Nonlinear programming approach to optimal scaling of partially ordered categories
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.
- Abrham, J., Arri, P. S. (1973) Approximation of separable functions in convex programming. Canadian Journal of Operational Research and Information Processing 11: pp. 245-252
- Bock, R. D. (1956) The selection of judges for preference testing. Psychometrika 21: pp. 349-366
- Bock, R. D. Methods and applications of optimal scaling.The University of North Carolina Psychometric Laboratory Research Memorandum, No. 25, 1960.
- Bradley, R. A., Katti, S. K., Coons, I. J. (1962) Optimal scaling for ordered categories. Psychometrika 27: pp. 355-374
- Dantzig, G. B.Linear programming and extensions. Princeton University Press, 1963.
- Edgerton, H. A., Kolbe, L. E. (1936) The method of minimum variation for the combination of criteria. Psychometrika 1: pp. 183-187
- Fisher, R. A. (1938) Statistical methods for research workers. Oliver and Boyd, Edinburgh
- Fox, L. (1964) An introduction to numerical linear algebra. Oxford University Press, Oxford
- Guttman, L. The quantification of a class of attributes: a theory and method of scale construction. In: Horst, P. eds. (1941) The prediction of personal adjustment. Social Science Research Council, New York, pp. 319-348
- Guttman, L. (1946) An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics 17: pp. 144-163
- Guttman, L. The principal components of scale analysis. In: Stouffer, S. A. eds. (1950) Measurement and prediction. Princeton University Press, Princeton, pp. 312-361
- Hadley, G.Linear programming. Addison-Wesley, 1962.
- Hadley, G.Nonlinear and dynamic programming. Addison-Wesley, 1964.
- Hayashi, C. On the quantification of qualitative data from the mathematico-statistical point of view.Annals of Institute of Statistical Mathematics,3, No. 1, 1950.
- Hayashi, C. On the prediction of phenomena from qualitative data and quantification of qualitative data from the mathematico-statistical point of view.Annals of Institute of Statistical Mathematics,3, No. 2, 1952.
- Horst, P. (1936) Obtaining a composite measure from a number of different measures of the same attribute. Psychometrika 1: pp. 53-60
- Johnson, P. O. (1950) The quantification of qualitative data in discriminant analysis. Journal of American Statistical Association 45: pp. 65-70
- Lord, F. M. (1958) Some relations between Guttman's principal components of scale analysis and other psychometric theory. Psychometrika 23: pp. 291-296
- McDonald, R. P. (1968) A unified treatment of the weighting problem. Psychometrika 33: pp. 351-381
- Miller, C. E. The simplex method for local separable programming. In Graves, R. and Wolfe P. (eds.)Recent advances in mathematical programming. McGraw-Hill, 1963.
- Mosteller, F. A theory of scalogram analysis, using noncumulative types of items: a new approach to Thurstone's method of scaling attitude.Harvard University Laboratory of Social Relations, Report No.9, 1949.
- Nishisato, S. (1971) Analysis of variance through optimal scaling. Proceeding of the First Canadian Conference on Applied Statistics. Sir George Williams University Press, Montreal, pp. 306-316
- Nishisato, S. Analysis of variance of categorical data through selective scaling.Proceedings of the 20th International Congress of Psychology, Tokyo, 1972, 279.
- Nishisato, S. Optimal scaling of partially ordered categories.Paper presented at the Spring Meeting of the Psychometric Society, 1973.
- Nishisato, S., Inukai, Y. (1972) Partially optimal scaling of items with ordered categories. Japanese Psychological Research 14: pp. 109-119
- Shanno, D. F., Weil, R. L. (1972) Management science: a view from nonlinear programming. Communications of the ACM 15: pp. 542-549
- Shiba, S. (1965) A method for scoring multicategory items. Japanese Psychological Research 7: pp. 75-79
- Slater, P. Canonical analysis of discriminance. In: Eysenk, H. J. eds. (1960) Experiments in Psychology. Routledge and Kegan Paul, London, pp. 256-270
- Wilks, S. S. (1938) Weighting systems for linear function of correlated variables when there is no dependent variable. Psychometrika 3: pp. 23-40
- Nonlinear programming approach to optimal scaling of partially ordered categories
Volume 40, Issue 4 , pp 525-548
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors