Bayesian Estimation of Hierarchical Linear Models from Incomplete Data: Cluster-Level Interaction Effects and Small Sample Sizes
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| Format: | Preprint |
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2024
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| _version_ | 1866909470417747968 |
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| author | Shin, Dongho Shin, Yongyun Hagiwara, Nao |
| author_facet | Shin, Dongho Shin, Yongyun Hagiwara, Nao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_21020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian Estimation of Hierarchical Linear Models from Incomplete Data: Cluster-Level Interaction Effects and Small Sample Sizes Shin, Dongho Shin, Yongyun Hagiwara, Nao Methodology 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. |
| title | Bayesian Estimation of Hierarchical Linear Models from Incomplete Data: Cluster-Level Interaction Effects and Small Sample Sizes |
| topic | Methodology |
| url | https://arxiv.org/abs/2405.21020 |