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The dimensionality of discrete factor analyses

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  • John Levi Martin

    (University of Chicago)

Abstract

This article discusses a solution to Coombs’s project of a discrete, ordinal factor analysis for dichotomous data that is structurally homologous to Galois lattice analysis and to other related algebraic approaches. It compares this approach to the better known “biorder” approach to the same problem. In contrast to the biorder approach which is NP-hard, here the set of minimal solutions can be determined with a reasonably simple coloration algorithm. The dimensionality of the resulting solution may be larger than that retrieved by the closely related biorder approach, but the underlying space may be more parsimonious in that there are fewer possible regions. In a class of reasonably important cases, the two are equivalent.

Suggested Citation

  • John Levi Martin, 2016. "The dimensionality of discrete factor analyses," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(6), pages 2451-2467, November.
    • Handle: RePEc:spr:qualqt:v:50:y:2016:i:6:d:10.1007_s11135-015-0271-4
    DOI: 10.1007/s11135-015-0271-4
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    References listed on IDEAS

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    1. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
    2. Doignon, Jean-Paul & Falmagne, Jean-Claude, 1984. "Matching relations and the dimensional structure of social choices," Mathematical Social Sciences, Elsevier, vol. 7(3), pages 211-229, June.
    3. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
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