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Volumn 52, Issue 10, 2008, Pages 4673-4684

A maximum likelihood method for an asymmetric MDS model

Author keywords

[No Author keywords available]

Indexed keywords

CURVE FITTING; DATA REDUCTION; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD; SCALING LAWS; STATISTICAL TESTS;

EID: 44349111762     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.03.011     Document Type: Article
Times cited : (7)

References (61)
  • 2
    • 0038569061 scopus 로고
    • Maximum-likelihood estimation procedures and associated tests of significance
    • Aitchison J., and Silvey S.D. Maximum-likelihood estimation procedures and associated tests of significance. J. Roy. Statist. Soc. Ser. B 22 (1960) 154-171
    • (1960) J. Roy. Statist. Soc. Ser. B , vol.22 , pp. 154-171
    • Aitchison, J.1    Silvey, S.D.2
  • 3
    • 0000501656 scopus 로고
    • Information theory and an extension of the maximum likelihood principle
    • Petrov B.N., and Csaki F. (Eds), Akadémiai Kiadó, Budapest
    • Akaike H. Information theory and an extension of the maximum likelihood principle. In: Petrov B.N., and Csaki F. (Eds). The Second International Symposium on Information Theory (1973), Akadémiai Kiadó, Budapest 267-281
    • (1973) The Second International Symposium on Information Theory , pp. 267-281
    • Akaike, H.1
  • 4
    • 0000443648 scopus 로고
    • Toward a unified theory of similarity and recognition
    • Ashby F.G., and Perrin N.A. Toward a unified theory of similarity and recognition. Psychol. Rev. 95 (1988) 124-150
    • (1988) Psychol. Rev. , vol.95 , pp. 124-150
    • Ashby, F.G.1    Perrin, N.A.2
  • 5
    • 0001515164 scopus 로고
    • Maximum likelihood in three-way contingency tables
    • Birch M.W. Maximum likelihood in three-way contingency tables. J. Roy. Statist. Soc. Ser. B 25 (1963) 220-233
    • (1963) J. Roy. Statist. Soc. Ser. B , vol.25 , pp. 220-233
    • Birch, M.W.1
  • 8
    • 0001499322 scopus 로고
    • A test for symmetry in contingency tables
    • Bowker A.H. A test for symmetry in contingency tables. J. Amer. Statist. Assoc. 43 (1948) 572-574
    • (1948) J. Amer. Statist. Assoc. , vol.43 , pp. 572-574
    • Bowker, A.H.1
  • 9
    • 0002678262 scopus 로고
    • Contribution à l'analyse statistique des tableaux de corrélation [Contributions to the statistical analysis of correlation matrices]
    • Caussinus H. Contribution à l'analyse statistique des tableaux de corrélation [Contributions to the statistical analysis of correlation matrices]. Annales de la Faculté des Sciences de l'Université de Toulouse 29 (1965) 77-182
    • (1965) Annales de la Faculté des Sciences de l'Université de Toulouse , vol.29 , pp. 77-182
    • Caussinus, H.1
  • 10
    • 0040977867 scopus 로고
    • A graphical technique for representing the asymmetric relationships between N objects
    • Chino N. A graphical technique for representing the asymmetric relationships between N objects. Behaviormetrika 5 (1978) 23-40
    • (1978) Behaviormetrika , vol.5 , pp. 23-40
    • Chino, N.1
  • 11
    • 0009932977 scopus 로고
    • A generalized inner product model for the analysis of asymmetry
    • Chino N. A generalized inner product model for the analysis of asymmetry. Behaviormetrika 27 (1990) 25-46
    • (1990) Behaviormetrika , vol.27 , pp. 25-46
    • Chino, N.1
  • 12
    • 44349124959 scopus 로고    scopus 로고
    • Chino, N., Saburi, S., 2006. Tests of symmetry in asymmetric MDS. Paper Presented at the 2nd German Japanese Symposium on Classification. Berlin, March
    • Chino, N., Saburi, S., 2006. Tests of symmetry in asymmetric MDS. Paper Presented at the 2nd German Japanese Symposium on Classification. Berlin, March
