IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p924-934.html
   My bibliography  Save this article

A unified Bayesian inference on treatment means with order constraints

Author

Listed:
  • Oh, Man-Suk
  • Shin, Dong Wan

Abstract

In some applications involving comparison of treatment means, it is known a priori that population means are ordered in a certain way. In such situations, imposing constraints on the treatment means can greatly increase the effectiveness of statistical procedures. This paper proposes a unified Bayesian method which performs a simultaneous comparison of treatment means and parameter estimation in ANOVA models with order constraints on the means. A continuous prior restricted to order constraints is employed, and posterior samples of parameters are generated using a Markov chain Monte Carlo method. Posterior probabilities of all possible hypotheses on the equality/inequality of treatment means are obtained using Savage-Dickey density ratios, for which we propose a simple and computationally efficient estimation method. Posterior densities and HPD intervals of parameters of interest are estimated with almost no extra cost, given some by-products from the test procedure. Simulation study results show that the proposed method outperforms the test without constraints and that the method is powerful in detecting the true hypothesis. The method is applied to the ramus bone sizes of 20 boys, which were measured at four time points. The proposed Bayesian test reveals that there are two growth spurts in the ramus bone size during the observed period, which could not be detected by pairwise comparisons of the means.

Suggested Citation

  • Oh, Man-Suk & Shin, Dong Wan, 2011. "A unified Bayesian inference on treatment means with order constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 924-934, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:924-934
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00313-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Park, Soo Jung & Wan Shin, Dong & Uk Park, Byeong & Chul Kim, Woo & Oh, Man-Suk, 2005. "Bayesian test for asymmetry and nonstationarity in MTAR model with possibly incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1192-1204, June.
    2. Oh, Man-Suk, 1999. "Estimation of posterior density functions from a posterior sample," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 411-427, February.
    3. Nashimoto, Kane & Wright, F.T., 2005. "A note on multiple comparison procedures for detecting differences in simply ordered means," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 393-401, July.
    4. Junfeng Shang & Joseph E. Cavanaugh & Farroll T. Wright, 2008. "A Bayesian Multiple Comparison Procedure for Order‐Restricted Mixed Models," International Statistical Review, International Statistical Institute, vol. 76(2), pages 268-284, August.
    5. David B. Dunson & Brian Neelon, 2003. "Bayesian Inference on Order-Constrained Parameters in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 59(2), pages 286-295, June.
    6. Nashimoto, Kane & Wright, F.T., 2005. "Multiple comparison procedures for detecting differences in simply ordered means," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 291-306, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Sysoev, O. & Burdakov, O. & Grimvall, A., 2011. "A segmentation-based algorithm for large-scale partially ordered monotonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2463-2476, August.
    2. Conde David & Salvador Bonifacio & Rueda Cristina & Fernández Miguel A., 2013. "Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 583-602, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Junfeng Shang & Joseph E. Cavanaugh & Farroll T. Wright, 2008. "A Bayesian Multiple Comparison Procedure for Order‐Restricted Mixed Models," International Statistical Review, International Statistical Institute, vol. 76(2), pages 268-284, August.
    2. Wright, F.T. & Nashimoto, Kane, 2011. "One-sided multiple comparisons for treatment means with a control mean," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1530-1539, April.
    3. Nashimoto, Kane & Wright, F.T., 2008. "Bayesian multiple comparisons of simply ordered means using priors with a point mass," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5143-5153, August.
    4. Nashimoto, Kane & Wright, F.T., 2007. "Nonparametric multiple-comparison methods for simply ordered medians," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5068-5076, June.
    5. Oh, Man-Suk, 2014. "Bayesian comparison of models with inequality and equality constraints," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 176-182.
    6. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    7. B. Nebiyou Bekele & Yisheng Li & Yuan Ji, 2010. "Risk-Group-Specific Dose Finding Based on an Average Toxicity Score," Biometrics, The International Biometric Society, vol. 66(2), pages 541-548, June.
    8. Nashimoto, Kane & Wright, F.T., 2005. "A note on multiple comparison procedures for detecting differences in simply ordered means," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 393-401, July.
    9. Ghosal, Rahul & Ghosh, Sujit K., 2022. "Bayesian inference for generalized linear model with linear inequality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    10. Margarita I. Cigarán-Méndez & Oscar J. Pellicer-Valero & José D. Martín-Guerrero & Umut Varol & César Fernández-de-las-Peñas & Esperanza Navarro-Pardo & Juan A. Valera-Calero, 2022. "Bayesian Linear Regressions Applied to Fibromyalgia Syndrome for Understanding the Complexity of This Disorder," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    11. Man-Suk Oh & Yong Bin Lim, 2001. "Bayesian analysis of time series Poisson data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 259-271.
    12. Lee, Kwangmin & Lee, Jaeyong, 2023. "Post-processed posteriors for sparse covariances," Journal of Econometrics, Elsevier, vol. 236(1).
    13. Guosheng Yin & Joseph G. Ibrahim, 2005. "A Class of Bayesian Shared Gamma Frailty Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 208-216, March.
    14. Rufibach, Kaspar, 2010. "An active set algorithm to estimate parameters in generalized linear models with ordered predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1442-1456, June.
    15. Yoon Young Jung & Dong Wan Shin & Man-Suk Oh, 2005. "Bayesian analysis of panel data using an MTAR model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(8), pages 841-854.
    16. Chris Hans & David B. Dunson, 2005. "Bayesian Inferences on Umbrella Orderings," Biometrics, The International Biometric Society, vol. 61(4), pages 1018-1026, December.
    17. Man-Suk Oh & Dong Wan Shin, 2002. "Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 771-789.
    18. Oh, Man-Suk, 2014. "Bayesian test on equality of score parameters in the order restricted RC association model," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 147-157.
    19. Park, Soo Jung & Wan Shin, Dong & Uk Park, Byeong & Chul Kim, Woo & Oh, Man-Suk, 2005. "Bayesian test for asymmetry and nonstationarity in MTAR model with possibly incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1192-1204, June.
    20. Perrakis, Konstantinos & Ntzoufras, Ioannis & Tsionas, Efthymios G., 2014. "On the use of marginal posteriors in marginal likelihood estimation via importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 54-69.

    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:eee:csdana:v:55:y:2011:i:1:p:924-934. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.