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Minimum phi-divergence estimators for multinomial logistic regression with complex sample design

Author

Listed:
  • Elena Castilla

    (Complutense University of Madrid)

  • Nirian Martín

    (Complutense University of Madrid)

  • Leandro Pardo

    (Complutense University of Madrid)

Abstract

This article develops the theoretical framework needed to study the multinomial regression model for complex sample design with pseudo-minimum phi-divergence estimators. The numerical example and the simulation study propose new estimators for the parameter of the logistic regression with overdispersed multinomial distributions for the response variables, the pseudo-minimum Cressie–Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The simulation study shows that the Binder’s method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo-minimum Cressie–Read divergence estimator, with $$\lambda =\frac{2}{3}$$ λ = 2 3 , is plugged.

Suggested Citation

  • Elena Castilla & Nirian Martín & Leandro Pardo, 2018. "Minimum phi-divergence estimators for multinomial logistic regression with complex sample design," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 381-411, July.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:3:d:10.1007_s10182-017-0311-6
    DOI: 10.1007/s10182-017-0311-6
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    2. A. Gupta & D. Kasturiratna & T. Nguyen & L. Pardo, 2006. "A New Family of BAN Estimators for Polytomous Logistic Regression Models based on ϕ- Divergence Measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 159-176, August.
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    4. Abhik Ghosh & Ayanendranath Basu, 2015. "Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2056-2072, September.
    5. C., E. A. Molina & Skinner, C. J., 1992. "Pseudo-likelihood and quasi-likelihood estimation for complex sampling schemes," Computational Statistics & Data Analysis, Elsevier, vol. 13(4), pages 395-405, May.
    6. J. Engel, 1988. "Polytomous logistic regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(4), pages 233-252, December.
    7. Theil, Henri, 1969. "A Multinomial Extension of the Linear Logit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 251-259, October.
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    Cited by:

    1. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2021. "Robust semiparametric inference for polytomous logistic regression with complex survey design," 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. 15(3), pages 701-734, September.

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