Empirical Bayes small area prediction under a zero‐inflated lognormal model with correlated random area effects

Lyu, Xiaodan; Berg, Emily; Hofmann, Heike

doi:10.1002/bimj.202000029

Cited by 8 publications

(9 citation statements)

References 37 publications

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“…We use the parametric bootstrap to define a set of replicate weights such that a resulting replication variance estimator approximates the second term in the MSE. Lyu et al (2020) use a parametric bootstrap MSE estimator of this form. The entire procedure involves constructing B variance estimation imputed values and 2B sets of replicate weights.…”

Section: Basic Imputation and Replication Variance Estimation Procedu...mentioning

confidence: 99%

Construction of Databases for Small Area Estimation

Berg

2022

Journal of Official Statistics

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The demand for small area estimates can conflict with the objective of producing a multi-purpose data set. We use donor imputation to construct a database that supports small area estimation. Appropriately weighted sums of observed and imputed values produce model-based small area estimates. We develop imputation procedures for both unit-level and area-level models. For area-level models, we restrict to linear models. We assume a single vector of covariates is used for a possibly multivariate response. Each record in the imputed data set has complete data, an estimation weight, and a set of replicate weights for mean square error (MSE) estimation. We compare imputation procedures based on area-level models to those based on unit-level models through simulation. We apply the methods to the Iowa Seat-Belt Use Survey, a survey designed to produce state-level estimates of the proportions of vehicle occupants who wear a seat-belt. We develop a bivariate unit-level model for prediction of county-level proportions of belted drivers and total occupants. We impute values for the proportions of belted drivers and vehicle occupants onto the full population of road segments in the sampling frame. The resulting imputed data set returns approximations for the county-level predictors based on the bivariate model.

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Section: Basic Imputation and Replication Variance Estimation Procedu...mentioning

confidence: 99%

Construction of Databases for Small Area Estimation

Berg

2022

Journal of Official Statistics

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“…In the framework of a unit-level lognormal model, Berg & Chandra (2014) develop closed-form expressions for an empirical Bayes predictor of a small area mean. Lyu et al (2020) and Zimmermann & Münnich (2018) extend the lognormal model to zero-inflated data and informative sampling, respectively. Berg & Chandra (2014), Lyu et al (2020), and Zimmermann & Münnich (2018) focus on prediction of means, but many small area parameters are more complex functions of the model response variable.…”

Section: Introductionmentioning

confidence: 99%

“…Lyu et al (2020) and Zimmermann & Münnich (2018) extend the lognormal model to zero-inflated data and informative sampling, respectively. Berg & Chandra (2014), Lyu et al (2020), and Zimmermann & Münnich (2018) focus on prediction of means, but many small area parameters are more complex functions of the model response variable. Molina & Rao (2010) obtain a Monte Carlo approximation for the best predictor of a general parameter, assuming that transformed study variables follow the nested error linear regression model.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Small Area Procedures based on Gamma Distributions with Extension to Informative Sampling

Cho¹,

Berg²

2023

Preprint

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The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction.We emphasize a model, called the gamma-gamma model, in which the area random effects have gamma distributions. We compare this model to a generalized linear mixed model.Each of these two models has been proposed independently in the literature, but the two models have not yet been formally compared. We evaluate the properties of two mean square error estimators for the gamma-gamma model, both of which incorporate corrections for the bias of the estimator of the leading term. Finally, we extend the gamma-gamma model to informative sampling. We conduct thorough simulation studies to assess the properties of the alternative predictors. We apply the proposed methods to data from an agricultural survey.

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“…Sample sizes in CEAP are too small to support reliable direct county estimates. Past analyses have explored a variety of issues that arise in the context of small area estimation using CEAP data (Erciulescu & Fuller 2016, Berg & Chandra 2014, Lyu et al 2020, Berg & Lee 2019.…”

Section: Introductionmentioning

confidence: 99%

“…As discussed in Lyu et al (2020), the task of obtaining covariates that are related to CEAP response variables and are known for the full population of cropland of interest is difficult. Use of variables collected in the CEAP survey as covariates is desirable for the purpose of simplifying data preparation.…”

Section: Introductionmentioning

confidence: 99%

An application of a small area procedure with correlation between measurement error and sampling error to the Conservation Effects Assessment Project

Berg¹,

Mosaferi²

2021

Preprint

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County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) survey are useful for program development and evaluation. As a result of small county sample sizes, small area estimation procedures are needed.One variable that is related to sheet and rill erosion is the quantity of water runoff. The runoff is collected in the CEAP survey 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 for sheet and rill erosion. 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. The proposed methodology has a genuine need in CEAP, where the same survey that supplies the response also provides auxiliary information. 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. We conclude with practical recommendations.

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Empirical Bayes small area prediction under a zero‐inflated lognormal model with correlated random area effects

Abstract: This article has earned an open data badge "Reproducible Research" for making publicly available the code necessary to reproduce the reported results. The results reported in this article were reproduced partially for data confidentiality reasons.

Cited by 8 publications

References 37 publications

Construction of Databases for Small Area Estimation

Construction of Databases for Small Area Estimation

Comparison of Small Area Procedures based on Gamma Distributions with Extension to Informative Sampling

An application of a small area procedure with correlation between measurement error and sampling error to the Conservation Effects Assessment Project

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