Asymmetric Multidimensional Scaling of N-Mode M-Way Categorical Data using a Log-Linear Model

Abstract

Asymmetric multidimensional scaling (AMDS) is a visualization method that can be applied to asymmetric (dis)similarity data, which are adopted in several areas such as marketing research, psychometrics, and information science. Several researchers within these fields have examined and applied AMDS. However, the combination of the number of modes and ways remains fixed across these AMDS. Thus, the choice of model is largely contingent on the number of modes and ways. To overcome this problem, we propose an AMDS using a log-linear model with an m-way frequency table. Using the log-linear model, we apply AMDS to (dis)similarity data without a fixed number of modes and ways. In addition, we were able to simultaneously visualize two types of circles.