Analysis of the Visibility Data for the Combinations of Foreground and Background Colors by Maximum Likelihood Asymmetric MDS Using the Multiplicative Error Model

Abstract

A maximum likelihood method for asymmetric multidimensional scaling, which was proposed by Saburi and Chino (Comput. Stat. Data Anal., 52:4673-4684, 2008), uses the additive error model in which the normally distributed error terms are added to the dissimilarities. In this study, we introduce in this method the multiplicative error model, where the log-normally distributed error terms are multiplied by the dissimilarities, and the corresponding representation of the dissimilarities. It was applied to the visibility data for the combinations of foreground and background colors, assuming the multiplicative as well as the additive error model. The optimal model was found with the multiplicative error model according to AIC.