and Welsh life expectancies.

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Section: The Effects Of External and Internal Benchmarking On Model P...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fully Bayesian Benchmarking of Small Area Estimation Models

Zhang

Bryant²

2020

Journal of Official Statistics

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“…Ghosh and Steorts (2013) derived the two‐stage benchmarking which satisfies constraints at the area level and the unit level. Ranalli et al (2018) suggested the method for maximizing the likelihood subject to the constraint in a logistic mixed model. See Pfeffermann (2013) and Ghosh (2020) for a good review on the benchmark problem.…”

Section: Introductionmentioning

confidence: 99%

Benchmarked linear shrinkage prediction in the Fay–Herriot small area model

Chikamatsu

Kubokawa

2022

Scandinavian J Statistics

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The empirical best linear unbiased predictor (EBLUP) is a linear shrinkage of the direct estimate toward the regression estimate and useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EBLUP is that the overall estimate for a larger geographical area based on a sum of EBLUP is not necessarily identical to the corresponding direct estimate like the overall sample mean. To fix this problem, the paper suggests a new method for benchmarking EBLUP in the Fay-Herriot model without assuming normality of random effects and sampling errors. The resulting benchmarked empirical linear shrinkage (BELS) predictor has novelty in the sense that coefficients for benchmarking are adjusted based on the data from each area. To measure the uncertainty of BELS, the second-order unbiased estimator of the mean squared error is derived.

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“…Marino et al (2019) propose a semiparametric approach allowing for a flexible random effects structure in unit-level models. Ranalli et al (2018) introduced benchmarking for logistic unit-level. Concerning the second aspect, medical routine data provided by official statistics or health insurance companies have been found to be promising data bases for regional prevalence estimation.…”

Section: Introductionmentioning

confidence: 99%

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

Krause

Burgard

Morales

2021

Metrika

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Regional prevalence estimation requires the use of suitable statistical methods on epidemiologic data with substantial local detail. Small area estimation with medical treatment records as covariates marks a promising combination for this purpose. However, medical routine data often has strong internal correlation due to diagnosis-related grouping in the records. Depending on the strength of the correlation, the space spanned by the covariates can become rank-deficient. In this case, prevalence estimates suffer from unacceptable uncertainty as the individual contributions of the covariates to the model cannot be identified properly. We propose an area-level logit mixed model for regional prevalence estimation with a new fitting algorithm to solve this problem. We extend the Laplace approximation to the log-likelihood by an $$\ell _2$$ ℓ 2 -penalty in order to stabilize the estimation process in the presence of covariate rank-deficiency. Empirical best predictors under the model and a parametric bootstrap for mean squared error estimation are presented. A Monte Carlo simulation study is conducted to evaluate the properties of our methodology in a controlled environment. We further provide an empirical application where the district-level prevalence of multiple sclerosis in Germany is estimated using health insurance records.

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Estimation of small area counts with the benchmarking property

Cited by 5 publications

References 34 publications

Fully Bayesian Benchmarking of Small Area Estimation Models

Fully Bayesian Benchmarking of Small Area Estimation Models

Benchmarked linear shrinkage prediction in the Fay–Herriot small area model

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

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