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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. Ulf Olsson, 1979. "Maximum likelihood estimation of the polychoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 443-460, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. Rolf Larsson, 2022. "Bartlett correction of an independence test in a multivariate Poisson model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 391-417, November.

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