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Discrete factor analysis using a dependent Poisson model

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  • Rolf Larsson

    (Uppsala University)

Abstract

In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson distribution. We try to find the model with the lowest AIC by employing a forward selection procedure. The probability to find the correct model is investigated in a simulation study. Moreover, we heuristically derive the corresponding asymptotic probabilities. An empirical study is also included.

Suggested Citation

  • Rolf Larsson, 2020. "Discrete factor analysis using a dependent Poisson model," Computational Statistics, Springer, vol. 35(3), pages 1133-1152, September.
  • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-020-00960-w
    DOI: 10.1007/s00180-020-00960-w
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4243-4258.
    3. Felix Famoye, 2015. "A Multivariate Generalized Poisson Regression Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 497-511, February.
    4. Ulf Olsson, 1979. "Maximum likelihood estimation of the polychoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 443-460, December.
    5. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," LSE Research Online Documents on Economics 43182, London School of Economics and Political Science, LSE Library.
    6. Wedel, Michel & Böckenholt, Ulf & Kamakura, Wagner A., 2003. "Factor models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 356-369, November.
    7. Peter Berkhout & Erik Plug, 2004. "A bivariate Poisson count data model using conditional probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 349-364, August.
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