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Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach

Author

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  • Fei Gu

    (McGill University)

  • Hao Wu

    (Boston College)

Abstract

The specifications of state space model for some principal component-related models are described, including the independent-group common principal component (CPC) model, the dependent-group CPC model, and principal component-based multivariate analysis of variance. Some derivations are provided to show the equivalence of the state space approach and the existing Wishart-likelihood approach. For each model, a numeric example is used to illustrate the state space approach. In addition, a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions. In order to cope with the nonnormality conditions, the robust standard errors are also computed. Finally, other possible applications of the state space approach are discussed at the end.

Suggested Citation

  • Fei Gu & Hao Wu, 2016. "Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 751-773, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-016-9504-2
    DOI: 10.1007/s11336-016-9504-2
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    References listed on IDEAS

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    1. Trendafilov, Nickolay T., 2010. "Stepwise estimation of common principal components," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3446-3457, December.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Henk Kiers & Jos Berge, 1989. "Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 467-473, September.
    4. Neuenschwander, Beat E. & Flury, Bernard D., 2000. "Common Principal Components for Dependent Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 163-183, November.
    5. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    6. Marieke Timmerman & Henk Kiers, 2003. "Four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 105-121, March.
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