Skip to main content
Log in

Rotation in the dynamic factor modeling of multivariate stationary time series

  • Articles
  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

A special rotation procedure is proposed for the exploratory dynamic factor model for stationary multivariate time series. The rotation procedure applies separately to each univariate component series of aq-variate latent factor series and transforms such a component, initially represented as white noise, into a univariate moving-average. This is accomplished by minimizing a so-called state-space criterion that penalizes deviations of the rotated solution from a generalized state-space model with only instantaneous factor loadings. Alternative criteria are discussed in the closing section. The results of an empirical application are presented in some detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, T.W. (1963). The use of factor analysis in the statistical analysis of multiple time series.Psychometrika, 28, 1–24.

    Article  Google Scholar 

  • Beijsterveldt, C.E.M., Molenaar, P.C.M., de Geus, E.C.J., & Boomsma, D.I. (1996). Heritability of human brain functioning as assessed by electroencephalography (EEG).American Journal of Human Genetics, 58, 562–573.

    PubMed  Google Scholar 

  • Cattell, R.B. (1952).Factor analysis. New York, NY: Harper.

    Google Scholar 

  • Cattell, R.B. (1963). The interaction of hereditary and environmental influences.The British Journal of Statistical Psychology, 16, 191–210.

    Google Scholar 

  • Cattell, R. B., Cattell, A. K. S., & Rhymer, R. M. (1947).P-technique demonstrated in determining psychophysical source traits in a normal individual.Psychometrika, 12, 267–288.

    Google Scholar 

  • Cattell, R. B., & Luborsky, L.B. (1950).P-technique demonstrated as a new clinical method for determining personality and symptom structure.The Journal of General Psychology, 42, 3–24.

    Google Scholar 

  • Engle, R., & Watson, M. (1981). A one-factor multivariate time series model of metropolitan wage rates.Journal of the American Statistical Association, 76, 774–781.

    Google Scholar 

  • Geweke, J.F., & Singleton, K.J. (1981). Maximum likelihood “confirmatory” factor analysis of economic time series.International Economic Review, 22, 37–54.

    Google Scholar 

  • Hannan, E.J. (1970).Multiple time series. New York: John Wiley & Sons.

    Google Scholar 

  • Holtzman, W.H. (1963). Statistical models for the study of change in the single case. In C. W. Harris (Ed.),Problems in measuring change (pp. 199–211). Madison, WI: University of Wisconsin Press.

    Google Scholar 

  • IMSL library reference manual. (1980). Houston: IMSL, Inc.

  • Jöreskog, K.G., & Sörbom, D. (1993). LISREL 8 user's reference guide. Chicago: Scientific Software International.

    Google Scholar 

  • Molenaar, P.C.M. (1985). A dynamic factor model for the analysis of multivariate time series.Psychometrika, 50, 181–202.

    Article  Google Scholar 

  • Molenaar, P.C.M. (1987). Dynamic factor analysis in the frequency domain: Causal modeling of multivariate psychophysiological time series.Multivariate Behavioral Research, 22, 329–353.

    Article  Google Scholar 

  • Molenaar, P.C.M. (1994a). Dynamic factor analysis of psychophysiological signals. In J.R. Jennings, P. Ackles, & M.G.H. Coles (Eds.),Advances in psycho-physiology (Vol. 5, pp. 229–302). London: Jessica Kingsley Publishers.

    Google Scholar 

  • Molenaar, P.C.M. (1994b). Dynamic latent variable models in developmental psychology. In A. von Eye & C.C. Clogg (Eds.),Latent variables analysis: Applications for developmental research (pp. 155–180). Newbury Park, CA: Sage Publications.

    Google Scholar 

  • Molenaar, P.C.M., de Gooijer, J., & Schmitz, B. (1992). Dynamic factor analysis of nonstationary multivariate time series.Psychometrika, 57, 333–349.

    Article  Google Scholar 

  • Nesselroade, J.R., & Molenaar, P.C.M. (1999). Pooling lagged covariance structures based on short, multivariate time-series for dynamic factor analysis. In R.H. Hoyle (Ed.),Statistical strategies for small sample research (xxx-xxx). Newbury Park, CA: Sage Publications.

    Google Scholar 

  • Nunez, P.L. (1981).Electric fields of the brain: The neurophysics of EEG. New York: Oxford University Press.

    Google Scholar 

  • Nunez, P.L. (1995).Neocortical dynamics and human EEG rhythms. New York: Oxford University Press.

    Google Scholar 

  • Regan, D. (1989).Human electrophysiology: Evoked potentials and evoked magnetic fields in science and medicine. Amsterdam: Elsevier.

    Google Scholar 

  • Robinson, E.A. (1967).Multichannel time series analysis with digital computer programs. San Francisco: Holden-Day.

    Google Scholar 

  • Robinson, E.A., & De Silva, M.T. (1978).Digital signal processing and time series analysis. San Francisco: Holden-Day.

    Google Scholar 

  • Wood, P., & Brown, D. (1994). The study of intraindividual differences by means of dynamic factor models: Rationale, implementation, and interpretation.Psychological Bulletin, 116(1), 166–186.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter C. M. Molenaar.

Additional information

This research was supported by the Institute for Developmental and Health Research Methodology, University of Virginia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molenaar, P.C.M., Nesselroade, J.R. Rotation in the dynamic factor modeling of multivariate stationary time series. Psychometrika 66, 99–107 (2001). https://doi.org/10.1007/BF02295735

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02295735

Key words

Navigation