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Semi-parametric Dynamic Models for Longitudinal Ordinal Categorical Data

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  • Brajendra C. Sutradhar

    (Carleton University
    Memorial University)

Abstract

The over all regression function in a semi-parametric model involves a partly specified regression function in some primary covariates and a non-parametric function in some other secondary covariates. This type of semi-parametric models in a longitudinal setup has recently been discussed extensively both for repeated Poisson and negative binomial count data. However, when it is appropriate to interpret the longitudinal binary responses through a binary dynamic logits model, the inferences for semi-parametric Poisson and negative binomial models cannot be applied to such binary models as these models unlike the count data models produce recursive means and variances containing the dynamic dependence or correlation parameters. In this paper, we consider a general multinomial dynamic logits model in a semi-parametric setup first to analyze nominal categorical data in a semi-parametric longitudinal setup, and then modify this model to analyze ordinal categorical data. The ordinal responses are fitted by using a cumulative semi-parametric multinomial dynamic logits model. For the benefits of practitioners, a step by step estimation approach is developed for the non-parametric function, and for both regression and dynamic dependence parameters. In summary, a kernel-based semi-parametric weighted likelihood approach is used for the estimation of the non-parametric function. This weighted likelihood estimate for the non-parametric function is shown to be consistent. The regression and dynamic dependence parameters of the model are estimated by maximizing an approximate semi-parametric likelihood function for the parameters, which is constructed by replacing the non-parametric function with its consistent estimate. Asymptotic properties including the proofs for the consistency of the likelihood estimators of the regression and dynamic dependence parameters are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0100-z
    DOI: 10.1007/s13171-017-0100-z
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    References listed on IDEAS

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    1. Alan Agresti & Ranjini Natarajan, 2001. "Modeling Clustered Ordered Categorical Data: A Survey," International Statistical Review, International Statistical Institute, vol. 69(3), pages 345-371, December.
    2. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    3. Yi G.Y. & Cook R.J., 2002. "Marginal Methods for Incomplete Longitudinal Data Arising in Clusters," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1071-1080, December.
    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. 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.
    6. 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.
    7. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    8. Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
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