A maximum likelihood method for additive clustering and its applications

HIROSHI HOJO

doi:10.4992/psycholres1954.25.191

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Keywords: scaling, maximum likelihood estimation, representation of similarity, additive clustering, extraction of features

JOURNAL FREE ACCESS

1983 Volume 25 Issue 4 Pages 191-201

DOI https://doi.org/10.4992/psycholres1954.25.191

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Published: March 01, 1984 Received: April 13, 1983 Available on J-STAGE: February 24, 2009 Accepted: November 19, 1983 Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : We present a maximum likelihood estimation procedure for Shepard Arabic ADCLUS (for “ADditive CLUStering”) model. The major advantages of our maximum likelihood ADCLUS (MLADCLUS) over theirs are two: (1) that MLADCLUS is capable of permitting hypothesis testing; (2) that MLADCLUS distinguishes and incorporates three types of models, “the representation model, ” “the error model, ” and “the response model, ” which are necessary for any reasonable psychological scaling. Applications of MLADCLUS to two different types of data gave the following results: (a) A solution with 13 semantic features such as “divide something three-dimensional into parts by force so as to cause damage, ” “cut something non-rigid into pieces by force, ” and “sever continuity” can give a good account of pair comparisons data of seven Japanese ‘break’ verbs. (b) An 8-cluster solution including such clusters as {P, R}, {F, P}, and {C, G} appears to best describe the structure of confusion matrix among six letters C, E, F, G, P, and R. (c) Both of these verbs and letters are better represented by the additive clustering model than by multidimensional scaling model.
Right : We present a maximum likelihood estimation procedure for Shepard-Arabie ADCLUS (for “A Dditive CLU Stering”) model. The major advantages of our maximum likelihood ADCLUS (MLADCLUS) over theirs are two: (1) that MLADCLUS is capable of permitting hypothesis testing; (2) that MLADCLUS distinguishes and incorporates three types of models, “the representation model, ” “the error model, ” and “the response model, ” which are necessary for any reasonable psychological scaling. Applications of MLADCLUS to two different types of data gave the following results: (a) A solution with 13 semantic features such as “divide something three-dimensional into parts by force so as to cause damage, ” “cut something non-rigid into pieces by force, ” and “sever continuity” can give a good account of pair comparisons data of seven Japanese ‘break’ verbs. (b) An 8-cluster solution including such clusters as {P, R}, {F, P}, and {C, G} appears to best describe the structure of confusion matrix among six letters C, E, F, G, P, and R. (c) Both of these verbs and letters are better represented by the additive clustering model than by multidimensional scaling model.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Arabie, P., & Carroll, J. D. 1980 MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. Psychometrika, 45, 211-235.
Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Hojo, H. 1982 Confusion-choice model for multidimensional scaling: Modification of Nakatani's model. Japanese Psychological Research, 24, 211-215.
Kruskal, J. B., & Wish, M. 1978 Multidimensional scaling. Beverly Hills, Calif.: Sage Publications.
Kunihiro, T. 1970 Aspects of meaning. Sanseido. (In Japanese)
Nakatani, L. H. 1972 Confusion-choice model for multidimensional psychophysics. Journal of Mathematical Psychology, 9, 104-127.
Pruzansky, S., Tversky, A., & Carroll, J. D. 1982 Spatial versus tree representations of proximity data. Psychometrika, 47, 3-19.
Ramsay, J. O. 1980 Some small sample results for maximum likelihood estimation in multidimensional scaling. Psychometrika, 45, 139-144.
Shepard, R. N., & Arabie, P. 1979 Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87-123.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory. Japanese Psychological Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y. 1982 The method of triadic combinations: A new treatment and its application. Behariormetrika, 11, 37-48.
Takane, Y., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 46, 389-405.
Tone, K. 1981 BASIC. (Microcomputer programs series 1) Baifukan. (In Japanese)
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.

Right : Arabic, P., & Carroll, J. D. 1980 MAPCLUS: A mathematical programming approach to fitting the ADCLUS model.Psychomelrika, 45, 211-235.
Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Hojo, H. 1982 Confusion-choice model for multidimensional scaling: Modification of Nakatani's model. Japanese Psychological Research, 24, 211-215.
Kruskai, J. B., & Wish, M. 1978 Multidimensional scaling. Beverly Hills, Calif.: Sage Publications. Kunihiro, T. 1970 Aspects of meaning. Sanseido.(In Japanese)
Nakatani, L. H. 1972 Confusion-choice model for multidimensional psychophysics. Journal of Mathematical Psychology, 9, 104-127.
Pruzansky, S., Tversky, A., & Carroll, J. D. 1982 Spatial versus tree representations of proximity data. Psychomelrika, 47, 3-19.
Ramsay, J. O. 1980 Some small sample results for maximum likelihood estimation in multidimensional scaling.Psychometrika, 45, 139-144.
Shepard, R. N., & Arabic, P. 1979 Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87-123.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory.Japanese Psychological Research, 20, 7-l7.
Takane, V. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, V. 1982 The method of triadic combinations: A new treatment and its application. Beharionnetrika, 11, 37-48.
Takane, V., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychoenetrika, 46, 389-405.
Tone, K. 1981 BASIC.(Microcomputer programs series 1) Baifukan.(In Japanese)
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.

