Loglinear, Association and Quasi-symmetry Models

Loglinear, association and quasi-symmetry models are related in many respects. These are important options for the analysis of some kinds of agreement data. For a thorough discussion of these methods the reader is referred to the primary references listed below. A good place to begin is Barlow (1998).

A few general comments can be made as follows:

  • These models are better developed for analysis of agreement among two raters (i.e., data summarized as a two-way table), than for agreement among more than two raters.

  • Here, the term "loglinear model" refers only to basic loglinear models such as described by Tanner and Young (1983a, b). Technically, both association models and quasi-symmetry models are special cases of loglinear modeling.

  • Of the three approaches, the quasi-symmetry model has the best theoretical basis. The parameters of the quasi-symmetry model can be understood as corresponding to actual characteristics of raters and rated objects. This is somewhat less true of loglinear and association models.

  • Many of these models can be estimated with SAS PROC CATMOD and with the LEM program.



    Agresti A. Modelling patterns of agreement and disagreement. Statistical Methods in Medical Research, 1992, 1(2), 201-218.

    Barlow W. Modeling of categorical agreement. In: Armitage P, Colton T (eds), The encyclopedia of biostatistics (pp. 541-545). New York: Wiley, 1998.

    Uebersax JS. A review of modeling approaches for the analysis of observer agreement. Investigative Radiology, 1992, 27, 738-743.

Loglinear Models

Begin with the two Tanner & Young papers. The other citations are general works on loglinear modeling.

    Bishop YMM, Fienberg SE, Holland PW. Discrete multivariate analysis: theory and practice. Cambridge, Mass.: MIT Press, 1975

    Fienberg SE The analysis of cross-classified categorical data. Cambridge, Mass.: MIT Press, 1977.

    Haberman SJ. Qualitative data analysis (Vols. 1 & 2). New York: Academic Press, 1979.

    Tanner MA, Young MA. Modelling agreement among raters. Journal of the American Statistical Association, 1985a, 80, 175-180.

    Tanner MA, Young MA. Modeling ordinal scale disagreement. Psychological Bulletin, , 1985b, 98, 408-415.

Quasi-symmetry Models

Begin with Darroch & McCloud, 1986.

    Agresti A, Lang JB. Quasi-symmetric latent class models, with application to rater agreement. Biometrics, 1993, 49, 131-139.

    Becker MP. Quasisymmetric models for the analysis of square contingency tables. Journal of the Royal Statistical Society Ser. B (Applied Statistics), 1990, 52, 369-378.

    Darroch JN, McCloud PI. Category distinguishability and observer agreement. Australian Journal of Statistics, 1986, 28, 371-388.

    Darroch JN, McCloud PI. Quasisymmetry models of observer agreement. [Reference incomplete--1991?]

Association Models

    Agresti A. Categorical data analysis. New York: Wiley, 1990.

    Agresti A. Analysis of ordinal categorical data. New York: Wiley, 1984.

    Agresti A. A model for agreement between ratings on an ordinal scale, Biometrics, 1988, 44, 539-548.

    Becker MP. Using association models to analyse agreement data: two examples. Statistics in Medicine, 1989, 8, 1199-1207.

    Becker MP, Agresti A. Log-linear modelling of pairwise interobserver agreement on a categorical scale. Statistics In Medicine, 1992, 11(1), 101-114.

    Goodman LA. Simple models for the analysis of association in cross-classifications having ordered categories. Journal of the American Statistical Association, 1979, 74, 537-551.

    Goodman LA. Measures, models, and graphical displays in the analysis of cross-classified data (with discussion). Journal of the American Statistical Association, 1991, 86, 1085-1111.

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Revised: 21 September 2000

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