The DOI matches its Crossref record; 27 of the 28 references it cites were found in a registry or an index.
Inference for Multivariate Normal Hierarchical Models
Abstract
Summary: This paper provides a new method and algorithm for making inferences about the parameters of a two-level multivariate normal hierarchical model. One has observed J p-dimensional vector outcomes, distributed at level 1 as multivariate normal with unknown mean vectors and with known covariance matrices. At level 2, the unknown mean vectors also have normal distributions, with common unknown covariance matrix A and with means depending on known covariates and on unknown regression coefficients. The algorithm samples independently from the marginal posterior distribution of A by using rejection procedures. Functions such as posterior means and covariances of the level 1 mean vectors and of the level 2 regression coefficient are estimated by averaging over posterior values calculated conditionally on each value of A drawn. This estimation accounts for the uncertainty in A, unlike standard restricted maximum likelihood empirical Bayes procedures. It is based on independent draws from the exact posterior distributions, unlike Gibbs sampling. The procedure is demonstrated for profiling hospitals based on patients' responses concerning p=2 types of problems (non-surgical and surgical). The frequency operating characteristics of the rule corresponding to a particular vague multivariate prior distribution are shown via simulation to achieve their nominal values in that setting.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Hierarchical Linear Models: Applications and Data Analysis Methods.
Longford, N. T., Bryk, A. S., & Raudenbush, S. W. (1993) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2075823 · Cited by 18,773
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,929
Hierarchical Linear Models: Applications and Data Analysis Methods.
Goldstein, H., Bryk, A. S., & Raudenbush, S. W. (1993) · Journal of the American Statistical Association · doi:10.2307/2290750 · Cited by 3,320
Courgeau, D., & Goldstein, H. (1997) · Population · doi:10.2307/1534624 · Cited by 2,596
Estimation with Quadratic Loss
James, W., & Stein, C. M. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_30 · Cited by 2,319
Ripley, B. D. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316726 · Cited by 2,241
Bayes and Empirical Bayes Methods for Data Analysis
Carlin, B. P., & Louis, T. A. (2001) · Technometrics · doi:10.1198/tech.2001.s608 · Cited by 2,110
Sampling-Based Approaches to Calculating Marginal Densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.2307/2289776 · Cited by 1,531
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448
Self-citation
Research works printed but not linked: 2
- Everson, P. (1995) Inference for multivariate normal hierarchical models. PhD Dissertation. Department of Statistics, Harvard University, Cambridge.
- Hox, J. (1998) Multilevel modeling in windows: a review of MLWin. Multilev Modllng Newslett., 10, no. 2, 2±5.
Cited by
Sorted by citations
Fine Particulate Air Pollution and Hospital Admission for Cardiovascular and Respiratory Diseases
Dominici, F., Peng, R. D., Bell, M. L., Pham, L. D., McDermott, A., Zeger, S. L., & Samet, J. M. (2006) · JAMA · doi:10.1001/jama.295.10.1127 · Cited by 2,686
Anderson, B. G., & Bell, M. L. (2009) · Epidemiology · doi:10.1097/ede.0b013e318190ee08 · Cited by 1,233
Anderson, G. B., & Bell, M. L. (2011) · Environmental Health Perspectives · doi:10.1289/ehp.1002313 · Cited by 1,191
Heat Effects on Mortality in 15 European Cities
Baccini, M., Biggeri, A., Accetta, G., Kosatsky, T., Katsouyanni, K., Analitis, A., Anderson, H. R., Bisanti, L., D’Ippoliti, D., Dáňová, J., et al. (2008) · Epidemiology · doi:10.1097/ede.0b013e318176bfcd · Cited by 887
Model Choice in Time Series Studies of Air Pollution and Mortality
Peng, R. D., Dominici, F., & Louis, T. A. (2006) · Journal of the Royal Statistical Society Series A: Statistics in Society · doi:10.1111/j.1467-985x.2006.00410.x · Cited by 583
Metadata
- Authors
- Everson, P. J., & Morris, C. N.
- Affiliations
- Swarthmore College (US)
- Harvard University (US)
- Corresponding author
- Everson, Philip J.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2000-07-01
- Volume
- 62
- Issue
- 2
- Pages
- 399-412
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W1992951219
- Cited by
- 107
- References
- 28
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 3 · 2020: 1 · 2019: 4 · 2018: 3 · 2017: 5 · 2016: 7 · 2015: 7 · 2014: 6 · 2013: 9 · 2012: 11
- FWCI
- 3.99
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Works - Scholarship, Research, & Creative Expression (Swarthmore College) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- Harvard University
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- two-level model, marginal posterior distributions, rejection sampling, empirical Bayes, posterior mean estimation, operating characteristics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
