Equivalence and Differences Between Structural Equation Modeling and State-Space Modeling Techniques

REFERENCES

• Ansley , C. F. and Kohn , R. 1985 . Estimation, filtering and smoothing in state space models with incompletely specified initial conditions . Annals of Statistics , 13 : 1286 – 1316 .
   Web of Science ®Google Scholar
• Azzelini , A. 1996 . Statistical inference based on the likelihood. London : Chapman & Hall. .
   Google Scholar
• Boker , S. M. and Bisconti , T. L. 2006 . “ Dynamical systems modeling in aging research. ” . In Quantitative methodology in aging research Edited by: Bergeman , C. S. and Boker , S. M. 185 – 229 . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Bollen , K. A. 1989 . Structural equations with latent variables. New York : Wiley. .
   Google Scholar
• Browne , M. W. and Nesselroade , J. R. 2005 . “ Representing psychological processes with dynamic factor models: Some promising uses and extensions of ARMA time series models. ” . In Contemporary psychometrics: A Festschrift for Roderick P. McDonald (multivariate applications book) Edited by: Maydeu-Olivares , A. and McArdle , J. J. 415 – 452 . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Browne , M. W. and Zhang , G. 2005 . DyFA: Dynamic factor analysis of lagged correlation matrices, version 2.03 [computer software and manual]. Available at: http://quantrm2.psy.ohio-state.edu/browne/
   Google Scholar
• Bryk , A. S. and Raudenbush , S. W. 1987 . Application of hierarchical linear models to assessing change . Psychological Bulletin , 101 : 147 – 158 .
   Web of Science ®Google Scholar
• Cattell , R. B. , Cattell , A. K. S. and Rhymer , R. M. 1947 . P-technique demonstrated in determining psychophysical source traits in a normal individual . Psychometrika , 12 : 267 – 288 .
   PubMed Web of Science ®Google Scholar
• Chow , S.-M. , Ferrer , E. and Nesselroade , J. R. 2007 . An unscented Kalman filter approach to the estimation of nonlinear dynamical systems models . Multivariate Behavioral Research , 42 : 283 – 321 .
   PubMed Web of Science ®Google Scholar
• Chow , S.-M. , Nesselroade , J. R. , Shifren , K. and McArdle , J. J. 2004 . Dynamic structure of emotions among individuals with Parkinsons disease . Structural Equation Modeling , 11 : 560 – 582 .
   Web of Science ®Google Scholar
• Daumer , M. and Falk , M. 1998 . On-line change-point detection (for state space models) using multi-process Kalman filters . Linear Algebra and Its Applications , 284 ( 1–3 ) : 125 – 135 .
   Google Scholar
• De Jong , P. 1991 . The diffuse Kalman filter . The Annals of Statistics , 19 : 1073 – 1083 .
   Web of Science ®Google Scholar
• De Jong , P. and Mazzi , S. 2001 . Modeling and smotohing unequally spaced sequence data . Statistical Inference for Stochastic Processes , 4 : 53 – 71 .
   Google Scholar
• Dolan , C. V. 2002 . MKF provisional documentation (Unpublished mkfm6 user manual), University of Amsterdam
   Google Scholar
• Dolan , C. V. and Molenaar , P. C. M. 1991 . A note on the calculation of latent trajectories in the quasi Markov simplex model by means of regression method and the discrete Kalman filter . Kwantitatieve Methoden , 38 : 29 – 44 .
   Google Scholar
• Doornik , J. A. 1998 . Object-oriented matrix programming using Ox 2.0. London : Timberlake Consultants Press. .
   Google Scholar
• Durbin , J. and Koopman , S. J. 2001 . Time series analysis by state-space methods. New York : Oxford University Press .
   Google Scholar
• du Toit , S. H. C. and Browne , M. W. 2001 . “ The covariance structure of a vector ARMA time series. ” . In Structural equation modeling: Present and future Edited by: Cudeck , R. , du Toit , S. H. C. and Sorbom , D. 279 – 314 . Chicago, IL : Scientific Software International .
