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Preliminary estimators for a mixture model of ordinal data

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  • Maria Iannario

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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  • Maria Iannario, 2012. "Preliminary estimators for a mixture model of ordinal data," 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. 6(3), pages 163-184, October.
    • Handle: RePEc:spr:advdac:v:6:y:2012:i:3:p:163-184
    DOI: 10.1007/s11634-012-0111-5
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    References listed on IDEAS

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    1. Maria Iannario, 2010. "On the identifiability of a mixture model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 87-94.
    2. 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.
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    4. 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.
    5. 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.
    6. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    7. 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.
    8. Richard Breen & Ruud Luijkx, 2010. "Mixture Models for Ordinal Data," Sociological Methods & Research, , vol. 39(1), pages 3-24, August.
    9. 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.
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    Keywords

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