  • 13
    • 0040977865 scopus 로고
    • Geometrical structures of some non-distance models for asymmetric MDS
    • Chino N., and Shiraiwa K. Geometrical structures of some non-distance models for asymmetric MDS. Behaviormetrika 20 (1993) 35-47
    • (1993) Behaviormetrika , vol.20 , pp. 35-47
    • Chino, N.1    Shiraiwa, K.2
  • 14
    • 0002398198 scopus 로고
    • Graphical representation of asymmetric matrices
    • Constantine A.G., and Gower J.C. Graphical representation of asymmetric matrices. Appl. Statist. 27 (1978) 297-304
    • (1978) Appl. Statist. , vol.27 , pp. 297-304
    • Constantine, A.G.1    Gower, J.C.2
  • 16
    • 0012149264 scopus 로고
    • A special jackknife for multidimensional scaling
    • de Leeuw J., and Meulman J. A special jackknife for multidimensional scaling. J. Classif. 3 (1986) 97-112
    • (1986) J. Classif. , vol.3 , pp. 97-112
    • de Leeuw, J.1    Meulman, J.2
  • 17
    • 0742317535 scopus 로고    scopus 로고
    • A distance representation of the quasi-symmetry model and related distance models
    • Yanai H., Okada A., Shigemasu K., Kano Y., and Meulman J.J. (Eds), Springer, Tokyo
    • De Rooij M., and Heiser W.J. A distance representation of the quasi-symmetry model and related distance models. In: Yanai H., Okada A., Shigemasu K., Kano Y., and Meulman J.J. (Eds). New Developments in Psychometrics (2003), Springer, Tokyo 487-494
    • (2003) New Developments in Psychometrics , pp. 487-494
    • De Rooij, M.1    Heiser, W.J.2
  • 18
    • 14944364410 scopus 로고    scopus 로고
    • Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data
    • De Rooij M., and Heiser W.J. Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data. Psychometrika 70 (2005) 99-122
    • (2005) Psychometrika , vol.70 , pp. 99-122
    • De Rooij, M.1    Heiser, W.J.2
  • 19
    • 0002775137 scopus 로고
    • Analyse factorielle des matrices carrees non symetriques [Factor analysis of square asymmetric matrices]
    • Diday E., et al. (Ed), North-Holland, Amsterdam
    • Escoufier Y., and Grorud A. Analyse factorielle des matrices carrees non symetriques [Factor analysis of square asymmetric matrices]. In: Diday E., et al. (Ed). Data Analysis and Informatics (1980), North-Holland, Amsterdam 263-276
    • (1980) Data Analysis and Informatics , pp. 263-276
    • Escoufier, Y.1    Grorud, A.2
  • 20
    • 84935196069 scopus 로고
    • The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with or without missing entries
    • Goodman L.A. The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with or without missing entries. J. Amer. Statist. Assoc. 63 (1968) 1091-1131
    • (1968) J. Amer. Statist. Assoc. , vol.63 , pp. 1091-1131
    • Goodman, L.A.1
  • 21
    • 0003083206 scopus 로고
    • The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries
    • Goodman L.A. The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries. Ann. Statist. 13 (1985) 10-69
    • (1985) Ann. Statist. , vol.13 , pp. 10-69
    • Goodman, L.A.1
  • 22
    • 0002552587 scopus 로고
    • The analysis of asymmetry and orthogonality
    • Barra J.R., Brodeau F., Romer G., and van Cutsem B. (Eds), North-Holland, Amsterdam
    • Gower J.C. The analysis of asymmetry and orthogonality. In: Barra J.R., Brodeau F., Romer G., and van Cutsem B. (Eds). Recent Developments in Statistics (1977), North-Holland, Amsterdam 109-123
    • (1977) Recent Developments in Statistics , pp. 109-123
    • Gower, J.C.1
  • 23
    • 44349093531 scopus 로고    scopus 로고
    • Harshman, R.A., 1978. Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. Hamilton, Canada
    • Harshman, R.A., 1978. Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. Hamilton, Canada
