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E-ReMI: Extended Maximal Interaction Two-mode Clustering

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Listed:
  • Zaheer Ahmed

    (Maastricht University)

  • Alberto Cassese

    (Maastricht University)

  • Gerard Breukelen

    (Maastricht University
    Maastricht University)

  • Jan Schepers

    (Maastricht University)

Abstract

In this paper, we present E-ReMI, a new method for studying two-way interaction in row by column (i.e., two-mode) data. E-ReMI is based on a probabilistic two-mode clustering model that yields a two-mode partition of the data with maximal interaction between row and column clusters. The proposed model extends REMAXINT by allowing for unequal cluster sizes for the row clusters, thus introducing more flexibility in the model. In the manuscript, we use a conditional classification likelihood approach to derive the maximum likelihood estimates of the model parameters. We further introduce a test statistic for testing the null hypothesis of no interaction, discuss its properties and propose an algorithm to obtain its distribution under this null hypothesis. Free software to apply the methods described in this paper is developed in the R language. We assess the performance of the new method and compare it with competing methodologies through a simulation study. Finally, we present an application of the methodology using data from a study of person by situation interaction.

Suggested Citation

  • Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    • Handle: RePEc:spr:jclass:v:40:y:2023:i:2:d:10.1007_s00357-023-09434-2
    DOI: 10.1007/s00357-023-09434-2
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    References listed on IDEAS

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    1. Jan Schepers & Hans-Hermann Bock & Iven Mechelen, 2017. "Maximal Interaction Two-Mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 49-75, April.
    2. Peter Bryant, 1991. "Large-sample results for optimization-based clustering methods," Journal of Classification, Springer;The Classification Society, vol. 8(1), pages 31-44, January.
    3. Jeffrey W. Miller & Matthew T. Harrison, 2018. "Mixture Models With a Prior on the Number of Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 340-356, January.
    4. Bhatia, Parmeet Singh & Iovleff, Serge & Govaert, Gérard, 2017. "blockcluster: An R Package for Model-Based Co-Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i09).
    5. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    6. Franck, Christopher T. & Nielsen, Dahlia M. & Osborne, Jason A., 2013. "A method for detecting hidden additivity in two-factor unreplicated experiments," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 95-104.
    7. Bock, Hans H., 1996. "Probabilistic models in cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 5-28, November.
    8. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    9. Justin B. Post & Howard D. Bondell, 2013. "Factor Selection and Structural Identification in the Interaction ANOVA Model," Biometrics, The International Biometric Society, vol. 69(1), pages 70-79, March.
    10. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
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