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Preliminary estimators for a mixture model of ordinal data

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  • Maria Iannario

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    Abstract

    In this paper, we propose preliminary estimators for the parameters of a mixture distribution introduced for the analysis of ordinal data where the mixture components are given by a Combination of a discrete Uniform and a shifted Binomial distribution ( cub model). After reviewing some preliminary concepts related to the meaning of parameters which characterize such models, we introduce estimators which are related to the location and heterogeneity of the observed distributions, respectively, in order to accelerate the EM procedure for the maximum likelihood estimation. A simulation experiment has been performed to investigate their main features and to confirm their usefulness. A check of the proposal on real case studies and some comments conclude the paper. Copyright Springer-Verlag 2012

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    File URL: http://hdl.handle.net/10.1007/s11634-012-0111-5
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    Bibliographic Info

    Article provided by Springer in its journal Advances in Data Analysis and Classification.

    Volume (Year): 6 (2012)
    Issue (Month): 3 (October)
    Pages: 163-184

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    Handle: RePEc:spr:advdac:v:6:y:2012:i:3:p:163-184

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    Web page: http://www.springer.com/statistics/statistical+theory+and+methods/journal/11634

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    Related research

    Keywords: Ordinal data; cub models; Preliminary estimators; 6207; 62E17; 62F10;

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    1. Greene, William H. & Hensher, David A., 2003. "A latent class model for discrete choice analysis: contrasts with mixed logit," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 681-698, September.
    2. Bettina GrĂ¼n & Friedrich Leisch, 2008. "Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects," Journal of Classification, Springer, vol. 25(2), pages 225-247, November.
    3. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    4. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    5. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    6. Richard Breen & Ruud Luijkx, 2010. "Mixture Models for Ordinal Data," Sociological Methods & Research, , vol. 39(1), pages 3-24, August.
    7. Nettleton, Dan, 2009. "Testing for the Supremacy of a Multinomial Cell Probability," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1052-1059.
    8. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer, vol. 12(1), pages 21-55, March.
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