  • 24
    • 0001190592 scopus 로고
    • A model for the analysis of asymmetric data in marketing research
    • Harshman R.A., Green P.E., Wind Y., and Lundy M.E. A model for the analysis of asymmetric data in marketing research. Market. Sci. 1 (1982) 205-242
    • (1982) Market. Sci. , vol.1 , pp. 205-242
    • Harshman, R.A.1    Green, P.E.2    Wind, Y.3    Lundy, M.E.4
  • 25
    • 0000768526 scopus 로고
    • Monotonic models for asymmetric proximities
    • Holman E.W. Monotonic models for asymmetric proximities. J. Math. Psychol. 20 (1979) 1-15
    • (1979) J. Math. Psychol. , vol.20 , pp. 1-15
    • Holman, E.W.1
  • 26
    • 0015617881 scopus 로고
    • The logistic distribution as an approximation to the normal curve
    • Jeffres L.A. The logistic distribution as an approximation to the normal curve. J. Acoust. Soc. Amer. 53 (1973) 1296
    • (1973) J. Acoust. Soc. Amer. , vol.53 , pp. 1296
    • Jeffres, L.A.1
  • 27
    • 21344498265 scopus 로고
    • A generalization of GIPSCAL for the analysis of nonsymmetric data
    • Kiers H.A.L., and Takane Y. A generalization of GIPSCAL for the analysis of nonsymmetric data. J. Classif. 11 (1994) 79-99
    • (1994) J. Classif. , vol.11 , pp. 79-99
    • Kiers, H.A.L.1    Takane, Y.2
  • 28
    • 0000424981 scopus 로고
    • Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density
    • Krumhansl C.L. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychol. Rev. 85 (1978) 445-463
    • (1978) Psychol. Rev. , vol.85 , pp. 445-463
    • Krumhansl, C.L.1
  • 29
    • 0041654220 scopus 로고
    • Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
    • Kruskal J.B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29 (1964) 1-27
    • (1964) Psychometrika , vol.29 , pp. 1-27
    • Kruskal, J.B.1
  • 30
    • 24944533365 scopus 로고
    • Nonmetric multidimensional scaling: A numerical method
    • Kruskal J.B. Nonmetric multidimensional scaling: A numerical method. Psychometrika 29 (1964) 115-129
    • (1964) Psychometrika , vol.29 , pp. 115-129
    • Kruskal, J.B.1
  • 31
    • 0000742860 scopus 로고
    • Geometrical models and badness-of-fit functions
    • Krishnaiah P.K. (Ed), Academic Press, New York
    • Kruskal J.B., and Carroll J.D. Geometrical models and badness-of-fit functions. In: Krishnaiah P.K. (Ed). Multivariate Analysis II (1969), Academic Press, New York 639-671
    • (1969) Multivariate Analysis II , pp. 639-671
    • Kruskal, J.B.1    Carroll, J.D.2
  • 33
    • 0000717718 scopus 로고
    • Detection and recognition
    • Luce R.D., Bush R.R., and Galanter E. (Eds), Wiley, New York
    • Luce R.D. Detection and recognition. In: Luce R.D., Bush R.R., and Galanter E. (Eds). Handbook of Mathematical Psychology vol. 1 (1963), Wiley, New York 103-189
    • (1963) Handbook of Mathematical Psychology , vol.1 , pp. 103-189
    • Luce, R.D.1
  • 34
    • 0000596361 scopus 로고
    • Note on the sampling error of the difference between correlated proportions or percentages
    • McNemar Q. Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika 12 (1947) 153-157
    • (1947) Psychometrika , vol.12 , pp. 153-157
    • McNemar, Q.1
  • 35
    • 0002449033 scopus 로고
    • Stimulus bias, asymmetric similarity, and classification
    • Nosofsky R.M. Stimulus bias, asymmetric similarity, and classification. Cognit. Psychol. 23 (1991) 94-140
    • (1991) Cognit. Psychol. , vol.23 , pp. 94-140
    • Nosofsky, R.M.1
  • 36
    • 0009938850 scopus 로고
    • Nonmetric multidimensional scaling of asymmetric proximities
    • Okada A., and Imaizumi T. Nonmetric multidimensional scaling of asymmetric proximities. Behaviormetrika 21 (1987) 81-96
    • (1987) Behaviormetrika , vol.21 , pp. 81-96
