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An Application of the Mixed Effects Trend Vector Models to the Analysis of Asymmetric Square Contingency Tables with Auxiliary Variables

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Abstract

We propose to use the mixed effect trend vector model for modeling of repeated multinomial choice data in the form of a square contingency table. Such data often shows asymmetries where more people change from category a to b than the other way around. In many cases an investigator has, besides the actual choices of the participants, auxiliary variables that pertain to the subjects under study. Most methodologies for asymmetric data do not take into account such variables. We will show how to incorporate these auxiliary variables into the mixed effects trend vector model and how they can be used to study differential change. The models are illustrated in detail with data from the Dutch parliamentary election studies 2006.

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References

  • Constantine, A.G. and Gower, J.C. (1978). Graphical representation ol asymmetric matrices, Journal of the Royal Statistical Society, series C, 27, 297–304.

    MATH  Google Scholar 

  • De Rooij, M. (2009a). Ideal point discriminant analysis revisited with an emphasis on visualization. Psychometrika, 74 317–330.

    Article  MathSciNet  Google Scholar 

  • De Rooij, M. (2009b). Trend vector models for the analysis of change in continuous time for multiple groups. Computational Statistics and Data Analysis, 53, 3209–3216.

    Article  MathSciNet  Google Scholar 

  • De Rooij, M. and Schouteden, M. (2011). The mixed effects trend vector model. Submitted paper.

    Google Scholar 

  • De Rooij, M. and Heiser, W.J. (2000). Triadic distance models for the analysis of asymmetric three-way proximity data. British Journal of Mathematical and Statistical Psychology, 53, 99–119.

    Article  MathSciNet  Google Scholar 

  • Gower, J.C. (1977). The analysis of asymmetry and orthogonality. In: BArra, J.R., Brodeau, F., Romer, G., and Van Cutsen, B. (Eds.) Recent developments in statistics, pp.109–223. Amsterdam: North-Holland.

    Google Scholar 

  • Gower, J. C. and Hand, D. J (1996). Biplots. London: Chapman and Hall.

    MATH  Google Scholar 

  • Liang, K-Y. and Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models, Biometrika, 73, 13–22.

    Article  MathSciNet  Google Scholar 

  • Molenberghs, G. and Verbeke, G. (2005). Models for discrete longitudinal data. Springer: New York.

    MATH  Google Scholar 

  • Okada, A. and Imaizumi, T. (1997). Asymmetric multidimensional scaling of two-mode three-way proximities. Journal of Classification, 14, 195–224.

    Article  Google Scholar 

  • Pennings, P. and Keman, H. (2003). The Dutch parliamentary election studies in 2002 and 2003: The rise and decline of the Fortuyn movement. Acta Politica, 38, 51–68.

    Article  Google Scholar 

  • Takane, Y., Bozdogan, H., and Shibayama, T. (1987). Ideal point discriminant analysis. Psychometrika, 52 371–392.

    Article  MathSciNet  Google Scholar 

  • Van Holsteyn, J. J. M. and Irwin, G. A (2003). Never a dull moment: Pirn Fortuyn and the Dutch parliamentary election of 2002. West European Politics, 26, 41–66.

    Article  Google Scholar 

  • Yu, H.-T. and De Rooij, M. (2009). Model selection for the trend vector model. Submitted paper.

    Google Scholar 

  • Zielman, B. and Heiser, W.J. (1993). Analysis of asymmetry by a slide-vector. Psychometrika, 58, 101–114.

    Article  Google Scholar 

Download references

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de Rooij, M. An Application of the Mixed Effects Trend Vector Models to the Analysis of Asymmetric Square Contingency Tables with Auxiliary Variables. Behaviormetrika 39, 75–90 (2012). https://doi.org/10.2333/bhmk.39.75

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  • DOI: https://doi.org/10.2333/bhmk.39.75

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