A method of optimal scaling for multivariate ordinal data and its extensions

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.