Bayesian Estimation of Hierarchical Linear Models from Incomplete Data: Cluster-Level Interaction Effects and Small Sample Sizes
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| Title: | Bayesian Estimation of Hierarchical Linear Models from Incomplete Data: Cluster-Level Interaction Effects and Small Sample Sizes |
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| Language: | English |
| Authors: | Dongho Shin (ORCID |
| Source: | Grantee Submission. 2025 44. |
| Peer Reviewed: | Y |
| Page Count: | 11 |
| Publication Date: | 2025 |
| Sponsoring Agency: | National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) (DHHS/NIH) National Cancer Institute (NCI) (DHHS/NIH) National Institute of Nursing Research (NINR) (DHHS/NIH) Institute of Education Sciences (ED) |
| Contract Number: | R01DK112009 R01CA263501 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Bayesian Statistics, Hierarchical Linear Modeling, Multivariate Analysis, Data Analysis, Sample Size, Mathematical Formulas, Statistical Distributions |
| DOI: | 10.1002/sim.70051 |
| Abstract: | We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly measured at four time points, maximum-likelihood estimation is suboptimal. Existing Gibbs samplers impute missing values of C by a Metropolis algorithm using proposal densities that have constant variances while the target posterior distributions have nonconstant variances. Therefore, these samplers may not ensure compatibility with the HLM and, as a result, may not guarantee unbiased estimation of the HLM. We introduce a compatible Gibbs sampler that imputes parameters and missing values directly from the exact posterior distributions. We apply our Gibbs sampler to the longitudinal patient-physician encounter data and compare our estimators with those from existing methods by simulation. |
| Abstractor: | As Provided |
| IES Funded: | Yes |
| Entry Date: | 2025 |
| Accession Number: | ED673559 |
| Database: | ERIC |
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| Abstract: | We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly measured at four time points, maximum-likelihood estimation is suboptimal. Existing Gibbs samplers impute missing values of C by a Metropolis algorithm using proposal densities that have constant variances while the target posterior distributions have nonconstant variances. Therefore, these samplers may not ensure compatibility with the HLM and, as a result, may not guarantee unbiased estimation of the HLM. We introduce a compatible Gibbs sampler that imputes parameters and missing values directly from the exact posterior distributions. We apply our Gibbs sampler to the longitudinal patient-physician encounter data and compare our estimators with those from existing methods by simulation. |
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| DOI: | 10.1002/sim.70051 |
