Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike’s Information Criterion

Abstract

Akaike’s information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation data and real data demonstrate the utility of the Akaike’s information criterion in identifying the best approximating models in multidimensional scaling analyses.