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Factor models for multivariate count data

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  • Wedel, Michel
  • Böckenholt, Ulf
  • Kamakura, Wagner A.

Abstract

We develop a general class of factor-analytic models for the analysis of multivariate (truncated) count data. Dependencies in multivariate counts are of interest in many applications, but few approaches have been proposed for their analysis. Our model class allows for a variety of distributions of the factors in the exponential family. The proposed framework includes a large number of previously proposed factor and random effect models as special cases and leads to many new models that have not been considered so far. Whereas previously these models were proposed separately as different cases, our framework unifies these models and enables one to study them simultaneously. We estimate the Poisson factor models with the method of simulated maximum likelihood. A Monte-Carlo study investigates the performance of this approach in terms of estimation bias and precision. We illustrate the approach in an analysis of TV channels data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:356-369
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    References listed on IDEAS

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    1. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    2. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-435, October.
    3. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
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    Cited by:

    1. Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-François, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 73-85.
    2. Robert C. Jung & Roman Liesenfeld & Jean-François Richard, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 73-85, January.
    3. David I. Warton, 2011. "Regularized Sandwich Estimators for Analysis of High-Dimensional Data Using Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 67(1), pages 116-123, March.
    4. Kim, Hea-Jung & Choi, Taeryon & Jo, Seongil, 2016. "Bayesian factor analysis with uncertain functional constraints about factor loadings," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 110-128.
    5. Brooke E. Magnus & David Thissen, 2017. "Item Response Modeling of Multivariate Count Data With Zero Inflation, Maximum Inflation, and Heaping," Journal of Educational and Behavioral Statistics, , vol. 42(5), pages 531-558, October.
    6. Carrie B. Myers & Scott M. Myers & Martha Peters, 2019. "The Longitudinal Connections Between Undergraduate High Impact Curriculum Practices and Civic Engagement in Adulthood," Research in Higher Education, Springer;Association for Institutional Research, vol. 60(1), pages 83-110, February.
    7. Y Chen & X Li, 2022. "Determining the number of factors in high-dimensional generalized latent factor models [Eigenvalue ratio test for the number of factors]," Biometrika, Biometrika Trust, vol. 109(3), pages 769-782.
    8. Bijwaard, Govert E. & Franses, Philip Hans, 2009. "The effect of rounding on payment efficiency," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1449-1461, February.
    9. Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    10. Peter Congdon, 2011. "The Spatial Pattern of Suicide in the US in Relation to Deprivation, Fragmentation and Rurality," Urban Studies, Urban Studies Journal Limited, vol. 48(10), pages 2101-2122, August.
    11. Rolf Larsson, 2020. "Discrete factor analysis using a dependent Poisson model," Computational Statistics, Springer, vol. 35(3), pages 1133-1152, September.

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