Title: Cluster and structural equation multidimensional scaling for response and predictor spaces in distance-based regression
Authors: J Fernando Vera - University of Granada (Spain)
Eva Boj - University of Barcelona (Spain) [presenting]
Abstract: In cluster-based distance regression analysis, the use of cluster analysis in conjunction with MDS is an advisable procedure to reduce the number of elements to be represented using dissimilarities. Then, the projection of the vector of continuous responses in a Euclidean space of low dimensionality is given by multidimensional scaling. When two sets of variables constitute predictor and response space, clustering separately in both spaces may not be an advisable procedure for the prediction purpose. Nevertheless, two separate dissimilarity matrices measured between the observed elements in the predictor can be considered. Then, assuming both dissimilarity matrices are observations with error of an unknown symmetric dissimilarity matrix involving the overall information for the prediction and the response space, it is proposed to make clustering from the estimated values of this latent dissimilarity matrix using structural equation multidimensional scaling. From an estimated matrix of dissimilarities between the thus given clusters, distance-based regression analysis can thus be formulated between clustered elements. The performance of the proposed procedure is illustrated with the analysis of real data sets in an econometric context.