Simultaneous transformation into interval scales for a set of categorical variables

Abstract

The paper – related to the problem of ordinal scale transformations, extensively dealt with by Amato Herzel – examines some implications and an extension of the method heuristically proposed by Jones (1986) to simultaneously transform a set of observed categorical ordinal variables into interval scales, under the assumption that there exists a normal latent random variable corresponding to each of the categorical variables. The article, on the one hand, presents and discusses the statistical-probabilistic model at the basis of Jones’ method and on the other hand proposes its extension to other families of latent variables, besides the Normal distribution, when their probability distributions can be reduced to a location-scale type. An example of application to the Logistic-Weibull family of distributions is also illustrated.