IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v82y2020i1d10.1007_s13171-019-00168-1.html
   My bibliography  Save this article

Multiple Categorical Covariates-Based Multinomial Dynamic Response Model

Author

Listed:
  • R. Prabhakar Rao

    (Sri Sathya Sai Institute of Higher Learning)

  • Brajendra C. Sutradhar

    (Carleton University
    Memorial University)

Abstract

Regression models for multinomial responses with time dependent covariates have been studied recently both in longitudinal and time series setup. For practical importance, in this paper, we focus on a longitudinal multinomial response model with two categorical covariates to study their main and interaction effects after accommodating a lag 1 dynamic relationship between past and present multinomial responses. The proposed model could be generalized easily to accommodate multiple (more than two) categorical covariates and their interactions. As far as the estimation of the regression and the dynamic dependence parameters is concerned, we follow a recent parameter dimension-split based approach suggested by Sutradhar (Sankhya A80, 301–329 2018) but unlike the conditional method of moments (CMM) used in this study, we use a more efficient estimation approach, namely the so-called conditional generalized quasi-likelihood (CGQL) method for the estimation of the dynamic dependence parameters. The regression parameters are also estimated by using the same CGQL approach where responses become independent conditional on the past responses which is similar in principle to the likelihood estimation where the likelihood function is formed as a product of transitional probabilities conditional on the past responses. The asymptotic properties of the CGQL estimators are provided in details. The higher efficiency performance of the CGQL approach over the CMM approach is also demonstrated, for example, for the estimation of the dynamic dependence parameters.

Suggested Citation

  • R. Prabhakar Rao & Brajendra C. Sutradhar, 2020. "Multiple Categorical Covariates-Based Multinomial Dynamic Response Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 186-219, February.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:1:d:10.1007_s13171-019-00168-1
    DOI: 10.1007/s13171-019-00168-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-019-00168-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-019-00168-1?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. Brajendra C Sutradhar, 2018. "A Parameter Dimension-Split Based Asymptotic Regression Estimation Theory for a Multinomial Panel Data Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 301-329, August.
    2. Taslim S. Mallick & Brajendra C. Sutradhar, 2008. "GQL Versus Conditional GQL Inferences for Non‐Stationary Time Series of Counts with Overdispersion," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 402-420, March.
    3. Ludwig Fahrmeir & Heinz Kaufmann, 1987. "Regression Models For Non‐Stationary Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 147-160, March.
    4. Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    5. J. C. Loredo‐Osti & Brajendra C. Sutradhar, 2012. "Estimation of regression and dynamic dependence paremeters for non‐stationary multinomial time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 458-467, May.
    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. Brajendra C Sutradhar, 2018. "A Parameter Dimension-Split Based Asymptotic Regression Estimation Theory for a Multinomial Panel Data Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 301-329, August.
    2. Brajendra C. Sutradhar & Asokan M. Variyath, 2020. "A New Look at the Models for Ordinal Categorical Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 111-141, May.
    3. Sun-Joo Cho & Sarah Brown-Schmidt & Woo-yeol Lee, 2018. "Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 751-771, September.
    4. Brajendra C. Sutradhar & R. Prabhakar Rao, 2016. "Inferences in Longitudinal Count Data Models with Measurement Errors in Time Dependent Covariates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 39-65, May.
    5. Brajendra C. Sutradhar, 2018. "Semi-parametric Dynamic Models for Longitudinal Ordinal Categorical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 80-109, February.
    6. Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, May.
    7. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    8. H. Kaufmann, 1988. "On existence and uniqueness of maximum likelihood estimates in quantal and ordinal response models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 291-313, December.
    9. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    10. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    11. Brajendra C. Sutradhar & Vandna Jowaheer & R. Prabhakar Rao, 2016. "Semi-Parametric Models for Negative Binomial Panel Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 269-303, August.
    12. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    13. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    14. Moritz Berger & Gerhard Tutz, 2021. "Transition models for count data: a flexible alternative to fixed distribution models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1259-1283, October.
    15. Brajendra C. Sutradhar, 2022. "Multinomial Logistic Mixed Models for Clustered Categorical Data in a Complex Survey Sampling Setup," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 743-789, August.
    16. Peiming Wang & Martin Puterman, 1999. "Markov Poisson regression models for discrete time series. Part 1: Methodology," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 855-869.
    17. Zhen, X. & Basawa, I.V., 2009. "Observation-driven generalized state space models for categorical time series," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2462-2468, December.
    18. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    19. Song, Peter X.-K. & Freeland, R. Keith & Biswas, Atanu & Zhang, Shulin, 2013. "Statistical analysis of discrete-valued time series using categorical ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 112-124.
    20. Pushpakanthie Wijekoon & Alwell Oyet & Brajendra C. Sutradhar, 2019. "Pair-Wise Family-Based Correlation Model for Spatial Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 133-184, June.

    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:sankha:v:82:y:2020:i:1:d:10.1007_s13171-019-00168-1. 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.