Sensitivity and robustness in MDS configurations for mixed-type data: a study of the economic crisis impact on socially vulnerable Spanish people

摘要

Multidimensional scaling (MDS) techniques are initially proposed to produce pictorialrepresentations of distance, dissimilarity or proximity data. Sensitivity and robustnessassessment of multivariate methods is essential if inferences are to be drawn from the analysis.To our knowledge, the literature related to MDS for mixed-type data, including variablesmeasured at continuous level besides categorical ones, is quite scarce. The main motivation ofthis work was to analyze the stability and robustness of MDS configurations as an extension ofa previous study on a real data set, coming from a panel-type analysis designed to assess theeconomic crisis impact on Spanish people who were in situations of high risk of being sociallyexcluded. The main contributions of the paper on the treatment of MDS configurations formixed-type data are: (i) to propose a joint metric based on distance matrices computed forcontinuous, multi-scale categorical and/or binary variables, (ii) to introduce a systematicanalysis on the sensitivity of MDS configurations and (iii) to present a systematic search forrobustness and identification of outliers through a new procedure based on geometric variabilitynotions.