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Skewed factor models using selection mechanisms

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  • Kim, Hyoung-Moon
  • Maadooliat, Mehdi
  • Arellano-Valle, Reinaldo B.
  • Genton, Marc G.

Abstract

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.

Suggested Citation

  • Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:162-177
    DOI: 10.1016/j.jmva.2015.12.007
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    Cited by:

    1. Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.
    2. Sharon X. Lee & Tsung-I Lin & Geoffrey J. McLachlan, 2021. "Mixtures of factor analyzers with scale mixtures of fundamental skew normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 481-512, June.
    3. Lee, Sharon X. & McLachlan, Geoffrey J., 2021. "On formulations of skew factor models: Skew factors and/or skew errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    4. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    5. Cornelis J. Potgieter, 2020. "Density deconvolution for generalized skew-symmetric distributions," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.

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