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An heuristic scree plot criterion for the number of factors

Author

Listed:
  • Ard H. J. den Reijer

    (Sveriges Riksbank)

  • Pieter W. Otter

    (University of Groningen)

  • Jan P. A. M. Jacobs

    (University of Groningen, CAMA and CIRANO)

Abstract

Cattel’s (Multivar Behav Res 1:245–276, 1966) heuristic determines the number of factors as the elbow point between ‘steep’ and ‘not steep’ in the scree plot. In contrast, an elbow is by definition absent in points on a hyberbole with corresponding equisized surfaces. We formalize this heuristic and propose a criterion to determine the number of factors by comparing surfaces under the scree plot. Monte Carlo simulations shows that the finite-sample properties of our proposed criterion outperform benchmarks in the dynamic factor model literature.

Suggested Citation

  • Ard H. J. den Reijer & Pieter W. Otter & Jan P. A. M. Jacobs, 2024. "An heuristic scree plot criterion for the number of factors," Statistical Papers, Springer, vol. 65(6), pages 3991-4000, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-023-01517-x
    DOI: 10.1007/s00362-023-01517-x
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    References listed on IDEAS

    as
    1. John Horn, 1965. "A rationale and test for the number of factors in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 30(2), pages 179-185, June.
    2. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    3. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    4. Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
    5. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    6. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    7. Louis Guttman, 1954. "Some necessary conditions for common-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 19(2), pages 149-161, June.
    8. James H. James & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," Working Papers 2005-2, Princeton University. Economics Department..
    9. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Factor model; Number of factors; Scree test;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access

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