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

Zaheer Ahmed, Alberto Cassese, Gerard Breukelen and Jan Schepers ()
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Zaheer Ahmed: Maastricht University
Alberto Cassese: Maastricht University
Gerard Breukelen: Maastricht University
Jan Schepers: Maastricht University

Advances in Data Analysis and Classification, 2021, vol. 15, issue 4, No 7, 987-1013

Abstract: 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.

Keywords: Two-mode clustering; Conditional classification likelihood; Interaction effect parameters; $$max-F$$ m a x - F test; 62-07: Data analysis, 62F03: Hypothesis testing, 62F40: Bootstrap, jackknife and other resampling methods, 62H30: Classification and discrimination; cluster analysis, 62J10: Analysis of variance and covariance (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11634-021-00441-y

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