IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v184y2021ics0047259x21000191.html
   My bibliography  Save this article

A new general class of RC association models: Estimation and main properties

Author

Listed:
  • Forcina, Antonio
  • Kateri, Maria

Abstract

The paper introduces a new class of row-column (RC) association models for contingency tables by allowing the user to select both the scale on which interactions are measured as in Kateri and Papaioannou (1994) and the type of logit (local, global, continuation) suitable for the row and column classification variables as in Bartolucci and Forcina (2002). These choices determine the matrix of interactions which is subjected to rank constraints. Examples are provided where the new models fit substantially better than traditional ones; an intuitive explanation for this behavior is outlined and supported by numerical investigations. An extension of the optimality property in Kateri and Papaioannou (1994) is derived, leading to a general representation theorem and reconstruction formulas for the joint probabilities. These results are the key to show that, given marginal logits, the generalized interactions introduced in this paper determine uniquely the bivariate distribution; in addition, for each pair of logit types, we establish which kind of positive association is implied by our extended interactions being non negative. Quick model selection within this wide class can be performed by an efficient algorithm for computing maximum likelihood estimates which allows for additional linear constraints both on marginal logits and interactions.

Suggested Citation

  • Forcina, Antonio & Kateri, Maria, 2021. "A new general class of RC association models: Estimation and main properties," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000191
    DOI: 10.1016/j.jmva.2021.104741
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000191
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104741?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. Bartolucci F. & Forcina A., 2002. "Extended RC Association Models Allowing for Order Restrictions and Marginal Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1192-1199, December.
    2. Anders Ekholm & John W. McDonald & Peter W. F. Smith, 2000. "Association Models for a Multivariate Binary Response," Biometrics, The International Biometric Society, vol. 56(3), pages 712-718, September.
    3. Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.
    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. Kateri, Maria & Nikolov, Nikolay I., 2022. "A generalized Mallows model based on ϕ-divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

    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. Monia Lupparelli & Alberto Roverato, 2017. "Log-mean linear regression models for binary responses with an application to multimorbidity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 227-252, February.
    2. Robin J. Evans & Thomas S. Richardson, 2013. "Marginal log-linear parameters for graphical Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 743-768, September.
    3. Klimova, Anna & Rudas, Tamás, 2016. "On the closure of relational models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 440-452.
    4. Colombi, Roberto, 2020. "Selection tests for possibly misspecified hierarchical multinomial marginal models," Econometrics and Statistics, Elsevier, vol. 16(C), pages 136-147.
    5. Alberto Roverato, 2015. "Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 627-648, June.
    6. Lui Kung-Jong, 2016. "Testing Equality in Ordinal Data with Repeated Measurements: A Model-Free Approach," The International Journal of Biostatistics, De Gruyter, vol. 12(2), pages 1-10, November.
    7. Demirhan, Haydar, 2013. "Bayesian estimation of order-restricted and unrestricted association models," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 109-126.
    8. Guogen Shan & Changxing Ma, 2014. "Efficient tests for one sample correlated binary data with applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 175-188, June.
    9. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    10. Forcina, Antonio, 2023. "Marginal log-linear models and mediation analysis," Statistics & Probability Letters, Elsevier, vol. 194(C).
    11. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    12. Antonoio Forcina, 2019. "Estimation and testing of multiplicative models for frequency data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 807-822, October.
    13. A. Felipe & N. Martín & P. Miranda & L. Pardo, 2018. "Statistical inference in constrained latent class models for multinomial data based on $$\phi $$ ϕ -divergence measures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 605-636, September.
    14. Gadre M. P. & Rattihalli R. N., 2005. "Some Group Inspection Based Multi-Attribute Control Charts to Identify Process Deterioration," Stochastics and Quality Control, De Gruyter, vol. 20(2), pages 191-204, January.
    15. Jokinen, Jukka, 2006. "Fast estimation algorithm for likelihood-based analysis of repeated categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1509-1522, December.
    16. Anatolyev Stanislav, 2009. "Multi-Market Direction-of-Change Modeling Using Dependence Ratios," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-24, March.
    17. Carolyn Anderson, 2013. "Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 276-303, July.
    18. L. Ark & Marcel Croon & Klaas Sijtsma, 2008. "Mokken Scale Analysis for Dichotomous Items Using Marginal Models," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 183-208, June.
    19. Alan Agresti, 2014. "Two Bayesian/frequentist challenges for categorical data analyses," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 125-132, August.
    20. Gao, Wei & Kuriki, Satoshi, 2006. "Testing marginal homogeneity against stochastically ordered marginals for rxr contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1330-1341, July.

    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:jmvana:v:184:y:2021:i:c:s0047259x21000191. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.