IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v99y2016icp25-37.html
   My bibliography  Save this article

Testing hypothesis for a simple ordering in incomplete contingency tables

Author

Listed:
  • Li, Hui-Qiong
  • Tian, Guo-Liang
  • Jiang, Xue-Jun
  • Tang, Nian-Sheng

Abstract

A test for ordered categorical variables is of considerable importance, because they are frequently encountered in biomedical studies. This paper introduces a simple ordering test approach for the two-way r×c contingency tables with incomplete counts by developing six test statistics, i.e., the likelihood ratio test statistic, score test statistic, global score test statistic, Hausman–Wald test statistic, Wald test statistic and distance-based test statistic. Bootstrap resampling methods are also presented. The performance of the proposed tests is evaluated with respect to their empirical type I error rates and empirical powers. The results show that the likelihood ratio test statistic based on the bootstrap resampling methods perform satisfactorily for small to large sample sizes. A real example from a wheeze study in six cities is used to illustrate the proposed methodologies.

Suggested Citation

  • Li, Hui-Qiong & Tian, Guo-Liang & Jiang, Xue-Jun & Tang, Nian-Sheng, 2016. "Testing hypothesis for a simple ordering in incomplete contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 25-37.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:25-37
    DOI: 10.1016/j.csda.2016.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316000128
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.01.003?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
    ---><---

    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. B. Klingenberg & A. Solari & L. Salmaso & F. Pesarin, 2009. "Testing Marginal Homogeneity Against Stochastic Order in Multivariate Ordinal Data," Biometrics, The International Biometric Society, vol. 65(2), pages 452-462, June.
    2. Tang, Man-Lai & Wang Ng, Kai & Tian, Guo-Liang & Tan, Ming, 2007. "On improved EM algorithm and confidence interval construction for incomplete rxc tables," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2919-2933, March.
    3. Lucas, Larry A. & Wright, F. T., 1991. "Testing for and against a stochastic ordering between multivariate multinomial populations," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 167-186, August.
    4. El Barmi, Hammou & Dykstra, Richard L., 1996. "Restricted product multinomial and product Poisson maximum likelihood estimation based upon Fenchel duality," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 117-123, August.
    5. Hammou El Barmi & Hari Mukerjee, 2005. "Inferences Under a Stochastic Ordering Constraint: The k-Sample Case," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 252-261, March.
    Full references (including those not matched with items on IDEAS)

    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. Nianqing Liu & Yao Luo, 2017. "A Nonparametric Test For Comparing Valuation Distributions In First‐Price Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(3), pages 857-888, August.
    2. Ori Davidov & George Iliopoulos, 2012. "Estimating a distribution function subject to a stochastic order restriction: a comparative study," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 923-933, December.
    3. Elbarmi, Hammou & Mukerjee, Hari, 2009. "Peakedness and peakedness ordering in symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 594-603, April.
    4. Davidov, Ori, 2011. "Combining p-values using order-based methods," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2433-2444, July.
    5. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 1/08, Monash University, Department of Econometrics and Business Statistics.
    6. Cohen, Arthur & Kolassa, John & Sackrowitz, H.B., 2006. "A new test for stochastic order of k[greater-or-equal, slanted]3 ordered multinomial populations," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1017-1024, May.
    7. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 5/08, Monash University, Department of Econometrics and Business Statistics.
    8. Arboretti, Rosa & Bonnini, Stefano & Corain, Livio & Salmaso, Luigi, 2014. "A permutation approach for ranking of multivariate populations," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 39-57.
    9. Ori Davidov & Shyamal Peddada, 2013. "Testing for the Multivariate Stochastic Order among Ordered Experimental Groups with Application to Dose–Response Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 982-990, December.
    10. El Barmi, Hammou & Mukerjee, Hari, 2012. "Peakedness and peakedness ordering," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 222-233.
    11. Amiri, Mehdi & Izadkhah, Salman & Jamalizadeh, Ahad, 2020. "Linear orderings of the scale mixtures of the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    12. Ristl, Robin & Xi, Dong & Glimm, Ekkehard & Posch, Martin, 2018. "Optimal exact tests for multiple binary endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 1-17.
    13. Ori Davidov & Amir Herman, 2011. "Multivariate Stochastic Orders Induced by Case-Control Sampling," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 139-154, March.
    14. Alexander Henzi & Johanna F. Ziegel & Tilmann Gneiting, 2021. "Isotonic distributional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 963-993, November.
    15. Tian, Guo-Liang & Tang, Man-Lai & Yuen, Kam Chuen & Ng, Kai Wang, 2010. "Further properties and new applications of the nested Dirichlet distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 394-405, February.
    16. Seongoh Park & Johan Lim & Xinlei Wang & Sanghan Lee, 2019. "Permutation based testing on covariance separability," Computational Statistics, Springer, vol. 34(2), pages 865-883, June.
    17. Hammou El Barmi, 2020. "A test for the presence of stochastic ordering under censoring: the k-sample case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 451-470, April.
    18. Lok, Thomas M. & Tabri, Rami V., 2021. "An improved bootstrap test for restricted stochastic dominance," Journal of Econometrics, Elsevier, vol. 224(2), pages 371-393.
    19. Xinlei Wang & Johan Lim & Lynne Stokes, 2008. "A Nonparametric Mean Estimator for Judgment Poststratified Data," Biometrics, The International Biometric Society, vol. 64(2), pages 355-363, June.
    20. El Barmi, Hammou & Johnson, Matthew & Mukerjee, Hari, 2010. "Estimating cumulative incidence functions when the life distributions are constrained," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1903-1909, October.

    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:99:y:2016:i:c:p:25-37. 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.