    • Okada, A.1    Imaizumi, T.2
  • 37
    • 0031517183 scopus 로고    scopus 로고
    • Asymmetric multidimensional scaling of two-mode three-way proximities
    • Okada A., and Imaizumi T. Asymmetric multidimensional scaling of two-mode three-way proximities. J. Classif. 14 (1997) 195-224
    • (1997) J. Classif. , vol.14 , pp. 195-224
    • Okada, A.1    Imaizumi, T.2
  • 38
    • 0009079419 scopus 로고
    • Some small sample results for maximum likelihood estimation in multidimensional scaling
    • Ramsay J.O. Some small sample results for maximum likelihood estimation in multidimensional scaling. Psychometrika 45 (1980) 139-144
    • (1980) Psychometrika , vol.45 , pp. 139-144
    • Ramsay, J.O.1
  • 39
    • 0039534847 scopus 로고
    • Tests of symmetry in three-way contingency tables
    • Read C.B. Tests of symmetry in three-way contingency tables. Psychometrika 43 (1978) 409-420
    • (1978) Psychometrika , vol.43 , pp. 409-420
    • Read, C.B.1
  • 40
    • 0036017463 scopus 로고    scopus 로고
    • Rotation techniques in asymmetric multidimensional scaling
    • Rocci R., and Bove G. Rotation techniques in asymmetric multidimensional scaling. J. Comput. Graph. Statist. 11 (2002) 405-419
    • (2002) J. Comput. Graph. Statist. , vol.11 , pp. 405-419
    • Rocci, R.1    Bove, G.2
  • 41
    • 0000781697 scopus 로고
    • The peck orders of chickens: How do they develop and why are they linear?
    • Rushen J. The peck orders of chickens: How do they develop and why are they linear?. Anim. Behav. 30 (1982) 1129-1137
    • (1982) Anim. Behav. , vol.30 , pp. 1129-1137
    • Rushen, J.1
  • 42
    • 0002815671 scopus 로고
    • Analysis of asymmetric proximity matrix by a model of distance and additive terms
    • Saito T. Analysis of asymmetric proximity matrix by a model of distance and additive terms. Behaviormetrika 29 (1991) 45-60
    • (1991) Behaviormetrika , vol.29 , pp. 45-60
    • Saito, T.1
  • 43
    • 14644418909 scopus 로고
    • Multidimensional scaling of asymmetric proximity: Model and method
    • Saito T., and Takeda S. Multidimensional scaling of asymmetric proximity: Model and method. Behaviormetrika 28 (1990) 49-80
    • (1990) Behaviormetrika , vol.28 , pp. 49-80
    • Saito, T.1    Takeda, S.2
  • 44
    • 44349122189 scopus 로고
    • An analysis of sociometric data by MDS in Minkowski space
    • Matsushita K. (Ed), North-Holland, Amsterdam
    • Sato Y. An analysis of sociometric data by MDS in Minkowski space. In: Matsushita K. (Ed). Statistical Theory and Data Analysis II (1988), North-Holland, Amsterdam 385-396
    • (1988) Statistical Theory and Data Analysis II , pp. 385-396
    • Sato, Y.1
  • 45
    • 0005718706 scopus 로고
    • Fitting one matrix to another under choice of a central dilation and a rigid motion
    • Schönemann P.H., and Carroll R.M. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika 35 (1970) 245-255
    • (1970) Psychometrika , vol.35 , pp. 245-255
    • Schönemann, P.H.1    Carroll, R.M.2
  • 46
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • Schwarz G. Estimating the dimension of a model. Ann. Statist. 6 (1978) 461-464
    • (1978) Ann. Statist. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 47
    • 0345111705 scopus 로고
    • Models of identification
    • Nickerson R. (Ed), Erlbaum, Hillsdale, NJ
    • Smith J.E.K. Models of identification. In: Nickerson R. (Ed). Attention and Performance VIII (1980), Erlbaum, Hillsdale, NJ
    • (1980) Attention and Performance VIII
    • Smith, J.E.K.1
  • 48
    • 84981981465 scopus 로고
    • A test for homogeneity of the marginal distributions in a two-way classification
    • Stuart A. A test for homogeneity of the marginal distributions in a two-way classification. Biometrika 42 (1955) 412-416