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

Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : We present a maximum likelihood estimation procedure for Shepard-Arabie ADCLUS (for “A Dditive CLU Stering”) model. The major advantages of our maximum likelihood ADCLUS (MLADCLUS) over theirs are two: (1) that MLADCLUS is capable of permitting hypothesis testing; (2) that MLADCLUS distinguishes and incorporates three types of models, “the representation model, ” “the error model, ” and “the response model, ” which are necessary for any reasonable psychological scaling. Applications of MLADCLUS to two different types of data gave the following results: (a) A solution with 13 semantic features such as “divide something three-dimensional into parts by force so as to cause damage, ” “cut something non-rigid into pieces by force, ” and “sever continuity” can give a good account of pair comparisons data of seven Japanese ‘break’ verbs. (b) An 8-cluster solution including such clusters as {P, R}, {F, P}, and {C, G} appears to best describe the structure of confusion matrix among six letters C, E, F, G, P, and R. (c) Both of these verbs and letters are better represented by the additive clustering model than by multidimensional scaling model.
Right : We present a maximum likelihood estimation procedure for Shepard-Arabie ADCLUS (for “ADditive CLUStering”) model. The major advantages of our maximum likelihood ADCLUS (MLADCLUS) over theirs are two: (1) that MLADCLUS is capable of permitting hypothesis testing;(2) that MLADCLUS distinguishes and incorporates three types of models, “the representation model, ” “the error model, ” and “the response model, ” which are necessary for any reasonable psychological scaling. Applications of MLADCLUS to two different types of data gave the following results: (a) A solution with 13 semantic features such as “divide something three-dimensional into parts by force so as to cause damage, ” “cut something non-rigid into pieces by force, ” and “sever continuity” can give a good account of pair comparisons data of seven Japanese ‘break’ verbs.(b) An 8-cluster solution including such clusters as {P, R}, {F, P}, and {C, G} appears to best describe the structure of confusion matrix among six letters C, E, F, G, P, and R.(c) Both of these verbs and letters are better represented by the additive clustering model than by multidimensional scaling model.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Arabic, P., & Carroll, J. D. 1980 MAPCLUS: A mathematical programming approach to fitting the ADCLUS model.Psychomelrika, 45, 211-235.
Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Hojo, H. 1982 Confusion-choice model for multidimensional scaling: Modification of Nakatani's model. Japanese Psychological Research, 24, 211-215.
Kruskai, J. B., & Wish, M. 1978 Multidimensional scaling. Beverly Hills, Calif.: Sage Publications. Kunihiro, T. 1970 Aspects of meaning. Sanseido.(In Japanese)
Nakatani, L. H. 1972 Confusion-choice model for multidimensional psychophysics. Journal of Mathematical Psychology, 9, 104-127.
Pruzansky, S., Tversky, A., & Carroll, J. D. 1982 Spatial versus tree representations of proximity data. Psychomelrika, 47, 3-19.
Ramsay, J. O. 1980 Some small sample results for maximum likelihood estimation in multidimensional scaling.Psychometrika, 45, 139-144.
Shepard, R. N., & Arabic, P. 1979 Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87-123.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory.Japanese Psychological Research, 20, 7-l7.
Takane, V. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, V. 1982 The method of triadic combinations: A new treatment and its application. Beharionnetrika, 11, 37-48.
Takane, V., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychoenetrika, 46, 389-405.
Tone, K. 1981 BASIC.(Microcomputer programs series 1) Baifukan.(In Japanese)
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.

Right : Arabic, P., & Carroll, J. D. 1980 MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. Psychometrika, 45, 211-235.
Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Hojo, H. 1982 Confusion-choice model for multidimensional scaling: Modification of Nakatani's model. Japanese Psychological Research, 24, 211-215.
Kruskal, J. B., & Wish, M. 1978 Multidimensional scaling. Beverly Hills, Calif.: Sage Publications.
Kunihiro, T. 1970 Aspects of meaning. Sanseido.(In Japanese)
Nakatani, L. H. 1972 Confusion-choice model for multidimensional psychophysics. Journal of Mathematical Psychology, 9, 104-127.
Pruzansky, S., Tversky, A., & Carroll, J. D. 1982 Spatial versus tree representations of proximity data. Psychometrika, 47, 3-19.
Ramsay, J. O. 1980 Some small sample results for maximum likelihood estimation in multidimensional scaling. Psychometrika, 45, 139-144.
Shepard, R. N., & Arabie, P.1979 Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87-123.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory. Japanese Psychological Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y. 1982 The method of triadic combinations: A new treatment and its application. Behaviormetrika, 11, 37-48.
Takane, Y., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 46, 389-405.
Tone, K. 1981 BASIC.(Microcomputer programs series 1) Baifukan.(In Japanese)
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.

Abstract

We present a maximum likelihood estimation procedure for Shepard-Arabie ADCLUS (for “ADditive CLUStering”) model. The major advantages of our maximum likelihood ADCLUS (MLADCLUS) over theirs are two: (1) that MLADCLUS is capable of permitting hypothesis testing;(2) that MLADCLUS distinguishes and incorporates three types of models, “the representation model, ” “the error model, ” and “the response model, ” which are necessary for any reasonable psychological scaling. Applications of MLADCLUS to two different types of data gave the following results: (a) A solution with 13 semantic features such as “divide something three-dimensional into parts by force so as to cause damage, ” “cut something non-rigid into pieces by force, ” and “sever continuity” can give a good account of pair comparisons data of seven Japanese ‘break’ verbs.(b) An 8-cluster solution including such clusters as {P, R}, {F, P}, and {C, G} appears to best describe the structure of confusion matrix among six letters C, E, F, G, P, and R.(c) Both of these verbs and letters are better represented by the additive clustering model than by multidimensional scaling model.

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