DUAL SCALING OF SUCCESSIVE CATEGORIES DATA (original) (raw)

Correction information

Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : A method was developed to determine values of stimuli and category boundaries through differential weighting of subjects. The method transforms the data into the subjects_??_parameters (scale values of stimuli and category boundaries) matrix of incidences, and derives both weights for the subjects and estimates of the parameters which are the most discriminative in the least squares sense. A numerical example was presented to illustrate the procedure and points of interest.
Right : A method was developed to determine values of stimuli and category boundaries through differential weighting of subjects. The method transforms the data into the subjects-by-parameters (scale values of stimuli and category boundaries) matrix of incidences, and derives both weights for the subjects and estimates of the parameters which are the most discriminative in the least squares sense. A numerical example was presented to illustrate the procedure and points of interest.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BECHTEL, G. G., TucKER, L. R., & CHANG, W. 1971 A scalar product model for the multidimentional scaling of choice. Psychometrika, 36, 369-388.
BENZÉCRI, J. P. 1969 Statistical analysis as a tool to make patterns emerge from data. In S. Watanabe (Ed.), Methodologies of pattern recognition. New York: Academic Press. Pp. 35-74.
BLOXOM, B. 1968 Individual differences in multidimensional scaling. Research Bulletin 68-45, Educational Testing Service.
BLOXOM, B. 1974 An alternative method of fitting a model of individual differences in multidimensional scaling. Psychometrika, 39, 365-367.
BOCK, R. D. 1960 Methods and applications of optimal scaling. The Psychometric Laboratory, University of North Carolina, Report No. 25.
BOCK, R. D., & JONES, L. V. 1968 The measurement and prediction of judgment and choice. San Francisco: Holden-Day.
CARROLL, J. D. 1972 Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I. Theory. New York: Seminar Press, Inc. Pp. 105-155.
CARROLL, J. D., & CHANG, J. J. 1967 Relating preference data to multidimensional solutions via a generalization of Coombs' unfolding model. Paper presented at the meeting of the Psychometric Society.
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.
DAVISON, M. L. 1976a Fitting and testing Carroll's weighted unfolding model for preferences. Psychometrika, 41, 233-247.
DAVISON, M. L. 1976b External analyses of preference models. Psychometrika, 41, 557-558.
DELEEUW, J. 1973 Canonical analysis of categorical data. Unpublished doctoral dissertation, University of Leiden, the Netherlands.
FISHER, R. A. 1948 Statistical methods for research workers. 10th ed. London: Oliver and Boyd.
GABRIEL, K. R. 1971 The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
GOLD, E. M. 1973 Metric unfolding: data requirement for unique solution and clarification of Schönemann's algorithm.
GUTTMAN, L. 1946 An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 144-163.
HARSHMAN, R. A. 1970 Foundations of the PARA-FAC procedure: Models and conditions for an exploratory multi-modal factor analysis. Unpublished thesis, University of California.
HARSHMAN, R. A. 1972 PARAFAC 2: Mathematical and technical notes. University of California at Los Angeles Working Papers in Phonetics 22.
HARSHMAN, R. A. 1976 PARAFAC: Methods of three-way factor analysis and multidimensional scaling according to the principle of proportional profiles. Dissertation Abstracts International, 37/05-B, p. 2478.
HEISER, W. 1975 Individual difference scaling. M & T 001-75, Department of Psychology, University of Leiden, the Netherlands.
HILL, M. O. 1974 Correspondence analysis: A neglected multivariate method. Applied Statistics, 23, 340-354.
HORAN, C. B. 1969 Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 34, 139-165.
HORST, P. 1935 Measuring complex attitudes. Journal of Social Psychology, 6, 369-374.
KRUSKAL, J. B. 1968 How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Murray Hill, New Jersey: Bell Laboratories.
LINGOES, J. C. 1964 Simultaneous linear regres- sion: An IBM 7090 program for analyzing metric/nonmetric or linear/nonlinear data. Behavioral Science, 9, 87-88.
LINGOES, J. C. 1970 A general nonparametric model for representing objects and attributes in a joint metric space. In J. C. Gardin (Ed.), Archiologie et calculateurs. Paris: Editions du Centre National de la Recherche Scientifique. Pp. 277-298.
MCGEE, V. E. 1968 Multidimensional scaling of N sets of similarity measures: A nonmetric individual differences approach. Multivariate Behavioral Research, 3, 233-248.
