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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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