IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i1p159-187.html
   My bibliography  Save this article

Counting subsets of contingency tables

Author

Listed:
  • George Fishman

Abstract

We describe multistage Markov chain Monte Carlo (MSMCMC) procedures which, in addition to estimating the total number of contingency tables with given positive row and column sums, estimate the number, $$Q$$ Q , and the proportion, $$P$$ P , of those tables that satisfy an additional, possibly, nonlinear constraint. Three Options, A, B, and C, are studied. Options A and B exploit locally optimal statistical properties whereas judicious assignment of a particular parameter of Option C allows estimation with approximately minimal standard error. Ten examples of varying dimensions and total entries illustrate and compare the procedures, where $$Q$$ Q and $$P$$ P denote the number and proportion of chi-squared statistics less than a given value. For both small and large dimensional tables, the comparisons favor Options A and B for moderate $$P$$ P and Option C for small $$P$$ P . Additional comparison with sequential importance sampling estimates favors the latter for small dimensional tables and moderate $$P$$ P but favors Option C for large dimensional tables for both small and moderate $$P$$ P . The proposed options extend an earlier MSMCMC technique for estimating total count and, in principle, can be further extended to incorporate additional constraints. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • George Fishman, 2014. "Counting subsets of contingency tables," Computational Statistics, Springer, vol. 29(1), pages 159-187, February.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:1:p:159-187
    DOI: 10.1007/s00180-013-0442-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0442-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-013-0442-5?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. Kalantari, B. & Lari, I. & Rizzi, A. & Simeone, B., 1993. "Sharp bounds for the maximum of the chi-square index in a class of contingency tables with given marginals," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 19-34, June.
    2. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
    3. Sabatti C., 2002. "Measuring Dependency With Volume Tests," The American Statistician, American Statistical Association, vol. 56, pages 191-195, August.
    4. Fabio Rapallo & Ruriko Yoshida, 2010. "Markov bases and subbases for bounded contingency tables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 785-805, August.
    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. Abraham Martín del Campo & Sarah Cepeda & Caroline Uhler, 2017. "Exact Goodness-of-Fit Testing for the Ising Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 285-306, June.
    2. Dyer, Martin & Greenhill, Catherine & Kleer, Pieter & Ross, James & Stougie, Leen, 2021. "Sampling hypergraphs with given degrees," Other publications TiSEM 2d323767-8066-4c28-92cc-b, Tilburg University, School of Economics and Management.
    3. Zhang, Linjun & Small, Michael & Judd, Kevin, 2015. "Exactly scale-free scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 182-197.
    4. Ian Dinwoodie & Kruti Pandya, 2015. "Exact tests for singular network data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 687-706, August.
    5. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2024. "MCMC conditional maximum likelihood for the two-way fixed-effects logit," Econometric Reviews, Taylor & Francis Journals, vol. 43(6), pages 379-404, July.
    6. Jing Xi & Ruriko Yoshida & David Haws, 2013. "Estimating the number of zero-one multi-way tables via sequential importance sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 763-783, August.
    7. Clemens Draxler, 2018. "Bayesian conditional inference for Rasch models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 245-262, April.
    8. Stephen DeSalvo & James Zhao, 2020. "Random sampling of contingency tables via probabilistic divide-and-conquer," Computational Statistics, Springer, vol. 35(2), pages 837-869, June.
    9. Ogawa, Mitsunori & Takemura, Akimichi, 2012. "Markov bases for typical block effect models of two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 219-229.
    10. Sanda Micula, 2015. "Statistical Computer Simulations And Monte Carlo Methods," Romanian Economic Business Review, Romanian-American University, vol. 9(2), pages 384-394, December.
    11. Yuguo Chen & Dylan Small, 2005. "Exact tests for the rasch model via sequential importance sampling," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 11-30, March.
    12. David Kahle & Ruriko Yoshida & Luis Garcia-Puente, 2018. "Hybrid schemes for exact conditional inference in discrete exponential families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 983-1011, October.
    13. Radislav Vaisman & Zdravko Botev & Ad Ridder, 2013. "Sequential Monte Carlo for Counting Vertex Covers in General Graphs," Tinbergen Institute Discussion Papers 13-122/III, Tinbergen Institute.
    14. Radislav Vaisman & Dirk P. Kroese, 2017. "Stochastic Enumeration Method for Counting Trees," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 31-73, March.
    15. Rivest, Louis-Paul, 2021. "Limiting properties of an equiprobable sampling scheme for 0–1 matrices," Statistics & Probability Letters, Elsevier, vol. 172(C).
    16. repec:jss:jstsof:20:i04 is not listed on IDEAS
    17. Verhelst, Norman & Hatzinger, Reinhold & Mair, Patrick, 2007. "The Rasch Sampler," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i04).
    18. repec:jss:jstsof:17:i07 is not listed on IDEAS
    19. Norman Verhelst, 2008. "An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 705-728, December.
    20. Radislav Vaisman & Ofer Strichman & Ilya Gertsbakh, 2015. "Model Counting of Monotone Conjunctive Normal Form Formulas with Spectra," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 406-415, May.
    21. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    22. Caffo, Brian, 2006. "Exact Hypothesis Tests for Log-linear Models with exactLoglinTest," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i07).

    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:spr:compst:v:29:y:2014:i:1:p:159-187. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.