NISHISATO, S. 1975 Oyo shinri shakudoho: Shitsuteki data no bunseki to kaishaku (Applied Psychological Scaling: Analysis and Interpretation of Qualitative Data). Tokyo: Seishin Shobo Publishers, Ltd. (in Japanese).
NISHISATO, S. 1976 Optimal scaling as applied to different forms of data. Measurement and Evaluation of Categorical Data Technical Report, No. 4. Toronto: The Ontario Institute for Studies in Education.
NISHISATO, S. 1978a Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation. Psychometrika, 43, 263-271.
NISHISATO, S. 1978b Dual scaling of successive categories data. Paper presented at the annual meeting of the Psychometric Society, McMaster University, Hamilton.
NISHISATO, S. 1980 Analysis of categorical data: Dual scaling and its applications (Mathematical Expositions No. 24). Toronto: University of Toronto Press.
SCHÖNEMANN, P. H. 1970 On metric multidimensional unfolding. Psychometrika, 35, 349-366.
SCHÖNEMANN, P. H. 1972 An algebraic solution for a class of subjective metrics models. Psychometrika, 37, 441-451.
SCHÖNEMANN, P. H., & WANG, M. W. 1972 An individual differences model for the multidimensional scaling of preference data. Psychometrika, 37, 275-309.
SLATER, P. 1960 The analysis of personal preferences. British Journal of Statistical Psychology, 13, 119-135.
SRINIVASAN, V., & SHOCKER, A. D. 1973 Linear programming techniques for multidimensional analysis of preferences. Psychometrika, 38, 337-369.
TAKANE, Y., YOUNG, F. W., & DELEEUW, J. 1977 Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42,7-67.
TELL, H. 1975 Correspondence factor analysis: an outline of its method. Mathematical Geology, 7,3-12.
TORGERSON, W. S. 1958 Theory and methods of scaling. New York: Wiley.
TUCKER, L. R. 1972 Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3-27.
TUCKER, L. R., & MESSICK, S. 1963 An individual difference model for multidimensional scaling. Psychometrika, 28, 333-367.
WANG, M. M., SCHONEMANN, P. H., & RUSK, J. G. 1975 A conjugate gradient algorithm for the multidimensional analysis of preference data. Multivariate Behavioral Research, 10, 45-79.
YOUNG, F. W. 1969 Polynomial conjoint analysis of similarities: a model for constructing polynomial conjoint measurement algorithms. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No. 74.
YOUNG, F. W. 1972 A model for polynomial conjoint analysis algorithms. In R. N. Shepard, A.K. Romney, & S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I, Theory. New York: Seminar Press. Pp. 69-104.
YOUNG, F. W. 1973 Conjoint scaling. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No. 118.

Right : BECHTEL, G. G., TUCKER, L. R., &CHANG, W.1971 A scalar product model for the multidi-mentional scaling of choice. Psychometrika, 36, 369-388.
BENZÉCRI, J. P. 1969 Statistical analysis as a tool to make patterns emerge from data. In S. Watanabe (Ed.), Methodologies of pattern recognition. New York: Academic Press. Pp.35-74.
BLOXOM, B. 1968 Individual differences in multidi-mensional scaling. Research Bulletin 68-45, Educational Testing Service.
BLOXOM, B. 1974 An alternative method of fitting a model of individual differences in multidi-mensional scaling. Psychometrika, 39, 365-367.
BOCK, R. D. 1960 Methods and applications of optimal scaling. The Psychometric Laboratory, University of North Carolina, Report No.25.
BOCK, R. D., &JONES, L. V. 1968 The measurement and prediction of judgment and choice. San Francisco: Holden-Day.
CARROLL, J. D. 1972 Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in thebehavioral sciences, Vol.I. Theory. New York: Seminar Press, Inc. Pp.105-155.
CARROLL, J. D., &CHANG, J. J. 1967 Relating preference data to multidimensional solutions via a generalization of Coombs' unfolding model. Paper presented at the meeting of the Psychometric Society.
CARROLL, J. D., &CHANG, J. J. 1970 Analysisof individual differences in multidimensionalscaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 35, 283-319.
DAVISON, M. L. 1976a Fitting and testing Carroll's weighted unfolding model for preferences. Psychometrika, 41, 233-247.
DAVISON, M. L. 1976b External analyses of preference models. Psychometrika, 41, 557-558.
DELEEUW, J. 1973 Canonical analysis of categoricaldata. Unpublished doctoral dissertation, University of Leiden, the Netherlands.