   Google Scholar
• Enders , C. K. 2001 . A primer on maximum likelihood algorithms available for use with missing data . Structural Equation Modeling , 8 : 128 – 141 .
   Web of Science ®Google Scholar
• Gelb , A. 1974 . Applied optimal estimation. Cambridge, MA : MIT Press .
   Google Scholar
• Goodwin , G. C. and Payne , R. L. 1977 . Dynamic system identification: Experiment design and data analysis. New York : Academic Press. .
   Google Scholar
• Graham , J. W. , Hofer , S. M. and MacKinnon , D. P. 1996 . Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures . Multivariate Behavioral Research , 31 : 197 – 218 .
   PubMed Web of Science ®Google Scholar
• Gregson , R. A. M. 1983 . Time series in psychology. Hillsdale, NJ : Lawrence Erlbaum Associates, Inc. .
   Google Scholar
• Hamaker , E. L. , Dolan , C. V. and Molenaar , P. C. M. 2002 . On the nature of SEM estimates of ARMA parameters . Structural Equation Modeling , 9 : 347 – 368 .
   Web of Science ®Google Scholar
• Hamaker , E. L. , Dolan , C. V. and Molenaar , P. C. M. 2003 . ARMA-based SEM when the number of time points T exceeds the number of cases N: Raw data maximum likelihood . Structural Equation Modeling , 10 : 352 – 379 .
   Web of Science ®Google Scholar
• Hamerle , A. , Singer , H. and Nagl , W. 1993 . Identification and estimation of continuous time dynamic systems with exogenous variables using panel data . Econometric Theory , 9 : 283 – 295 .
   Web of Science ®Google Scholar
• Hamilton , J. D. 1994 . Time series analysis. Princeton, NJ : Princeton University Press .
   Google Scholar
• Harvey , A. C. 1989 . Forecasting, structural time series models and the Kalman filter. Princeton, NJ : Princeton University Press .
   Google Scholar
• Harvey , A. C. 2001 . Forecasting, structural time series models and the Kalman filter. Cambridge, , UK : Cambridge University Press .
   Google Scholar
• Heath , R. A. 2000 . Nonlinear dynamics: Techniques and applications in psychology. Mahwah, NJ : Lawrence Erlbaum Associates, Inc. .
   Google Scholar
• Hershberger , S. L. , Corneal , S. E. and Molenaar , P. C. M. 1994 . A dynamic factor analysis of the emotional response patterns underlying stepdaughter–stepfather relationships . Structural Equation Modeling , 2 : 31 – 52 .
   Web of Science ®Google Scholar
• Ho , M-H. R. , Shumway , R. and Ombao , H. 2006 . “ State-space models for longitudinal data with applications in the biological and social sciences. ” . In Models for intensive longitudinal data Edited by: Walls , T. and Shafer , J. L. 148 – 175 . New York : Oxford University Press .
   Google Scholar
• Jones , C. J. and Nesselroade , J. R. 1990 . Multivariate, replicated, single-subject designs and P-technique factor analysis: A selective review of the literature . Experimental Aging Research , 16 : 171 – 183 .
   PubMed Web of Science ®Google Scholar
• Jöreskog , K. G. 1974 . “ Analyzing psychological data by structural analysis of covariance matrices. ” . In Contemporary developments in mathematical psychology: Vol. 2. Measurement, psychophysics and neural information processing Edited by: Krantz , D. H. , Atkinson , R. C. , Duncan , R. L. and Suppes , P. 1 – 56 . San Francisco, CA : W. H. Freeman .
   Google Scholar
• Jöreskog , K. G. and Sörbom , D. 1981 . LISREL: Analysis of linear structural relationships by maximum likelihood and least squares methods. Chicago, IL : National Educational Resources. .
   Google Scholar
• Julier , S. J. , Uhlmann , J. K. and Durrant-Whyte , H. F. June 1995 . “ A new approach for filtering nonlinear systems ” . In Proceedings of the American ontrol Conference June , 1628 – 1632 . Seattle, WA : IEEE .
