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Estimation and testing of multiplicative models for frequency data

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  • Antonoio Forcina

    (University of Perugia)

Abstract

This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, like basket analysis, these models may be seen as a constrained version of quasi-independence. After reviewing the basic properties of the models, their geometric features as a curved exponential family are investigated. An improved algorithm for computing maximum likelihood estimates is introduced and new insights are provided on the underlying geometry. The asymptotic distribution of three statistics for hypothesis testing are derived and a small simulation study is presented to investigate the accuracy of asymptotic approximations.

Suggested Citation

  • Antonoio Forcina, 2019. "Estimation and testing of multiplicative models for frequency data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 807-822, October.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:7:d:10.1007_s00184-019-00709-6
    DOI: 10.1007/s00184-019-00709-6
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    References listed on IDEAS

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    1. Giudici, Paolo & Passerone, Gianluca, 2002. "Data mining of association structures to model consumer behaviour," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 533-541, February.
    2. Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.
    3. Klimova, Anna & Rudas, Tamás & Dobra, Adrian, 2012. "Relational models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 159-173, February.
    4. Anna Klimova & Tamás Rudas, 2015. "Iterative Scaling in Curved Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 832-847, September.
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    Cited by:

    1. Klimova, Anna & Rudas, Tamás, 2022. "Hierarchical Aitchison–Silvey models for incomplete binary sample spaces," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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