FISHER, R, A. 1948 Statistical methods for research workers. 10th ed. London: Oliver and Boyd.
GABRIEL, K. R. 1971 The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
GOLD, E. M. 1973 Metric unfolding: data requirement for unique solution and clarification of Schonemann's algorithm.
GUTTMAN, L. 1946 An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 114-163.
HARSHMAN, R. A. 1970 Foundations of the PARA-FAC procedure: Models and conditions for an exploratory multi-modal factor analysis. Unpublished thesis, University of California.
HARSHMAN, R. A. 1972 PARAFAC 2: Mathematical and technical notes. University of California at Los Angeles Working Papers in Phonetics 22.
HARSHMAN, R. A. 1976 PARAFAC: Methodsof three-way factor analysis and multidimen-sional scaling according to the principle of proportional profiles. Dissertation Abstracts International, 37/05-B, p.2478.
HEISER, W. 1975 Individual difference scaling. M&T 001-75, Department of Psychology, University of Leiden, the Netherlands.
HILL, M. O. 1974 Correspondence analysis: Aneglected multivariate method. Applied Statistics, 23, 340-354.
HORAN, C. B. 1969 Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 34, 139-165.
HORST, P.1935 Measuring complex attitudes. fournal of Social psychology, 6, 369-374.
KRUSKAL, J. B. 1968 How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Murray Hill, New Jersey: Bell Laboratories.
LINGOES, J. C. 1964 Simultaneous linear regression: An IBM 7090 program for analyzing metric/nonmetric or linear/nonlinear data. Behavioral Science, 9, 87-88.
LINGOES, J. C. 1970 A general nonparametricmodel for representing objects and attributes ina joint metric space. In J. C. Gardin (Ed.), Archeologie et calculateurs. Paris: Editions du Centre National de la Recherche Scientifique.Pp.277-298.
MCGEE, V. E. 1968 Multidimensional scaling of N sets of similarity measures: A nonmetric in-dividual differences approach. Multivariate Behavioral Research, 3, 233-248.
NISHISATO, S. 1975 Oyo shinri shakudolio: Shitsuteki data no bunseki to kaishaku (Applied Psychological Scaling: Analysis and Interpretation of Qualitative Data). Tokyo: Seishin Shobo Publishers, Ltd.(in Japanese).
NISHISATO, S. 1976 Optimal scaling as appliedto different forms of data. Measurement and Evaluation of Categorical Data Technical Report, No.4. Toronto: The Ontario Institute for Studiesin Education.
NISHISATO, S. 1978a Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation. Psychometrika, 43, 263-271.
NISHISATO, S. 1978b Dual scaling of successive categories data. Paper presented at the annual meeting of the Psychometric Society, McMaster University, Hamilton.
NISHISATO, S. 1980 Analysis of categorical data: Dual scaling and its applications (Mathematical Expositions No.24). Toronto: University of Toronto Press.
SCHöNEMANN, P. H. 1970 On metric multidi-mensional unfolding. Psychometrika, 35, 349-366.
SCHöNEMANN, P. H. 1972 An algebraic solutionfor a class of subjective metrics models. Psychometrika, 37, 441-451.
SCHöNEMANN, P. H., &WANG, M. W. 1972 Anindividual differences model for the multidimen-sional scaling of preference data. Psychometrika, 37, 275-309.
SLATER, P.1960 The analysis of personal preferences. British journal of Statistical Psychology, 13, 119-135.
SRINIVASAN, V., &SHOCKER, A. D. 1973 Linear programming techniques for multidimensional analysis of preferences. Psychometrika, 38, 337-369.
TAKANE, Y., YOUNG, F. W., &DELEEUW, J. 1977 Nonmetric individual differences multidimen-sional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42, 7-67.
TEIL, H. 1975 Correspondence factor analysis: an outline of its method. Mathematical Geology, 7, 3-12.
TORGERSON, W. S. 1958 Theory and methods of scaling. New York: Wiley.
TUCKER, L. R. 1972 Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3-27.
TUCKER, L. R., &MESSICK, S. 1963 An individual difference model for multidimensional scaling. Psychometrika, 28, 333-367.
WANG, M. M., SCHONEMANN, P. H., &RUSK, J. G.1975 A conjugate gradient algorithm for the multidimensional analysis of preference data. Multivariate Behavioral Research, 10, 45-79.
YOUNG, F. W. 1969 Polynomial conjoint analysis ofsimilarities: a model for constructing polynomial con-joint measurement algorithms. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No.74.
