has been generalized to the theory and procedures of "multiple scaling" which identifies the minimum number of scales needed for satisfactory reproducibility. As a procedure that ties substantive contents with logical aspects of data, Guttman scale heralded the advent of facet theory developed by Louis Guttman and his associates. Guttman scale in qualitative variables Guttman's original definition of a scale allows also for the exploratory scaling analysis of qualitative variables (nominal variables, or ordinal variables that do not necessarily belong to a pre-specified common attribute). This definition of Guttman scale relies on the prior definition of a simple function. For a totally ordered set X, say, 1,2,…,m , and another finite set, Y, with k elements k ≤ m, a function from X to Y is a simple function if X can be partitioned into k intervals which are in a one-to-one correspondence with the values of Y . A Guttman scale may then be defined for a data set of n variables, with the jth variable having kj (qualitative, not necessarily ordered) categories, thus: Definition: Guttman scale is a data set for which there exists an ordinal variable, X, with a finite number m of categories, say, 1,…,m with m≥ maxj(kj) and a permutation of subjects' profiles such that each variable in the data set is a simple function of X. Despite its seeming elegance and appeal for exploratory research, this definition has not been sufficiently studied or applied. References Further reading Coombs, C. H., Coombs, L. C., & Lingoes, J. C. (1978). "Stochastic cumulative scales". In S. Shye (Ed.), Theory construction and data analysis in the behavioral sciences. San Francisco: Jossey-Bass. Goodman, L. A. (1975). "A new model for scaling response patterns: An application of the quasi-independence concept". Journal of the American Statistical Association, 70, 755–768. Guttman, L. (1944). "A basis for scaling qualitative data". American Sociological Review, 9, 139–150. Green, B.F. (1956). "A method of scalogram analysis using summary statistics". Psychometrika, 21, 79-88. Psychometrics Multivariate statistics