TY - JOUR
T1 - A general class of small area estimation using calibrated hierarchical likelihood approach with applications to COVID-19 data
AU - Rathnayake, Nirosha
AU - Dai, Hongying Daisy
AU - Charnigo, Richard
AU - Schmid, Kendra
AU - Meza, Jane
N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - The direct estimation techniques in small area estimation (SAE) models require sufficiently large sample sizes to provide accurate estimates. Hence, indirect model-based methodologies are developed to incorporate auxiliary information. The most commonly used SAE models, including the Fay-Herriot (FH) model and its extended models, are estimated using marginal likelihood estimation and the Bayesian methods, which rely heavily on the computationally intensive integration of likelihood function. In this article, we propose a Calibrated Hierarchical (CH) likelihood approach to obtain SAE through hierarchical estimation of fixed effects and random effects with the regression calibration method for bias correction. The latent random variables at the domain level are treated as ‘parameters’ and estimated jointly with other parameters of interest. Then the dispersion parameters are estimated iteratively based on the Laplace approximation of the profile likelihood. The proposed method avoids the intractable integration to estimate the marginal distribution. Hence, it can be applied to a wide class of distributions, including generalized linear mixed models, survival analysis, and joint modeling with distinct distributions. We demonstrate our method using an area-level analysis of publicly available count data from the novel coronavirus (COVID-19) positive cases.
AB - The direct estimation techniques in small area estimation (SAE) models require sufficiently large sample sizes to provide accurate estimates. Hence, indirect model-based methodologies are developed to incorporate auxiliary information. The most commonly used SAE models, including the Fay-Herriot (FH) model and its extended models, are estimated using marginal likelihood estimation and the Bayesian methods, which rely heavily on the computationally intensive integration of likelihood function. In this article, we propose a Calibrated Hierarchical (CH) likelihood approach to obtain SAE through hierarchical estimation of fixed effects and random effects with the regression calibration method for bias correction. The latent random variables at the domain level are treated as ‘parameters’ and estimated jointly with other parameters of interest. Then the dispersion parameters are estimated iteratively based on the Laplace approximation of the profile likelihood. The proposed method avoids the intractable integration to estimate the marginal distribution. Hence, it can be applied to a wide class of distributions, including generalized linear mixed models, survival analysis, and joint modeling with distinct distributions. We demonstrate our method using an area-level analysis of publicly available count data from the novel coronavirus (COVID-19) positive cases.
KW - COVID-19
KW - Small area estimation
KW - bias correction
KW - hierarchical -likelihood
UR - http://www.scopus.com/inward/record.url?scp=85139222888&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85139222888&partnerID=8YFLogxK
U2 - 10.1080/02664763.2022.2112556
DO - 10.1080/02664763.2022.2112556
M3 - Article
C2 - 37969889
AN - SCOPUS:85139222888
SN - 0266-4763
VL - 50
SP - 3384
EP - 3404
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
IS - 16
ER -