YOUNG, F. W. 1972 A model for polynomial conjoint analysis algorithms. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidi-mensional scaling: Theory and applications in the behavioral sciences, Vol.I, Theory. New York: Seminar Press. Pp.69-104.
YOUNG, F. W. 1973 Conjoint scaling. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No.118.

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BECHTEL, G. G., TUCKER, L. R., &CHANG, W.1971 A scalar product model for the multidi-mentional scaling of choice. Psychometrika, 36, 369-388.
BENZÉCRI, J. P. 1969 Statistical analysis as a tool to make patterns emerge from data. In S. Watanabe (Ed.), Methodologies of pattern recognition. New York: Academic Press. Pp.35-74.
BLOXOM, B. 1968 Individual differences in multidi-mensional scaling. Research Bulletin 68-45, Educational Testing Service.
BLOXOM, B. 1974 An alternative method of fitting a model of individual differences in multidi-mensional scaling. Psychometrika, 39, 365-367.
BOCK, R. D. 1960 Methods and applications of optimal scaling. The Psychometric Laboratory, University of North Carolina, Report No.25.
BOCK, R. D., &JONES, L. V. 1968 The measurement and prediction of judgment and choice. San Francisco: Holden-Day.
CARROLL, J. D. 1972 Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in thebehavioral sciences, Vol.I. Theory. New York: Seminar Press, Inc. Pp.105-155.
CARROLL, J. D., &CHANG, J. J. 1967 Relating preference data to multidimensional solutions via a generalization of Coombs' unfolding model. Paper presented at the meeting of the Psychometric Society.
CARROLL, J. D., &CHANG, J. J. 1970 Analysisof individual differences in multidimensionalscaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 35, 283-319.
DAVISON, M. L. 1976a Fitting and testing Carroll's weighted unfolding model for preferences. Psychometrika, 41, 233-247.
DAVISON, M. L. 1976b External analyses of preference models. Psychometrika, 41, 557-558.
DELEEUW, J. 1973 Canonical analysis of categoricaldata. Unpublished doctoral dissertation, University of Leiden, the Netherlands.
FISHER, R, A. 1948 Statistical methods for research workers. 10th ed. London: Oliver and Boyd.
GABRIEL, K. R. 1971 The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
GOLD, E. M. 1973 Metric unfolding: data requirement for unique solution and clarification of Schonemann's algorithm.
GUTTMAN, L. 1946 An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 114-163.
HARSHMAN, R. A. 1970 Foundations of the PARA-FAC procedure: Models and conditions for an exploratory multi-modal factor analysis. Unpublished thesis, University of California.
HARSHMAN, R. A. 1972 PARAFAC 2: Mathematical and technical notes. University of California at Los Angeles Working Papers in Phonetics 22.
HARSHMAN, R. A. 1976 PARAFAC: Methodsof three-way factor analysis and multidimen-sional scaling according to the principle of proportional profiles. Dissertation Abstracts International, 37/05-B, p.2478.
HEISER, W. 1975 Individual difference scaling. M&T 001-75, Department of Psychology, University of Leiden, the Netherlands.
HILL, M. O. 1974 Correspondence analysis: Aneglected multivariate method. Applied Statistics, 23, 340-354.
HORAN, C. B. 1969 Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 34, 139-165.
HORST, P.1935 Measuring complex attitudes. fournal of Social psychology, 6, 369-374.
KRUSKAL, J. B. 1968 How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Murray Hill, New Jersey: Bell Laboratories.
LINGOES, J. C. 1964 Simultaneous linear regression: An IBM 7090 program for analyzing metric/nonmetric or linear/nonlinear data. Behavioral Science, 9, 87-88.
LINGOES, J. C. 1970 A general nonparametricmodel for representing objects and attributes ina joint metric space. In J. C. Gardin (Ed.), Archeologie et calculateurs. Paris: Editions du Centre National de la Recherche Scientifique.Pp.277-298.
MCGEE, V. E. 1968 Multidimensional scaling of N sets of similarity measures: A nonmetric in-dividual differences approach. Multivariate Behavioral Research, 3, 233-248.
NISHISATO, S. 1975 Oyo shinri shakudolio: Shitsuteki data no bunseki to kaishaku (Applied Psychological Scaling: Analysis and Interpretation of Qualitative Data). Tokyo: Seishin Shobo Publishers, Ltd.(in Japanese).
