A Formulation of the Latent Class Vector Model for Pairwise Data
In this research, a latent class vector model for pairwise data is formulated. As compared to the basic vector model, this model yields consistent estimates of the parameters since the number of parameters to be estimated does not increase with the number of subjects. The result of the analysis reveals that the model was stable and could classify each subject to the latent classes representing the typical scales used by these subjects.
[1] J. Arbuckle and J. H. Nugent, "A general procedure for parameter
estimation for the law of comparative judgement," British Journal of
Mathematical and Statistical Psychology, vol. 26, 1973, pp. 240-260.
[2] P. Slater, "The analysis of personal preferences," British Journal of
Statistical Psychology, 13, 1960, pp. 119-135.
[3] L. R. Tucker, "Intra-individual and Inter-individual multidimensionality",
in Psychological scaling: Theory and Applications, H. Gulliksen, and S.
Messick Eds, New York: Wiley, 1960, pp. 155-167.
[4] J. F. Bennett and W. L. Hays, "Multidimensional unfolding: determining
the dimensionality of ranked preference data," Psychometrika, vol. 25,
1960, pp. 27-43.
[5] J. D. Carroll, Individual differences and multidimensional scaling. in
Multidimensional scaling, R. N. Shepard, A. K. Romney, and S. B.
Nerlove Eds, New York: Seminar Press, 1972, pp. 105-155.
[6] Y. Takane, "Maximum likelihood estimation in the generalized case of
Thurstone's model of comparativejudgment," Japanese Psychological
Research, 22, 1980, pp. 188-196.
[7] Y. Takane, "Analysis of covariance structures and probabilistic binary
choice data," in New developments in psychological choice modeling
advances in psychology, G. DeSoete, H. Feger, and K. C. Klauer Eds,
Amsterdam: Elsevier Science Ltd, 1989, pp. 139-160.
[8] Y. Takane, "Choice model analysis of the ``pick any/n'' type of binary
data," Japanese Psychological Research, 40, 1998, pp. 31-39.
[9] U. Böckenholt, and I. Böckenholt, "Constrained latent class analysis:
Simultaneous classification and scaling of discrete choice data,"
Psychometrika, 56, 1991, pp. 699-716.
[10] L. A. Goodman, "Exploratory latent structure analysis using both
identifiable and unidentifiable models," Biometrika, 61, 1974, pp.
215-231.
[11] P. F. Lazarsfeld, and N. W. Henry, Latent structure analysis. Boston:
Houghton Mifflin Company, 1968.
[12] A. P. Dempster, N. M. Laired, and D. B. Rubin, "Maximum likelihood
from incomplete sata via the EM algorithm," Journal of Royal Statistical
Society, Series B, 39, 1977, pp. 1-38.
[13] G. DeSoete, and S. Winsberg, "A latent class vector model for preference
ratings," Journal of Classification, 10, 1993, pp. 195-218.
[14] U. Böckenholt, "A Thurstonian analysis of preference change," Journal of
Mathematical Psychology, 46, 2002, pp. 300-314.
[1] J. Arbuckle and J. H. Nugent, "A general procedure for parameter
estimation for the law of comparative judgement," British Journal of
Mathematical and Statistical Psychology, vol. 26, 1973, pp. 240-260.
[2] P. Slater, "The analysis of personal preferences," British Journal of
Statistical Psychology, 13, 1960, pp. 119-135.
[3] L. R. Tucker, "Intra-individual and Inter-individual multidimensionality",
in Psychological scaling: Theory and Applications, H. Gulliksen, and S.
Messick Eds, New York: Wiley, 1960, pp. 155-167.
[4] J. F. Bennett and W. L. Hays, "Multidimensional unfolding: determining
the dimensionality of ranked preference data," Psychometrika, vol. 25,
1960, pp. 27-43.
[5] J. D. Carroll, Individual differences and multidimensional scaling. in
Multidimensional scaling, R. N. Shepard, A. K. Romney, and S. B.
Nerlove Eds, New York: Seminar Press, 1972, pp. 105-155.
[6] Y. Takane, "Maximum likelihood estimation in the generalized case of
Thurstone's model of comparativejudgment," Japanese Psychological
Research, 22, 1980, pp. 188-196.
[7] Y. Takane, "Analysis of covariance structures and probabilistic binary
choice data," in New developments in psychological choice modeling
advances in psychology, G. DeSoete, H. Feger, and K. C. Klauer Eds,
Amsterdam: Elsevier Science Ltd, 1989, pp. 139-160.
[8] Y. Takane, "Choice model analysis of the ``pick any/n'' type of binary
data," Japanese Psychological Research, 40, 1998, pp. 31-39.
[9] U. Böckenholt, and I. Böckenholt, "Constrained latent class analysis:
Simultaneous classification and scaling of discrete choice data,"
Psychometrika, 56, 1991, pp. 699-716.
[10] L. A. Goodman, "Exploratory latent structure analysis using both
identifiable and unidentifiable models," Biometrika, 61, 1974, pp.
215-231.
[11] P. F. Lazarsfeld, and N. W. Henry, Latent structure analysis. Boston:
Houghton Mifflin Company, 1968.
[12] A. P. Dempster, N. M. Laired, and D. B. Rubin, "Maximum likelihood
from incomplete sata via the EM algorithm," Journal of Royal Statistical
Society, Series B, 39, 1977, pp. 1-38.
[13] G. DeSoete, and S. Winsberg, "A latent class vector model for preference
ratings," Journal of Classification, 10, 1993, pp. 195-218.
[14] U. Böckenholt, "A Thurstonian analysis of preference change," Journal of
Mathematical Psychology, 46, 2002, pp. 300-314.
@article{"International Journal of Information, Control and Computer Sciences:58103", author = "Tomoya Okubo and Kuninori Nakamura and Shin-ichi Mayekawa", title = "A Formulation of the Latent Class Vector Model for Pairwise Data", abstract = "In this research, a latent class vector model for pairwise data is formulated. As compared to the basic vector model, this model yields consistent estimates of the parameters since the number of parameters to be estimated does not increase with the number of subjects. The result of the analysis reveals that the model was stable and could classify each subject to the latent classes representing the typical scales used by these subjects.
", keywords = "finite mixture models, latent class analysis,Thrustone's paired comparison method, vector model", volume = "3", number = "6", pages = "1577-4", }
