Abstract
As a method to ascertain the structure of intra-individual variation,P-technique has met difficulties in the handling of a lagged covariance structure. A new statistical technique, coined dynamic factor analysis, is proposed, which accounts for the entire lagged covariance function of an arbitrary second order stationary time series. Moreover, dynamic factor analysis is shown to be applicable to a relatively short stretch of observations and therefore is considered worthwhile for psychological research. At several places the argumentation is clarified through the use of examples.
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References
Anderson, T. W. (1963). The use of factor analysis in the statistical analysis of multiple time series.Psychometrika, 28, 1–25.
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures.Psychological Bulletin, 88, 588–606.
Box, G. E. P., & Jenkins, G. M. (1970).Time series analysis: Forecasting and control. San Francisco: Holden-Day.
Box, G. E. P., & Tiao, G. C. (1977). A canonical analysis of multiple time series.Biometrika, 64, 355–365.
Brillinger, D. R. (1975).Time series: Data analysis and theory. New York: Holt, Rinehart & Winston.
Cattell, R. B. (1952)Factor analysis. New York: Harper.
Cattell, R. B. (1957).Personality and motivation: Structure and measurement. Yonkers-on-Hudson: World Book.
Cattell, R. B. (1963). The structuring of change byP-technique and incrementalR-technique. In C. W. Harris (Ed.),Problems in measuring change. Madison: The University of Wisconsin Press.
Duffy, E. (1962).Activation and behavior. New York: Wiley.
Eiting, M. H., & Mellenbergh, G. J. (1980). Testing covariance matrix hypotheses: An example from the measurement of musical abilities.Multivariate Behavioral Research, 15, 203–223.
Grossberg, S. (1982).Studies of mind and brain: Neural principles of learning, perception, development, cognition, and motor control. Dordrecht: Reidel.
Hannan, E. J. (1970).Multiple time series. New York: Wiley.
Haykin, S. (Ed.). (1979).Nonlinear methods of spectral analysis. New York: Springer-Verlag.
Holtzman, W. H. (1962). Methodological issues inP-technique.Psychological Bulletin, 59, 243–256.
Holtzman, W. H. (1963). Statistical methods for the study of change in the single case. In C. W. Harris (Ed.),Problems in measuring change. Madison: The University of Wisconsin Press.
Hutt, S. J., Lenard, H. G., & Prechtl, H. F. R. (1969). Psychophysiological studies in newborn infants. In L. P. Lipsitt & H. W. Reese (Eds.),Advances in child development and behavior. New York: Academic Press.
Jazwinsky, A. H. (1970).Stochastic processes and filtering theory. New York: Academic Press.
Jenkins, G. M., & Watts, D. G. (1968).Spectrum analysis and its applications. San Francisco: Holden-Day.
Jöreskog, K. G. (1976).Structural equation models in the social sciences: Specification, estimation, and testing (Research Rep. 76-9). Uppsala: University of Uppsala.
Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices.Psychometrika, 43, 443–477.
Jöreskog, K. G., & Sörbom, D. (1978).LISREL IV: Analysis of linear structural relationships by the method of maximum likelihood. Chicago: International Educational Services.
Kashyap, R. L., & Rao, R. A. (1976).Dynamic stochastic models from empirical data. New York: Academic Press.
Molenaar, P. C. M. (1981).Dynamical factor models. Unpublished doctoral dissertation, State University of Utrecht, Utrecht.
Molenaar, P. C. M. (1982a, September).A dynamic factor model for short sample paths of a time series. Paper presented at the meeting of the European Mathematical Psychology, Bielefeld, West-Germany.
Molenaar, P. C. M. (1982b).On the validity of basic ERP waveforms obtained by principal component analysis and by confirmatory component analysis. Unpublished manuscript.
Molenaar, P. C. M. (1984, August).Dynamic factor analysis of a multivariate non-stationary time series. Paper presented at the meeting of the European Mathematical Psychology, Zeist, Holland.
Porges, S. W., Bohrer, R. E., Keren, G., Cheung, M. N., Franks, G. J., & Drasgow, F. (1981). The influence of methylphenidate on spontaneous autonomic activity and behavior in children diagnosed as hyperactive.Psychophysiology, 18, 42–48.
Priestley, M. B., Subba Rao, T., & Tong, H. (1973). Identification of the structure of multivariable stochastic systems. In P. R. Krishnaiah (Ed.),Multivariate analysis III. New York: Academic Press.
Stone, R. (1947). On the interdependence of blocks of transactions.Journal of the Royal Statistical Society B, 9, 1–32.
Subba Rao, T. (1975). An innovation approach to the reduction of the dimensions in a multivariate stochastic system.International Journal of Control, 21, 673–680.
Subba Rao, T., & Tong, H. (1974). Identification of the covariance structure of state space models.Bulletin of the Institute of Mathematics and its Applications, 10, 201–203.
Tukey, J. W. (1978, May). Can we predict where “time series” should go next? In D. R. Brillinger & G. C. Tiao (Eds.),Directions in time series. Proceedings of the IMS special topics meeting on time series analysis, Iowa State University, Ames.
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I would like to thank WM. van der Molen, G. J. Mellenbergh and L. H. M. Oppenheimer, who provided valuable ideas that led to this formulation.
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Molenaar, P.C.M. A dynamic factor model for the analysis of multivariate time series. Psychometrika 50, 181–202 (1985). https://doi.org/10.1007/BF02294246
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DOI: https://doi.org/10.1007/BF02294246