A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance-Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series

• Published in: Multivariate behavioral research Vol. 33; no. 3; pp. 313 - 342
• Main Authors: Molenaar, Peter C.M., Nesselroade, John R.
• Format: Journal Article
• Language: English
• Published: United States Lawrence Erlbaum Associates, Inc 01.07.1998
• Subjects: Chi Square; Comparative Analysis; Covariance Matrices; Covariance Structure Models; Error of Measurement; Estimation (Mathematics); Factor Analysis; Maximum Likelihood Statistics; Monte Carlo Methods; Simulation; Time Series Analysis
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1207/s15327906mbr3303_1

The study of intraindividual variability pervades empirical inquiry in virtually all subdisciplines of psychology. The statistical analysis of multivariate time-series data - a central product of intraindividual investigations -requires special modeling techniques. The dynamic factor model (DFM), which is a generalization of the traditional common factor model, has been proposed by Molenaar (1985) for systematically extracting information from multivariate time- series via latent variable modeling. Implementation of the DFM model has taken several forms, one of which involves specifying it as a covariance-structure model and estimating its parameters from a block-Toeplitz matrix derived from the multivariate time-ser~es. We compare two methods for estimating DFM parameters within a covariance-structure framework - pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation - by means of a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates of comparable precision, but only the ADF method gives standard errors and chi-square statistics that appear to be consistent. The relative ordering of the values of all estimates appears to be very similar across methods. When the manifest time-series is relatively short, the two methods appear to perform about equally well.