Bayesian multidimensional scaling for the estimation of a Minkowski exponent

The Minkowski property of psychological space has long been of interest to researchers. A common strategy has been calculating the stress in multidimensional scaling for many Minkowski exponent values and choosing the one that results in the lowest stress. However, this strategy has an arbitrariness problem-that is, a loss function. Although a recently proposed Bayesian approach could solve this problem, the method was intended for individual subject data. It is unknown whether this method is directly applicable to averaged or single data, which are common in psychology and behavioral science. Therefore, we first conducted a simulation study to evaluate the applicability of the method to the averaged data problem and found that it failed to recover the true Minkowski exponent. Therefore, a new method is proposed that is a simple extension of the existing Euclidean Bayesian multidimensional scaling to the Minkowski metric. Another simulation study revealed that the proposed method could successfully recover the true Minkowski exponent. BUGS codes used in this study are given in the Appendix.