DOI: 10.1007/bf02289726. On a Connection Between Factor Analysis and Multidimensional Unfolding

On a Connection Between Factor Analysis and Multidimensional Unfolding

10.1007/bf02289726

Crossref journal-article

Cambridge University Press (CUP)

Psychometrika (56)

Abstract

Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space of r dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space of r + 1 dimensions with the original r-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.

Bibliography

Coombs, C. H., & Kao, R. C. (1960). On a Connection Between Factor Analysis and Multidimensional Unfolding. Psychometrika, 25(3), 219â231.

Authors 2

Clyde H. Coombs (first)
Richard C. Kao (additional)

References 15 Referenced 70

{'volume-title': 'A theory of psychological scaling', 'year': '1952', 'author': 'Coombs', 'key': 'S0033312300043453_CR8'} / A theory of psychological scaling by Coombs (1952)
10.1111/j.2044-8317.1951.tb00299.x
10.21236/AD0047524
{'volume-title': 'An introduction to multivariate statistical analysis', 'year': '1958', 'author': 'Anderson', 'key': 'S0033312300043453_CR1'} / An introduction to multivariate statistical analysis by Anderson (1958)
{'key': 'S0033312300043453_CR3', 'first-page': '337', 'article-title': 'The effect of standardization on aχ2-approximation in factor analysis', 'volume': '38', 'author': 'Bartlett', 'year': '1951', 'journal-title': 'Biometrika'} / Biometrika / The effect of standardization on aχ2-approximation in factor analysis by Bartlett (1951)
{'key': 'S0033312300043453_CR5', 'first-page': '23', 'volume-title': 'Uppsala symposium on psychological factor analysis', 'author': 'Bartlett', 'year': '1953'} / Uppsala symposium on psychological factor analysis by Bartlett (1953)
[11] Hays, W. L. and Bennett, J. F. Multidimensional unfolding: determining configuration from complete rank order preference data. Psychometrika. (in press).
10.1037/h0060984
10.1111/j.2044-8317.1950.tb00285.x
10.3406/rfsp.1958.392454
10.1111/j.2517-6161.1950.tb00042.x
{'key': 'S0033312300043453_CR9', 'first-page': '69', 'volume-title': 'Decision processes', 'author': 'Coombs', 'year': '1954'} / Decision processes by Coombs (1954)
{'volume-title': 'A million random digits with 100,000 normal deviates', 'year': '1955', 'key': 'S0033312300043453_CR14'} / A million random digits with 100,000 normal deviates (1955)
10.1007/BF02288932
10.1037/h0044694

Dates

Type	When
Created	19 years, 7 months ago (Jan. 25, 2006, 12:58 p.m.)
Deposited	5 months ago (April 2, 2025, 11:47 p.m.)
Indexed	4 weeks ago (Aug. 7, 2025, 4:58 p.m.)
Issued	65 years ago (Sept. 1, 1960)
Published	65 years ago (Sept. 1, 1960)
Published Online	8 months ago (Jan. 1, 2025)
Published Print	65 years ago (Sept. 1, 1960)