    • (1955) Biometrika , vol.42 , pp. 412-416
    • Stuart, A.1
  • 49
    • 0002245844 scopus 로고
    • Multidimensional successive categories scaling: A maximum likelihood method
    • Takane Y. Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika 46 (1981) 9-28
    • (1981) Psychometrika , vol.46 , pp. 9-28
    • Takane, Y.1
  • 50
    • 18244388340 scopus 로고
    • Comparison of models for stimulus recognition data
    • de Leeuw J., Heiser W., Meulman J., and Critchley F. (Eds), DSWO Press, Leiden
    • Takane Y., and Shibayama T. Comparison of models for stimulus recognition data. In: de Leeuw J., Heiser W., Meulman J., and Critchley F. (Eds). Multidimensional Data Analysis (1986), DSWO Press, Leiden 119-138
    • (1986) Multidimensional Data Analysis , pp. 119-138
    • Takane, Y.1    Shibayama, T.2
  • 51
    • 0031143181 scopus 로고    scopus 로고
    • Reduction of asymmetry by rank-one matrices
    • ten Berge J.M.F. Reduction of asymmetry by rank-one matrices. Comput. Statist. Data Anal. 24 (1997) 357-366
    • (1997) Comput. Statist. Data Anal. , vol.24 , pp. 357-366
    • ten Berge, J.M.F.1
  • 52
    • 0002781451 scopus 로고
    • Spatial interaction patterns
    • Tobler W. Spatial interaction patterns. J. Environ. Syst. 6 (1976-77) 271-301
    • (1976) J. Environ. Syst. , vol.6 , pp. 271-301
    • Tobler, W.1
  • 54
    • 0346456865 scopus 로고
    • Mathematical models of recognition and confusion in psychology
    • Townsend J.T., and Landon D.E. Mathematical models of recognition and confusion in psychology. Math. Soc. Sci. 4 (1983) 25-71
    • (1983) Math. Soc. Sci. , vol.4 , pp. 25-71
    • Townsend, J.T.1    Landon, D.E.2
  • 55
    • 0141791131 scopus 로고    scopus 로고
    • GIPSCAL revisited. A projected gradient approach
    • Trendafilov N.T. GIPSCAL revisited. A projected gradient approach. Statist. Comput. 12 (2002) 135-145
    • (2002) Statist. Comput. , vol.12 , pp. 135-145
    • Trendafilov, N.T.1
  • 56
    • 84925623234 scopus 로고
    • Tests of statistical hypotheses concerning several parameters when the number of observations is large
    • Wald A. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 (1943) 426-482
    • (1943) Trans. Amer. Math. Soc. , vol.54 , pp. 426-482
    • Wald, A.1
  • 57
    • 0007210549 scopus 로고
    • Restricted multidimensional scaling models for asymmetric proximities
    • Weeks D.G., and Bentler P.M. Restricted multidimensional scaling models for asymmetric proximities. Psychometrika 47 (1982) 201-208
    • (1982) Psychometrika , vol.47 , pp. 201-208
    • Weeks, D.G.1    Bentler, P.M.2
  • 58
    • 0012889305 scopus 로고
    • A quasi-nonmetric method for multidimensional scaling via an extended Euclidean model
    • Winsberg S., and Carroll J.D. A quasi-nonmetric method for multidimensional scaling via an extended Euclidean model. Psychometrika 54 (1989) 217-229
    • (1989) Psychometrika , vol.54 , pp. 217-229
    • Winsberg, S.1    Carroll, J.D.2
  • 59
    • 27944460480 scopus 로고    scopus 로고
    • Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation
    • Yang Y. Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation. Biometrika 92 (2005) 937-950
    • (2005) Biometrika , vol.92 , pp. 937-950
    • Yang, Y.1
  • 60
    • 44349108195 scopus 로고    scopus 로고
    • Young, F.W., 1975. An asymmetric Euclidian model for multi-process asymmetric data. Paper presented at US-Japan Seminar on MDS, San Diego, USA. pp. 79-88
    • Young, F.W., 1975. An asymmetric Euclidian model for multi-process asymmetric data. Paper presented at US-Japan Seminar on MDS, San Diego, USA. pp. 79-88


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