Robustness study of normality-based likelihood ratio tests for testing maximal interaction two-mode clustering and a permutation-based alternative

In many applications involving quantitative two-mode data, an interesting research ques-tion is about the presence of interaction between the two modes. Testing the null hypothesisof no interaction in two-mode data can be done by using the likelihood ratio testing approachthat is considered in extended maximal interaction two-mode clustering (E-ReMI) (Ahmedet al., 2021). This testing approach is based on the assumption of normality. However, inreal-life applications, this assumption is rarely met. This paper is concerned with studyingthis likelihood ratio testing approach when the assumption of normality is violated, andhas two main goals. Firstly, we investigate in a simulation study whether the normality-based testing approach in E-ReMI is robust against a violation of normality. Secondly, weintroduce a new permutation-based likelihood ratio testing approach as an alternative, andevaluate its performance by means of a simulation study. We further discuss an applicationto data from a person by situation study.