Funders 0

None

BibTeX

@article{Coombs_1960, title={On a Connection Between Factor Analysis and Multidimensional Unfolding}, volume={25}, ISSN={1860-0980}, url={http://dx.doi.org/10.1007/bf02289726}, DOI={10.1007/bf02289726}, number={3}, journal={Psychometrika}, publisher={Cambridge University Press (CUP)}, author={Coombs, Clyde H. and Kao, Richard C.}, year={1960}, month=sep, pages={219–231} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        7
      ]
    ],
    "date-time": "2025-08-07T20:58:21Z",
    "timestamp": 1754600301983,
    "version": "3.40.3"
  },
  "reference-count": 15,
  "publisher": "Cambridge University Press (CUP)",
  "issue": "3",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2025,
            1,
            1
          ]
        ],
        "date-time": "2025-01-01T00:00:00Z",
        "timestamp": 1735689600000
      },
      "content-version": "unspecified",
      "delay-in-days": 23498,
      "URL": "https://www.cambridge.org/core/terms"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1960,
        9
      ]
    ]
  },
  "abstract": "<jats:p>Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space of <jats:italic>r</jats:italic> dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space of <jats:italic>r</jats:italic> + 1 dimensions with the original <jats:italic>r</jats:italic>-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.</jats:p>",
  "DOI": "10.1007/bf02289726",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        1,
        25
      ]
    ],
    "date-time": "2006-01-25T17:58:15Z",
    "timestamp": 1138211895000
  },
  "page": "219-231",
  "source": "Crossref",
  "is-referenced-by-count": 70,
  "title": "On a Connection Between Factor Analysis and Multidimensional Unfolding",
  "prefix": "10.1017",
  "volume": "25",
  "author": [
    {
      "given": "Clyde H.",
      "family": "Coombs",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Richard C.",
      "family": "Kao",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "56",
  "published-online": {
    "date-parts": [
      [
        2025,
        1,
        1
      ]
    ]
  },
  "reference": [
    {
      "volume-title": "A theory of psychological scaling",
      "year": "1952",
      "author": "Coombs",
      "key": "S0033312300043453_CR8"
    },
    {
      "key": "S0033312300043453_CR4",
      "doi-asserted-by": "publisher",
      "DOI": "10.1111/j.2044-8317.1951.tb00299.x"
    },
    {
      "key": "S0033312300043453_CR15",
      "doi-asserted-by": "publisher",
      "DOI": "10.21236/AD0047524"
    },
    {
      "volume-title": "An introduction to multivariate statistical analysis",
      "year": "1958",
      "author": "Anderson",
      "key": "S0033312300043453_CR1"
    },
    {
      "key": "S0033312300043453_CR3",
      "first-page": "337",
      "article-title": "The effect of standardization on a\u03c72-approximation in factor analysis",
      "volume": "38",
      "author": "Bartlett",
      "year": "1951",
      "journal-title": "Biometrika"
    },
    {
      "key": "S0033312300043453_CR5",
      "first-page": "23",
      "volume-title": "Uppsala symposium on psychological factor analysis",
      "author": "Bartlett",
      "year": "1953"
    },
    {
      "key": "S0033312300043453_CR11",
      "unstructured": "[11] Hays, W. L. and Bennett, J. F. Multidimensional unfolding: determining configuration from complete rank order preference data. Psychometrika. (in press)."
    },
    {
      "key": "S0033312300043453_CR7",
      "doi-asserted-by": "publisher",
      "DOI": "10.1037/h0060984"
    },
    {
      "key": "S0033312300043453_CR2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1111/j.2044-8317.1950.tb00285.x"
    },
    {
      "key": "S0033312300043453_CR13",
      "doi-asserted-by": "publisher",
      "DOI": "10.3406/rfsp.1958.392454"
    },
    {
      "key": "S0033312300043453_CR12",
      "doi-asserted-by": "publisher",
      "DOI": "10.1111/j.2517-6161.1950.tb00042.x"
    },
    {
      "key": "S0033312300043453_CR9",
      "first-page": "69",
      "volume-title": "Decision processes",
      "author": "Coombs",
      "year": "1954"
    },
    {
      "volume-title": "A million random digits with 100,000 normal deviates",
      "year": "1955",
      "key": "S0033312300043453_CR14"
    },
    {
      "key": "S0033312300043453_CR6",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF02288932"
    },
    {
      "key": "S0033312300043453_CR10",
      "doi-asserted-by": "publisher",
      "DOI": "10.1037/h0044694"
    }
  ],
  "container-title": "Psychometrika",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF02289726.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF02289726/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033312300043453",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2025,
        4,
        3
      ]
    ],
    "date-time": "2025-04-03T03:47:25Z",
    "timestamp": 1743652045000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.cambridge.org/core/product/identifier/S0033312300043453/type/journal_article"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1960,
        9
      ]
    ]
  },
  "references-count": 15,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1960,
          9
        ]
      ]
    }
  },
  "alternative-id": [
    "S0033312300043453"
  ],
  "URL": "http://dx.doi.org/10.1007/BF02289726",
  "relation": {},
  "ISSN": [
    "0033-3123",
    "1860-0980"
  ],
  "subject": [],
  "container-title-short": "Psychometrika",
  "published": {
    "date-parts": [
      [
        1960,
        9
      ]
    ]
  }
}