E-ReMI: Extended Maximal Interaction Two-mode Clustering

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.