Error structure and identification condition in maximum likelihood nonmetric multidimensional scaling

European Journal of Operational Research

Volumn 111, Issue 2, 1998, Pages 216-227

  Abe, Makoto ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Logit model; Maximum likelihood estimation; MDS

Indexed keywords

ERROR ANALYSIS; ESTIMATION; MATHEMATICAL MODELS; PLANNING;

MAXIMUM LIKELIHOOD ESTIMATION;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0032302695     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(98)00146-5     Document Type: Article

References (19)

1. Bock, R.D., Gibbons, R.D., 1996. High-dimensional multivariate probit analysis. Biometrics 52, 1183-1194.
2. Carroll, J.D., Chang, J.J., 1970. Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika 35, 283-319.
3. Guttman, L.A., 1968. A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Psychometrika 33, 469-506.
4. Katahira, H., 1990. Perceptual mapping using ordered logit analysis. Marketing Science 9, 1-17.
5. Kruskal, J.B., 1964. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29, 1-27.
6. Kruskal, J.B., 1965. Analysis of factorial experiments by estimation monotone transformation of the data. Journal of Royal Statistical Society B 27, 251-263.
7. Little, R.J.A., Rubin, D.B., 1987. Statistical Analysis with Missing Data. Wiley, New York.
8. Mackay, D.B., Zinnes, J.L., 1986. A probabilistic model for the multidimensional scaling of proximity and preference data. Marketing Science 5, 325-344.
9. Malhotra, N.K., Jain, A.K., Pinson, C., 1988. The robustness of MDS configurations in the case of incomplete data. Journal of Marketing Research 25, 95-102.
10. Ramsay, J.O., 1977. Maximum likelihood estimation in multidimensional scaling. Psychometrika 42, 241-266.
11. Ramsay, J.O., 1978. Confidence Regions for Multidimensional Scaling Analysis. Psychometrika 43, 145-160.
12. Shepard, R.N., 1962. The analysis of proximities: Multidimensional scaling with an unknown distance function, I & II. Psychometrika 27, 125-140, 219-246.
13. Stevens, S.S., 1975. Psychophysics: Introduction to its Perceptual, Neural, and Social Prospects. Wiley, New York.
14. Takane, Y., 1981. Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika 46, 9-28.
15. Takane, Y., Carroll, J.D., 1981. Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika 46, 389-405.
16. Takane, Y., Young, F.W., Leeuw, J.D., 1977. Nonmetric individual differences multidimensional scaling: An alternative least squares method with optional scaling features. Psychometrika 42, 7-67.
17. Togerson, W.S., 1952. Multidimensional Scaling: I. Theory and method. Psychometrika 17, 401-419.
18. Young, F.W., 1987. Multidimensional Scaling: History, Theory, and Applications. Lawrence Erlbaum, Hillsdale, NJ.
19. Zinnes, J.L., Mackay, D.B., 1983. Probabilistic multidimensional scaling: Complete and incomplete data. Psychometrika 48, 27-48.