   Google Scholar
• Kalman , R. E. 1960 . A new approach to linear filtering and prediction problems . Transactions of the ASME–Journal of Basic Engineering , 82 ( Series D ) : 35 – 45 .
   Google Scholar
• Kim , C.-J. and Nelson , C. R. 1999 . State-space models with regime switching: Classical and Gibbs-sampling approaches with applications. Cambridge, MA : MIT Press .
   Google Scholar
• Koopman , S. J. , Shephard , N. and Doornik , J. A. 1999 . Statistical algorithms for models in state space using ssfpack 2.2 . Econometrics Journal , 2 : 113 – 166 .
   Google Scholar
• Laird , N. M. and Ware , J. H. 1982 . Random-effects models for longitudinal data . Biometrics , 38 : 963 – 974 .
   PubMed Web of Science ®Google Scholar
• Lawley , D. N. and Maxwell , M. A. 1971 . Factor analysis as a statistical method, , 2nd ed. London : Butterworths .
   Google Scholar
• Ljung , L. and Söderström , T. 1983 . Theory and practice of recursive identification. Cambridge, MA : MIT Press .
   Google Scholar
• MacCallum , R. C. and Ashby , G. F. 1986 . Relationships between linear systems theory and covariance structure modeling . Journal of Mathematical Psychology , 30 ( 1 ) : 1 – 27 .
   Web of Science ®Google Scholar
• MacCallum , R. C. , Browne , M. and Sugawara , H. M. 1996 . Power analysis and determination of sample size for covariance structure modeling . Psychological Methods , 1 ( 2 ) : 130 – 149 .
   Web of Science ®Google Scholar
• Mauss , I. , McCarter , L. , Levenson , R. , Wilhelm , F. and Gross , J. 2005 . The tie that binds? Coherence among emotion experience, behavior and physiology . Emotion , 5 : 175 – 190 .
   PubMed Web of Science ®Google Scholar
• McArdle , J. J. 1994 . Structural factor analysis experiments with incomplete data . Multivariate Behavioral Research , 29 : 409 – 454 .
   PubMed Web of Science ®Google Scholar
• McArdle , J. J. and Epstein , D. B. 1987 . Latent growth curves within developmental structural equation models . Child Development , 58 : 110 – 133 .
   PubMed Web of Science ®Google Scholar
• McArdle , J. J. and Hamagami , F. 2001 . “ Latent difference score structural models for linear dynamic analysis with incomplete longitudinal data. ” . In New methods for the analysis of change Edited by: Collins , L. and Sayer , A. 139 – 175 . Washington, DC : American Psychological Association .
   Google Scholar
• McArdle , J. J. and Woodcock , R. W. 1997 . Expanding test-retest design to include developmental time-lag components . Psychological Methods , 2 : 403 – 435 .
   Web of Science ®Google Scholar
• McArdle , J. J. , Hamagami , F. , Jones , K. , Jolesz , F. , Kikinis , R. Spiro , A. I. 2004 . Structural modeling of dynamic changes in memory and brain structure using longitudinal data from the normative aging study . The Journal of Gerentology: Psychological Studies , 59 : 294 – 304 .
   Google Scholar
• McArdle , J. J. and McDonald , R. P. 1984 . Some algebraic properties of the reticular action model for moment structures . British Journal of Mathematical and Statistical Psychology , 27 : 234 – 251 .
   Google Scholar
• Meredith , W. and Tisak , J. 1990 . Latent curve analysis . Psychometrika , 55 : 107 – 122 .
   Web of Science ®Google Scholar
• Molenaar , P. C. M. 1985 . A dynamic factor model for the analysis of multivariate time series . Psychometrika , 50 : 181 – 202 .
   Web of Science ®Google Scholar
• Molenaar , P. C. M. and Nesselroade , J. R. 1998 . 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 . Multivariate Behavioral Research , 33 : 313 – 342 .
