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Multidimensional Association Models

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  • RAYMOND SIN-KWOK WONG

    (University of California, Santa Barbara)

Abstract

This article develops several multidimensional multilinear association models for sociologists and other social science researchers to analyze the relationship between categorical variables in multiway cross-classification tables. The proposed multilinear approach not only provides satisfactory fit by conventional standards in the illustrative examples but also offers better understanding of the complex relationship between variables. This study highlights the relationship between two alternative decompositions in the multilinear framework—the PARAFAC/CANDECOMP and the Tucker 3-mode methods to decompose log-linear parameters—as well as the relationship between the multilinear approach and the log-multiplicative association models developed by Goodman and others. In addition, the author discusses empirical strategies to determine whether some or all cross-dimensional and other identifying restrictions can be relaxed in certain restricted models and to account for the proper degrees of freedom for these models.

Suggested Citation

  • Raymond Sin-Kwok Wong, 2001. "Multidimensional Association Models," Sociological Methods & Research, , vol. 30(2), pages 197-240, November.
    • Handle: RePEc:sae:somere:v:30:y:2001:i:2:p:197-240
    DOI: 10.1177/0049124101030002003
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    References listed on IDEAS

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    1. Becker, Mark P., 1992. "Exploratory analysis of association models using loglinear models and singular value decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 13(3), pages 253-267, April.
    2. Carolyn Anderson, 1996. "The analysis of three-way contingency tables by three-mode association models," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 465-483, September.
    3. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    4. Vartan Choulakian, 1996. "Generalized bilinear models," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 271-283, June.
    5. Mark P. Becker, 1990. "Maximum Likelihood Estimation of the RC(M) Association Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(1), pages 152-167, March.
    6. Henk Kiers & Jos Berge & Roberto Rocci, 1997. "Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 349-374, September.
    7. Siciliano, Roberta & Mooijaart, Ab, 1997. "Three-factor association models for three-way contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 337-356, May.
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    Cited by:

    1. Mark de Rooij, 2008. "The analysis of change, Newton's law of gravity and association models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 137-157, January.

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