Residual analysis for unidimensional scaling in the L₂-norm

ABSTRACT

We present a procedure (RAUS) for residual analysis of a dissimilarity matrix whereby unidimensional scaling is successively applied to the absolute value of residuals. A key advantage of RAUS is that the efficient Defays formulation of unidimensional scaling can be used for the fitting of each scale. An example using U.S. Supreme Court voting data is provided to illustrate the interpretation of successive scales. A simulation study was performed to evaluate RAUS.

KEYWORDS:

• Combinatorial data analysis
• Least-squares unidimensional scaling: Residual analysis
• Simulated annealing