   PubMed Web of Science ®Google Scholar
• Molenaar , P. C. M. and Raijmakers , M. E. J. 1998 . “ Fitting nonlinear dynamical models directly to observed time series. ” . In Applications of nonlinear dynamics to developmental process modeling Edited by: Newell , K. M. and Molenaar , P. C. M. 269 – 297 . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Neale , M. C. , Boker , S. M. , Xie , G. and Maes , H. H. 1999 . Mx: Statistical modeling, , 5th ed. Richmond, VA : Department of Psychiatry, Virginia Commonwealth University .
   Google Scholar
• Nesselroade , J. R. , McArdle , J. J. , Aggen , S. H. and Meyers , J. M. 2002 . “ Alternative dynamic factor models for multivariate time-series analyses. ” . In Modeling intraindividual variability with repeated measures data: Advances and techniques Edited by: Moskowitz , D. M. and Hershberger , S. L. 235 – 265 . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Otter , P. 1986 . Dynamic structure systems under indirect observation: Indentifiability and estimation aspects from a system theoretic perspective . Psychometrika , 51 : 415 – 428 .
   Web of Science ®Google Scholar
• Oud , J. H. L. and Jansen , R. A. R. G. 2000 . Continuous time state space modeling of panel data by means of SEM . Psychometrika , 65 : 199 – 215 .
   Web of Science ®Google Scholar
• Oud , J. H. L. , van den Bercken , J. H. and Essers , R. J. 1990 . Longitudinal factor score estimation using the Kalman filter . Applied Psychological Measurement , 14 : 395 – 418 .
   Web of Science ®Google Scholar
• Rao , C. R. 1958 . Some statistical methods for the comparison of growth curves . Biometrics , 14 : 1 – 17 .
   Web of Science ®Google Scholar
• Satorra , A. and Saris , W. 1985 . Power of the likelihood ratio test in covariance structure analysis . Psychometrika , 50 : 83 – 90 .
   Web of Science ®Google Scholar
• Schafer , J. L. and Graham , J. W. 2002 . Missing data: Our view of the state of the art . Psychological Methods , 7 : 147 – 177 .
   PubMed Web of Science ®Google Scholar
• Shumway , R. H. 2000 . Dynamic mixed models for irregularly observed time series . Resenhas—Reviews of the Institute of Mathematics and Statistics , 4 : 433 – 456 .
   Google Scholar
• Shumway , R. H. and Stoffer , D. S. 2004 . Time series analysis and its applications. New York : Springer-Verlag. .
   Google Scholar
• Singer , H. 1998 . Continuous panel models with time dependent parameters . Journal of Mathematical Sociology , 23 : 77 – 98 .
   Web of Science ®Google Scholar
• Tucker , L. R. 1958 . Determination of parameters of a functional relation by factor analysis . Psychometrika , 23 : 19 – 23 .
   Web of Science ®Google Scholar
• Van der Merwe , R. 2003 . ReBEL: Recursive Baysian Estimation Library (ReBEL online documentation) Oregon Health & Science University .
   Google Scholar
• Wood , P. and Brown , D. 1994 . The study of intraindividual differences by means of dynamic factor models: Rationale, implementation, and interpretation . Psychological Bulletin , 116 : 166 – 186 .
   Web of Science ®Google Scholar
• Zarchan , P. and Musoff , H. 2000 . Fundamentals of Kalman filtering: A practical approach. Reston, VA : American Institute of Aeronautics and Astronautics, Inc. .
   Google Scholar
• Zhang , G. 2010 . “ Dynamic factor analysis with ordinal variables ” . In Notre Dame series on quantitative methodology (vol. 4). Statistical methods for modeling human dynamics: An interdisciplinary dialogue. Edited by: Chow , S.-M. , Ferrer , E. and Hsieh , F. New York : Taylor & Francis. .
   Google Scholar
• Zhang , Z. , Hamaker , E. L. and Nesselroade , J. R. 2008 . Comparison of four methods for estimating a dynamic factor model . Structural Equation Modeling , 15 : 377 – 402 .
   Web of Science ®Google Scholar