Here we propose methodological research on multidimsional scaling methods in response to research topic 108.c in the program description for NIMH. Multidimensional scaling (MDS) is a psychometric method with wide application in general behavioral science research. We propose to investigate and develop software for a new class of individual differences MDS (INDSCAL) models. In these new models parameters associated with individuals are modeled as random effects rather than as fixed parameters. For the INDSCAL models, these parameters are the subject weights. The resulting random effects MDS model has many advantages over its classical counterpart. For example, we are able to compute individual estimates of all subject weights even when only one dissimilarity is observed on the individual, and we are able to directly use our results in inferences about the sampled population of subject weights. We propose to study computational algorithms for computing estimates in this new class of MDS models, and to develop model building and other statistical techniques appropriate for the method. Also important during Phase I is demonstrating the advantages of these new models by using the prototypical software developed in Phase I to analyze real data sets.
Multidimensional scaling is a psychometric method widely used in market research, psychology, the social sciences, genetics, chemometrics, and other areas of behavioral and scientific research. The proposed models have significant advantages over existing techniques. A well designed and comprehensive module for implementing these models will find a ready market.
