Assessing fit and dimensionality in least squares metric multidimensional scaling using Akaike's information criterion

Educational and Psychological Measurement

Volumn 70, Issue 2, 2010, Pages 199-214

  Ding, Cody S ^a   Davison, Mark L ^b  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

AIC; Assessing dimensionality; MDS

Indexed keywords

EID: 77949589359     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164409344554     Document Type: Article

References (42)

1. Abelson, R.P., & Sermat, V. (1962). Multidimensional scaling of facial expressions. Journal of Experimental Psychology, 63, 546-554.
2. Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Second international symposium on information theory (pp. 267-281). Budapest, Hungary: Akademiai Kiado.
3. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
4. Bijmolt, T.H.A., & Wedel, M. (1999). A comparison of multidimensional scaling methods for perceptual mapping. Journal of Marketing Research, 36, 277-285.
5. Borg, I., & Groenen, P. (1997). Modern multidimensional scaling: Theory and applications. New York: Springer.
6. Borg, I., & Groenen, P.J.F. (2005). Modern multidimensional scaling: Theory and applications (2nd ed.). New York: Springer.
7. Burnham, K.P. & Anderson, D.R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). New York: Springer.
8. Cohen, H.S., & Jones, L.E. (1973). The effects of random error and subsampling of dimensions on recovery of configurations by non-metric multidimensional scaling. Psychometrika, 39, 69-90.
9. Cox, M.A.A., & Cox, T.F. (1992). Interpretation of Stress in non-metric multidimensional scaling. Statistica Applicata, 4, 611-618.
10. DeSarbo, W.S., & Cron, W.L. (1988). A maximum likelihood methodology for clusterwise linear regression. Journal of Classification, 5, 249-282.
11. Diederich, G., Messick, S.J., & Tucker, L.R. (1957). A general least squares solution for successive intervals. Psychometrika, 22, 159-173.
12. Ding, C.S., & Davison, M.L. (2005). A longitudinal study of math achievement gains for initially low achieving students. Contemporary Educational Psychology, 30, 81-95.
13. Ding, C.S., Davison, M.L., & Petersen, A.C. (2005). Multidimensional scaling analysis of growth and change. Journal of Educational Measurement, 42, 171-191.
14. Engen, T., Levy, N., & Schlosberg, H. (1958). The dimensional analysis of a new series of facial expressions. Journal of Experimental Psychology, 55, 454-458.
15. Goodrum, A.A. (2001). Multidimensional scaling of video surrogates. Journal of the American Society for Information Science and Technology, 52, 174-182.
16. Guiasu, S. (1977). Information theory with application. New York: McGraw-Hill.
17. Heady, R.B., & Lucas, J.L. (2006). PERMAP 11.6: Operation manual. Lafayett: University of Louisiana at Lafayette.
18. Isaac, P., & Poor, D. (1974). On the determination of appropriate dimensionality in data with error. Psychometrika, 39, 91-109.
19. Johnson, L. (1995). A multidimensional analysis of the vocational aspirations of college students. Measurement and Evaluation in Counseling and Development, 28, 25-44.
20. Kakeuchi, K. (1976). Distribution of informational statistics and a criterion of model fitting. Suri-Kagaku (Mathematic Sciences), 153, 12-18.
21. Kruskal, J.B. (1964a). Nonmetric scaling: A numerical method. Psychometrika, 29, 28-42.
22. Kruskal, J.B. (1964b). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-28.
23. Kuha, J. (2004). AIC and BIC: Comparisons of Assumptions and Performance. Sociological Methods Research, 33, 188-229.
24. MacKay, D.B., & Zinnes, J. (2005). ProScaL professional: A program for probabilistic scaling. Retrieved July 22, 2009, from www.proscal.com.
25. McWhirter, B.T., Palombi, B., & Garbin, C.P. (2000). University employees' perceptions of university counseling center services and consultation activities: A multidimensional scaling analysis. Journal of College Counseling, 3, 142-157.
26. Petersen, A.C. (1989). Coping with early adolescent challenges: Gender-related mental health outcomes (Grant no. 89127289). New York: William T. Grant Foundation.
27. Ramsay, J.O. (1977). Maximum likelihood estimation in multidimensional scaling. Psychometrika, 42, 241-266.
28. Ramsay, J.O. (1991). MULTISCALE manual (extended version). Montreal, Quebec, Canada: McGill University.
29. SAS Institute Inc. (2008). SAS/STAT®9.2 User's Guide. Cary, NC: Author.
30. Sireci, S.G., & Geisinger, K.F. (1992). Analyzing test content using cluster analysis and multidimensional scaling. Applied Psychological Measurement, 16, 17-31.
31. Spence, I., & Graef, J. (1974). The determination of the underlying dimensionality of an empirically obtained matrix of proximities. Multivariate Behavioral Research, 9, 331-341.
32. Spence, I., & Ogilvie, J.C. (1973). A table of expected stress values for random rankings in nonmetric multidimensional scaling. Multivariate Behavioral Research, 8, 511-517.
33. Stension, H.H., & Knoll, R.L. (1969). Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure. Psychological Bulletin, 71, 122-126.
34. Sugiura, N. (1978). Further analysis of the data by Akaike's information criterion and the finite corrections. Communications in Statistics, Theory and Methods, A7, 13-26.
35. Takane, Y. (1981). Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
36. Takane, Y., & Carroll, D.J. (1981). Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 46, 389-405.
37. Takane, Y., & Carroll, G.J. (1979). How to use MAXSCAL-4.1. Unpublished manuscript, Bell Laboratories.
38. Treat, T.A., McFall, R.M., Viken, R.J., Nosofsky, R.M., MacKay, D.B., & Kruschke, J.K. (2002). Assessing clinically relevant perceptual organization with multidimensional scaling techniques. Psychological Assessment, 14, 239-252.
39. Wagenaar, W.A., & Padmos, P. (1971). Quantitative interpretation of stress in Kruskal's multidimensional scaling technique. British Journal of Mathematical and Statistical Psychology, 24, 101-110.
40. Ye, J. (1998). On measuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association, 93, 120-131.
41. Young, F.W. (1970). Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 35, 455-473.
42. Young, F.W., & Lewyckyj, R. (1979). ALSCAL 4 user's guide (2nd ed.). Chapel Hill, NC: Data Analysis and Theory Associates.