Parametric bootstrap mean squared error of a small area multivariate EBLUP

Moretti, Angelo; Shlomo, Natalie; Sakshaug, Joseph W.

doi:10.1080/03610918.2018.1498889

Cited by 7 publications

(18 citation statements)

References 24 publications

(34 reference statements)

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“…In particular, they show that the parametric bootstrap may provide more accurate MSE estimates compared with analytical approximations due to its second‐order accuracy. Moretti et al () extended the parametric bootstrap approach to multivariate SAE and also account for

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when n d =0 based on the prediction error as in standard linear regression models. In addition, Moretti et al () account for the error in the factor analysis models in the bootstrap algorithm.…”

Section: Multivariate Empirical Best Linear Unbiased Predictormentioning

confidence: 99%

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Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators

Moretti

Shlomo

Sakshaug

2019

Int Statistical Rev

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Summary Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well‐being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit‐level small area estimation approach to predict a vector of means of factor scores representing well‐being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.

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when n d =0 based on the prediction error as in standard linear regression models. In addition, Moretti et al () account for the error in the factor analysis models in the bootstrap algorithm.…”

Section: Multivariate Empirical Best Linear Unbiased Predictormentioning

confidence: 99%

“…The MSEs of the EBLUPs of factor score means are estimated as in Moretti et al (). The MSEs of the MEBLUPs are estimated as in Moretti et al (), taking into account the variability arising from the CFA model as proposed in Moretti et al ().…”

Section: Applicationmentioning

confidence: 99%

Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators

Moretti

Shlomo

Sakshaug

2019

Int Statistical Rev

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“…It is essential to obtain an accurate estimator of MSE to reflect the true variability associated with the EBLUP estimators. MSE estimators have been studied using variance component estimators under the MFH model [11,12]. The performance of small area estimates under the MFH model was assessed by the coefficient of variation (CV %) and root MSE [10,13].…”

Section: Introductionmentioning

confidence: 99%

Multivariate small area estimation of undernutrition for children under five using official statistics

Yilema

Shiferaw

Zewotir

et al. 2022

SJI

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Surveys are mainly used to obtain reliable estimates for planned domains at national and regional levels. However, the unplanned domains (lower administrative layers) with small sample sizes must be estimated. The direct survey estimates of the non-planned domains with small sample sizes lead to large sampling variability. Thus, small area estimations dealt with managing this variability by borrowing the strength of neighboring areas. The target variables of the study were obtained from the 2016 Ethiopian demographic and health survey (EDHS) and the auxiliary variables taken from the 2007 population and housing census data. Multivariate Fay Herriot (MFH) model was used by incorporating the correlations among the target variables. The model diagnostic measures assured the normality assumption, and the consistency of multivariate small area estimates are valid. Multivariate EBLUPs of the target variables produced the lowest percent coefficient of variation (CV) and root mean square error (MSE). Therefore, multivariate EBLUP has improved the direct survey estimates of undernutrition (stunting, wasting, and underweight) for small sample sizes (even zero sample sizes). It also provided better estimates compared to the univariate EBLUPs. Generally, multivariate EBLUPs of undernutrition produced the best reliable, efficient, and precise estimates for small sample sizes in all zones. Zones are essential domains for planning and monitoring purposes in the country, and therefore these results provide valuable estimates for policymakers, planners, and legislative organs of the government. One of the novelties of this paper is estimating the non-sampled zones, and therefore the policymakers will give equal attention similar to the sampled zones.

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“…is the sum of n i values of HIV infection for sampled individuals from the i-th district while X j2S 0p ij is the sum over the estimated probability of infection for the non-sampled individuals in district i, and N i corresponds to number of individuals in each PLOS ONE district. Model fitting and parameter estimation were implemented using the SAE [31] package in R software, version 3.6.2 [31] The MSE ofp i is obtained using the parametric bootstrap estimation method for finite populations [33,34] as described in S2 File.…”

Section: Plos Onementioning

confidence: 99%

Model-based small area estimation methods and precise district-level HIV prevalence estimates in Uganda

et al. 2021

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Background Model-based small area estimation methods can help generate parameter estimates at the district level, where planned population survey sample sizes are not large enough to support direct estimates of HIV prevalence with adequate precision. We computed district-level HIV prevalence estimates and their 95% confidence intervals for districts in Uganda. Methods Our analysis used direct survey and model-based estimation methods, including Fay-Herriot (area-level) and Battese-Harter-Fuller (unit-level) small area models. We used regression analysis to assess for consistency in estimating HIV prevalence. We use a ratio analysis of the mean square error and the coefficient of variation of the estimates to evaluate precision. The models were applied to Uganda Population-Based HIV Impact Assessment 2016/2017 data with auxiliary information from the 2016 Lot Quality Assurance Sampling survey and antenatal care data from district health information system datasets for unit-level and area-level models, respectively. Results Estimates from the model-based and the direct survey methods were similar. However, direct survey estimates were unstable compared with the model-based estimates. Area-level model estimates were more stable than unit-level model estimates. The correlation between unit-level and direct survey estimates was (β1 = 0.66, r2 = 0.862), and correlation between area-level model and direct survey estimates was (β1 = 0.44, r2 = 0.698). The error associated with the estimates decreased by 37.5% and 33.1% for the unit-level and area-level models, respectively, compared to the direct survey estimates. Conclusions Although the unit-level model estimates were less precise than the area-level model estimates, they were highly correlated with the direct survey estimates and had less standard error associated with estimates than the area-level model. Unit-level models provide more accurate and reliable data to support local decision-making when unit-level auxiliary information is available.

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Parametric bootstrap mean squared error of a small area multivariate EBLUP

Cited by 7 publications

References 24 publications

Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators

Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators

Multivariate small area estimation of undernutrition for children under five using official statistics

Model-based small area estimation methods and precise district-level HIV prevalence estimates in Uganda

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