The Choice of Initial Configurations in Multidimensional Scaling: Local Minima, Fit, and Interpretability

Abstract

Multidimensional scaling (MDS) algorithms can easily end up in local minima, depending on the starting configuration. This is particularly true for 2-dimensional ordinal MDS. A simulation study shows that there can be many local minima that all have an excellent model fit (i.e., small Stress) even if they do not recover a known latent configuration very well, and even if they differ substantially among each other. MDS programs give the user only one supposedly Stress-optimal solution. We here present a procedure for analyzing all MDS solutions resulting from using a variety of different starting configurations. The solutions are compared in terms of fit and configurational similarity. This allows the MDS user to identify different types of solutions with acceptable Stress, if they exist, and then pick the one that is best interpretable.