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Random effects clustering in multilevel modeling: choosing a proper partition

Author

Listed:
  • Claudio Conversano

    (University of Cagliari)

  • Massimo Cannas

    (University of Cagliari)

  • Francesco Mola

    (University of Cagliari)

  • Emiliano Sironi

    (Catholic University of Milan)

Abstract

A novel criterion for estimating a latent partition of the observed groups based on the output of a hierarchical model is presented. It is based on a loss function combining the Gini income inequality ratio and the predictability index of Goodman and Kruskal in order to achieve maximum heterogeneity of random effects across groups and maximum homogeneity of predicted probabilities inside estimated clusters. The index is compared with alternative approaches in a simulation study and applied in a case study concerning the role of hospital level variables in deciding for a cesarean section.

Suggested Citation

  • Claudio Conversano & Massimo Cannas & Francesco Mola & Emiliano Sironi, 2019. "Random effects clustering in multilevel modeling: choosing a proper partition," 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. 13(1), pages 279-301, March.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:1:d:10.1007_s11634-018-0347-9
    DOI: 10.1007/s11634-018-0347-9
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    References listed on IDEAS

    as
    1. Gerhard Tutz & Margret-Ruth Oelker, 2017. "Modelling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 204-227, August.
    2. Duncan, Craig & Jones, Kelvyn & Moon, Graham, 1998. "Context, composition and heterogeneity: Using multilevel models in health research," Social Science & Medicine, Elsevier, vol. 46(1), pages 97-117, January.
    3. Alessandra Guglielmi & Francesca Ieva & Anna M. Paganoni & Fabrizio Ruggeri & Jacopo Soriano, 2014. "Semiparametric Bayesian models for clustering and classification in the presence of unbalanced in-hospital survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 25-46, January.
    4. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    5. Jara, Alejandro & Hanson, Timothy & Quintana, Fernando A. & Müller, Peter & Rosner, Gary L., 2011. "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i05).
    6. M. Cannas & C. Conversano & F. Mola & E. Sironi, 2017. "Variation in caesarean delivery rates across hospitals: a Bayesian semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2095-2107, September.
    7. Meila, Marina, 2007. "Comparing clusterings--an information based distance," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 873-895, May.
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