NISHISATO, S. 1976 Optimal scaling as appliedto different forms of data. Measurement and Evaluation of Categorical Data Technical Report, No.4. Toronto: The Ontario Institute for Studiesin Education.
NISHISATO, S. 1978a Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation. Psychometrika, 43, 263-271.
NISHISATO, S. 1978b Dual scaling of successive categories data. Paper presented at the annual meeting of the Psychometric Society, McMaster University, Hamilton.
NISHISATO, S. 1980 Analysis of categorical data: Dual scaling and its applications (Mathematical Expositions No.24). Toronto: University of Toronto Press.
SCHöNEMANN, P. H. 1970 On metric multidi-mensional unfolding. Psychometrika, 35, 349-366.
SCHöNEMANN, P. H. 1972 An algebraic solutionfor a class of subjective metrics models. Psychometrika, 37, 441-451.
SCHöNEMANN, P. H., &WANG, M. W. 1972 Anindividual differences model for the multidimen-sional scaling of preference data. Psychometrika, 37, 275-309.
SLATER, P.1960 The analysis of personal preferences. British journal of Statistical Psychology, 13, 119-135.
SRINIVASAN, V., &SHOCKER, A. D. 1973 Linear programming techniques for multidimensional analysis of preferences. Psychometrika, 38, 337-369.
TAKANE, Y., YOUNG, F. W., &DELEEUW, J. 1977 Nonmetric individual differences multidimen-sional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42, 7-67.
TEIL, H. 1975 Correspondence factor analysis: an outline of its method. Mathematical Geology, 7, 3-12.
TORGERSON, W. S. 1958 Theory and methods of scaling. New York: Wiley.
TUCKER, L. R. 1972 Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3-27.
TUCKER, L. R., &MESSICK, S. 1963 An individual difference model for multidimensional scaling. Psychometrika, 28, 333-367.
WANG, M. M., SCHONEMANN, P. H., &RUSK, J. G.1975 A conjugate gradient algorithm for the multidimensional analysis of preference data. Multivariate Behavioral Research, 10, 45-79.
YOUNG, F. W. 1969 Polynomial conjoint analysis ofsimilarities: a model for constructing polynomial con-joint measurement algorithms. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No.74.
YOUNG, F. W. 1972 A model for polynomial conjoint analysis algorithms. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidi-mensional scaling: Theory and applications in the behavioral sciences, Vol.I, Theory. New York: Seminar Press. Pp.69-104.
YOUNG, F. W. 1973 Conjoint scaling. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No.118.

Right : BECHTEL, G. G., TUCKER, L. R., & CHANG, W. 1971 A scalar product model for the multidimentional scaling of choice. Psychometrika, 36, 369-388.
BENZÉCRI, J. P. 1969 Statistical analysis as a tool to make patterns emerge from data. In S.Watanabe (Ed.), Methodologies of pattern recognition. New York: Academic Press. Pp.35-74.
BLOXOM, B. 1968 Individual differences in multidimensional scaling. Research Bulletin 68-45, Educational Testing Service.
BLOXOM, B. 1974 An alternative method of fitting a model of individual differences in multidimensional scaling. Psychometrika, 39, 365-367.
BOCK, R. D. 1960 Methods and applications of optimal scaling. The Psychometric Laboratory, University of North Carolina, Report No.25.
BOCK, R. D., & JONES, L. V. 1968 The measurement and prediction of judgment and choice. San Francisco: Holden-Day.
CARROLL, J. D. 1972 Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences, Vol.I. Theory. New York: Seminar Press, Inc. Pp.105-155.
CARROLL, J. D., & CHANG, J. J. 1967 Relating preference data to multidimensional solutions via a generalization of Coombs' unfolding model. Paper presented at the meeting of the Psychometric Society.
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.
DAVISON, M. L. 1976a Fitting and testing Carroll's weighted unfolding model for preferences.Psychometrika, 41, 233-247.
DAVISON, M. L. 1976b External analyses of preference models. Psychometrika, 41, 557-558.
DELEEUW, J. 1973 Canonical analysis of categoricaldata. Unpublished doctoral dissertation, University of Leiden, the Netherlands.
FISHER, R, A. 1948 Statistical methods for research workers. 10th ed. London: Oliver and Boyd.
GABRIEL, K. R. 1971 The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
GOLD, E. M. 1973 Metric unfolding: data requirement for unique solution and clarification of Schönemann's algorithm.
GUTTMAN, L. 1946 An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 144-163.
