IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v15y2021i4d10.1007_s11634-021-00441-y.html
   My bibliography  Save this article

REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

Author

Listed:
  • Zaheer Ahmed

    (Maastricht University)

  • Alberto Cassese

    (Maastricht University)

  • Gerard Breukelen

    (Maastricht University
    Maastricht University)

  • Jan Schepers

    (Maastricht University)

Abstract

We present a novel method, REMAXINT, that captures the gist of two-way interaction in row by column (i.e., two-mode) data, with one observation per cell. REMAXINT is a probabilistic two-mode clustering model that yields two-mode partitions with maximal interaction between row and column clusters. For estimation of the parameters of REMAXINT, we maximize a conditional classification likelihood in which the random row (or column) main effects are conditioned out. For testing the null hypothesis of no interaction between row and column clusters, we propose a $$max-F$$ m a x - F test statistic and discuss its properties. We develop a Monte Carlo approach to obtain its sampling distribution under the null hypothesis. We evaluate the performance of the method through simulation studies. Specifically, for selected values of data size and (true) numbers of clusters, we obtain critical values of the $$max-F$$ m a x - F statistic, determine empirical Type I error rate of the proposed inferential procedure and study its power to reject the null hypothesis. Next, we show that the novel method is useful in a variety of applications by presenting two empirical case studies and end with some concluding remarks.

Suggested Citation

  • Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2021. "REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction," 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. 15(4), pages 987-1013, December.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-021-00441-y
    DOI: 10.1007/s11634-021-00441-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-021-00441-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-021-00441-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Bock, Hans H., 1996. "Probabilistic models in cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 5-28, November.
    5. Verbeke G. & Spiessens B. & Lesaffre E., 2001. "Conditional Linear Mixed Models," The American Statistician, American Statistical Association, vol. 55, pages 25-34, February.
    6. Jan Schepers & Eva Ceulemans & Iven Mechelen, 2008. "Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 67-85, June.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Alessio Farcomeni, 2009. "Robust Double Clustering: A Method Based on Alternating Concentration Steps," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 77-101, April.
    4. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," 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. 10(2), pages 209-224, June.
    5. Jiao Jieying & Hu Guanyu & Yan Jun, 2021. "A Bayesian marked spatial point processes model for basketball shot chart," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 77-90, June.
    6. repec:jss:jstsof:46:i06 is not listed on IDEAS
    7. Shouxiang Wang & Pengfei Dong & Yingjie Tian, 2017. "A Novel Method of Statistical Line Loss Estimation for Distribution Feeders Based on Feeder Cluster and Modified XGBoost," Energies, MDPI, vol. 10(12), pages 1-17, December.
    8. Pronello, Cristina & Camusso, Cristian, 2011. "Travellers’ profiles definition using statistical multivariate analysis of attitudinal variables," Journal of Transport Geography, Elsevier, vol. 19(6), pages 1294-1308.
    9. Im, Yunju & Tan, Aixin, 2021. "Bayesian subgroup analysis in regression using mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    10. Bouveyron, C. & Girard, S. & Schmid, C., 2007. "High-dimensional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 502-519, September.
    11. Ludkin, Matthew, 2020. "Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. Aurore Lomet & Gérard Govaert & Yves Grandvalet, 2018. "Model selection for Gaussian latent block clustering with the integrated classification likelihood," 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. 12(3), pages 489-508, September.
    13. Haedo, Christian & Mouchart, Michel, 2019. "Two-mode clustering through profiles of regions and sectors," LIDAM Discussion Papers ISBA 2019014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Griffin, Maryclare & Hoff, Peter D., 2019. "Lasso ANOVA decompositions for matrix and tensor data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 181-194.
    15. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," 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 33-64, March.
    16. van Dijk, A. & van Rosmalen, J.M. & Paap, R., 2009. "A Bayesian approach to two-mode clustering," Econometric Institute Research Papers EI 2009-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Dirk Depril & Iven Mechelen & Tom Wilderjans, 2012. "Lowdimensional Additive Overlapping Clustering," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 297-320, October.
    18. Weiß, Christian H. & Göb, Rainer, 2008. "Discovering patterns in categorical time series using IFS," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4369-4379, May.
    19. Betancourt, Brenda & Sosa, Juan & Rodríguez, Abel, 2022. "A prior for record linkage based on allelic partitions," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    20. Jee-Seon Kim & Edward Frees, 2006. "Omitted Variables in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 659-690, December.
    21. Tom Wilderjans & Dirk Depril & Iven Van Mechelen, 2013. "Additive Biclustering: A Comparison of One New and Two Existing ALS Algorithms," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 56-74, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-021-00441-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.