DOI QR코드

DOI QR Code

Asymptotic Test for Dimensionality in Probabilistic Principal Component Analysis with Missing Values

  • Published : 2004.04.01

Abstract

In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.

Keywords

References

  1. Annals of Mathematical Statistics v.34 Asymptotic Theory for Principal Component Analysis Anderson,T.W. https://doi.org/10.1214/aoms/1177704248
  2. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability v.Ⅴ Statistical Inference in Factor Anaysis Anderson,T.W.;Rubin,H.;J,Newman(ed.)
  3. Annals of Eugenics v.7 The use of multiple measurements in taxonomic problems Fisher,R.A. https://doi.org/10.1111/j.1469-1809.1936.tb02137.x
  4. Journal of the Royal Statistical Society,Series B v.52 On Use of the EM Algorithm for Penalized Likelihood Estimation Green,P.J.
  5. Journal of Educational Psychology v.24 Ananlysis of a Complex of Statistical Variables into Principal Components Hotelling,H. https://doi.org/10.1037/h0071325
  6. Applied Multivariate Statistical Analysis Johnson,R.A.;Wichern,R.A.
  7. Principal Component Analysis Jolliffe,I.T.
  8. Uppsala Symposium on Psychological Factor Analysis,Number 3 in Nordisk Psykologi Monograph Series, 35-42 A Modified Method of Estimation in Factor Analysis and Some Large Sample Results Lawley,D.N.
  9. Statistical Analysis with Missing Data Little,R.;Rubin,D.
  10. Analysis of Incomplete Multivariate Data by Simulation Schafer,L.
  11. Journal of the Royal Statistical Society,Series B v.61 Probabilistic Principal Component Analysis Tipping,M.E.;Bishop,C.M. https://doi.org/10.1111/1467-9868.00196
  12. Skamdinavisk Aktuarietidskrift v.36 On Principal Components and Least Square Methods of Factor Analysis Whittle,P.
  13. Psychometrika v.6 no.1 Maximum Likehood Estimation and Factor Analysis Young,G. https://doi.org/10.1007/BF02288574