IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v62y2000i2p399-412.html
   My bibliography  Save this article

Inference for multivariate normal hierarchical models

Author

Listed:
  • P. J. Everson
  • C. N. Morris

Abstract

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.

Suggested Citation

  • P. J. Everson & C. N. Morris, 2000. "Inference for multivariate normal hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 399-412.
  • Handle: RePEc:bla:jorssb:v:62:y:2000:i:2:p:399-412
    DOI: 10.1111/1467-9868.00239
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00239
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1467-9868.00239?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peng, Roger, 2008. "Caching and Distributing Statistical Analyses in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 26(i07).
    2. Figueroa-Zúñiga, Jorge I. & Arellano-Valle, Reinaldo B. & Ferrari, Silvia L.P., 2013. "Mixed beta regression: A Bayesian perspective," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 137-147.
    3. repec:jss:jstsof:26:i07 is not listed on IDEAS
    4. Roger D. Peng & Francesca Dominici & Leah J. Welty, 2009. "A Bayesian hierarchical distributed lag model for estimating the time course of risk of hospitalization associated with particulate matter air pollution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 3-24, February.
    5. G. Brooke Anderson & Keith W. Oleson & Bryan Jones & Roger D. Peng, 2018. "Classifying heatwaves: developing health-based models to predict high-mortality versus moderate United States heatwaves," Climatic Change, Springer, vol. 146(3), pages 439-453, February.
    6. Berger, James O. & Sun, Dongchu & Song, Chengyuan, 2020. "An objective prior for hyperparameters in normal hierarchical models," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    7. Roger D. Peng & Francesca Dominici & Thomas A. Louis, 2006. "Model choice in time series studies of air pollution and mortality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 179-203, March.
    8. Howard H. Chang & Jingwen Zhou & Montserrat Fuentes, 2010. "Impact of Climate Change on Ambient Ozone Level and Mortality in Southeastern United States," IJERPH, MDPI, vol. 7(7), pages 1-15, July.
    9. Francesca Dominici & Lianne Sheppard & Merlise Clyde, 2003. "Health Effects of Air Pollution: A Statistical Review," International Statistical Review, International Statistical Institute, vol. 71(2), pages 243-276, August.
    10. Roger Peng & Leah Welty & Aidan McDermott, 2004. "The National Morbidity, Mortality, and Air Pollution Study Database in R," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1044, Berkeley Electronic Press.
    11. Roger Peng & Francesca Dominici & Roberto Pastor-Barriuso & Scott Zeger & Jonathan Samet, 2004. "Seasonal Analyses of Air Pollution and Mortality in 100 U.S. Cities," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1041, Berkeley Electronic Press.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:62:y:2000:i:2:p:399-412. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.