HARSHMAN, R. A. 1970 Foundations of the PARAFAC procedure: Models and conditions for an exploratory multi-modal factor analysis. Unpublished thesis, University of California.
HARSHMAN, R. A. 1972 PARAFAC 2: Mathematical and technical notes. University of California at Los Angeles Working Papers in Phonetics 22.
HARSHMAN, R. A. 1976 PARAFAC: Methods of three-way factor analysis and multidimensional scaling according to the principle of proportional profiles. Dissertation Abstracts International, 37/05-B, p.2478.
HEISER, W. 1975 Individual difference scaling. M&T 001-75, Department of Psychology, University of Leiden, the Netherlands.
HILL, M. O. 1974 Correspondence analysis: A neglected multivariate method. Applied Statistics, 23, 340-354.
HORAN, C. B. 1969 Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 34, 139-165.
HORST, P.1935 Measuring complex attitudes. Journal of Social Psychology, 6, 369-374.
KRUSKAL, J. B. 1968 How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Murray Hill, New Jersey: Bell Laboratories.
LINGOES, J. C. 1964 Simultaneous linear regression: An IBM 7090 program for analyzing metric/nonmetric or linear/nonlinear data.Behavioral Science, 9, 87-88.
LINGOES, J. C. 1970 A general nonparametric model for representing objects and attributes in a joint metric space. In J. C. Gardin (Ed.), Archéologie et calculateurs. Paris: Editions du Centre National de la Recherche Scientifique.Pp.277-298.
MCGEE, V. E. 1968 Multidimensional scaling of N sets of similarity measures: A nonmetric in-dividual differences approach. Multivariate Behavioral Research, 3, 233-248.
NISHISATO, S. 1975 Oyo shinri shakudoho: Shitsuteki data no bunseki to kaishaku (Applied Psychological Scaling: Analysis and Interpretation of Qualitative Data). Tokyo: Seishin Shobo Publishers, Ltd.(in Japanese).
NISHISATO, S. 1976 Optimal scaling as applied to different forms of data. Measurement and Evaluation of Categorical Data Technical Report, No.4. Toronto: The Ontario Institute for Studies in Education.
NISHISATO, S. 1978a Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation. Psychometrika, 43, 263-271.
NISHISATO, S. 1978b Dual scaling of successive categories data. Paper presented at the annual meeting of the Psychometric Society, McMaster University, Hamilton.
NISHISATO, S. 1980 Analysis of categorical data: Dual scaling and its applications (Mathematical Expositions No.24). Toronto: University of Toronto Press.
SCHöNEMANN, P. H. 1970 On metric multidimensional unfolding. Psychometrika, 35, 349-366.
SCHöNEMANN, P. H. 1972 An algebraic solution for a class of subjective metrics models. Psychometrika, 37, 441-451.
SCHöNEMANN, P. H., & WANG, M. W. 1972 An individual differences model for the multidimensional scaling of preference data. Psychometrika, 37, 275-309.
SLATER, P. 1960 The analysis of personal preferences. British journal of Statistical Psychology, 13, 119-135.
SRINIVASAN, V., & SHOCKER, A. D. 1973 Linear programming techniques for multidimensional analysis of preferences. Psychometrika, 38, 337-369.
TAKANE, Y., YOUNG, F. W., & DELEEUW, J. 1977 Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42, 7-67.
TEIL, H. 1975 Correspondence factor analysis: an outline of its method. Mathematical Geology, 7, 3-12.
TORGERSON, W. S. 1958 Theory and methods of scaling. New York: Wiley.
TUCKER, L. R. 1972 Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3-27.
TUCKER, L. R., & MESSICK, S. 1963 An individual difference model for multidimensional scaling. Psychometrika, 28, 333-367.
WANG, M. M., SCHö NEMANN, P. H., &RUSK, J. G.1975 A conjugate gradient algorithm for the multidimensional analysis of preference data.Multivariate Behavioral Research, 10, 45-79.
YOUNG, F. W. 1969 Polynomial conjoint analysis of similarities: a model for constructing polynomial conjoint measurement algorithms. The L. L. Thurstone Psychometric Laboratory, University of North Carolina, Report No.74.
YOUNG, F. W. 1972 A model for polynomial conjoint analysis algorithms. In R. N. Shepard, A. K. Romney, &S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences, Vol.I, Theory. New York: Seminar Press. Pp.69-104.
YOUNG, F. W. 1973 Conjoint scaling. The L. L.Thurstone Psychometric Laboratory, University of North Carolina, Report No.118.