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Deterministic parallel analysis: an improved method for selecting factors and principal components

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  • Edgar Dobriban
  • Art B. Owen

Abstract

Factor analysis and principal component analysis are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of the most popular state of the art methods is parallel analysis (PA), which compares the observed factor strengths with simulated strengths under a noise‐only model. The paper proposes improvements to PA. We first derandomize it, proposing deterministic PA, which is faster and more reproducible than PA. Both PA and deterministic PA are prone to a shadowing phenomenon in which a strong factor makes it difficult to detect smaller but more interesting factors. We propose deflation to counter shadowing. We also propose to raise the decision threshold to improve estimation accuracy. We prove several consistency results for our methods, and test them in simulations. We also illustrate our methods on data from the human genome diversity project, where they significantly improve the accuracy.

Suggested Citation

  • Edgar Dobriban & Art B. Owen, 2019. "Deterministic parallel analysis: an improved method for selecting factors and principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(1), pages 163-183, February.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:1:p:163-183
    DOI: 10.1111/rssb.12301
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    Cited by:

    1. Daniel Czarnowske & Amrei Stammann, 2020. "Inference in Unbalanced Panel Data Models with Interactive Fixed Effects," Papers 2004.03414, arXiv.org.
    2. 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.
    3. Leeb, William, 2021. "A note on identifiability conditions in confirmatory factor analysis," Statistics & Probability Letters, Elsevier, vol. 178(C).
    4. 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.
    5. Chon, Sora, 2020. "International Inflation Synchronization and Implications," KDI Journal of Economic Policy, Korea Development Institute (KDI), vol. 42(2), pages 57-84.
    6. Juan Corral-Pérez & Laura Ávila-Cabeza-de-Vaca & Andrea González-Mariscal & Milagrosa Espinar-Toledo & Jesús G. Ponce-González & Cristina Casals & María Ángeles Vázquez-Sánchez, 2023. "Risk and Protective Factors for Frailty in Pre-Frail and Frail Older Adults," IJERPH, MDPI, vol. 20(4), pages 1-11, February.

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