Equivalence and differences between structural equation modeling and state-space modeling techniques

Structural Equation Modeling

Volumn 17, Issue 2, 2010, Pages 303-332

  Chow, Sy Miin ^a   Ho, Moon ho R ^b   Hamaker, Ellen L ^c   Dolan, Conor V ^d  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c UTRECHT UNIVERSITY   (Netherlands)

^d UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES;

COMMON FACTOR MODEL; COMPLEMENTARY TOOLS; DYNAMIC FACTOR ANALYSIS; INTER-INDIVIDUAL DIFFERENCES; REGRESSION PARAMETERS; STATE - SPACE MODELS; STRUCTURAL EQUATION MODELING; STRUCTURAL EQUATION MODELING TECHNIQUES;

EQUATIONS OF STATE;

EID: 77951663345     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705511003661553     Document Type: Article

References (72)

1. Ansley, C. F., & Kohn, R. (1985). Estimation, filtering and smoothing in state space models with incompletely specified initial conditions. Annals of Statistics, 13, 1286-1316.
2. Azzelini, A. (1996). Statistical inference based on the likelihood. London: Chapman & Hall.
3. Boker, S. M., & Bisconti, T. L. (2006). Dynamical systems modeling in aging research. In C. S. Bergeman & S. M. Boker (Eds.0029, Quantitative methodology in aging research (pp. 185-229). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
4. Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
5. Browne, M. W., & Nesselroade, J. R. (2005). Representing psychological processes with dynamic factor models: Some promising uses and extensions of ARMA time series models. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary psychometrics: A Festschrift for Roderick P. McDonald (multivariate applications book) (pp. 415-452). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
6. Browne, M. W., & 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/
7. Bryk, A. S., & Raudenbush, S. W. (1987). Application of hierarchical linear models to assessing change. Psychological Bulletin, 101, 147-158.
8. 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.
9. Chow, S.-M., Ferrer, E., & Nesselroade, J. R. (2007). An unscented Kalman filter approach to the estimation of nonlinear dynamical systems models. Multivariate Behavioral Research, 42, 283-321.
10. Chow, S.-M., Nesselroade, J. R., Shifren, K., & McArdle, J. J. (2004). Dynamic structure of emotions among individuals with Parkinsons disease. Structural Equation Modeling, 11, 560-582.
11. Daumer, M., & 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.
12. De Jong, P. (1991). The diffuse Kalman filter. The Annals of Statistics, 19, 1073-1083.
13. De Jong, P., & Mazzi, S. (2001). Modeling and smotohing unequally spaced sequence data. Statistical Inference for Stochastic Processes, 4, 53-71.
14. Dolan, C. V. (2002). MKF provisional documentation (Unpublished mkfm6 user manual), University of Amsterdam.
15. Dolan, C. V., & 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.
16. Doornik, J. A. (1998). Object-oriented matrix programming using Ox 2.0. London: Timberlake Consultants Press.
17. Durbin, J., & Koopman, S. J. (2001). Time series analysis by state-space methods. New York: Oxford University Press.
18. du Toit, S. H. C., & Browne, M. W. (2001). The covariance structure of a vector ARMA time series. In R. Cudeck, S. H. C. du Toit, & D. Sorbom, Structural equation modeling: Present and future (pp. 279-314). Chicago, IL: Scientific Software International.
19. Enders, C. K. (2001). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling, 8, 128-141.
20. Gelb, A. (1974). Applied optimal estimation. Cambridge, MA: MIT Press.
21. Goodwin, G. C., & Payne, R. L. (1977). Dynamic system identification: Experiment design and data analysis. New York: Academic Press.
22. Graham, J. W., Hofer, S. M., & 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.
23. Gregson, R. A. M. (1983). Time series in psychology. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
24. Hamaker, E. L., Dolan, C. V., & Molenaar, P. C. M. (2002). On the nature of SEM estimates of ARMA parameters. Structural Equation Modeling, 9, 347-368.
25. Hamaker, E. L., Dolan, C. V., & 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.
26. Hamerle, A., Singer, H., & Nagl, W. (1993). Identification and estimation of continuous time dynamic systems with exogenous variables using panel data. Econometric Theory, 9, 283-295.
27. Hamilton, J. D. (1994). Time series analysis. Princeton, NJ: Princeton University Press.
28. Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Princeton, NJ: Princeton University Press.
29. Harvey, A. C. (2001). Forecasting, structural time series models and the Kalman filter. Cambridge, UK: Cambridge University Press.
30. Heath, R. A. (2000). Nonlinear dynamics: Techniques and applications in psychology.Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
31. Hershberger, S. L., Corneal, S. E., & Molenaar, P. C. M. (1994). A dynamic factor analysis of the emotional response patterns underlying stepdaughter-stepfather relationships. Structural Equation Modeling, 2, 31-52.
32. Ho, M-H. R., Shumway, R., & Ombao, H. (2006). State-space models for longitudinal data with applications in the biological and social sciences. In T. Walls & J. L. Shafer (Eds.), Models for intensive longitudinal data (pp. 148-175). New York: Oxford University Press.
33. Jones, C. J., & 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.
34. Jöreskog, K. G. (1974). Analyzing psychological data by structural analysis of covariance matrices. In D. H. Krantz, R. C. Atkinson, R. L. Duncan, & P. Suppes (Eds.), Contemporary developments in mathematical psychology: Vol. 2. Measurement, psychophysics and neural information processing (pp. 1-56). San Francisco, CA: W. H. Freeman.
35. Jöreskog, K. G., & Sörbom, D. (1981). LISREL: Analysis of linear structural relationships by maximum likelihood and least squares methods. Chicago, IL: National Educational Resources.
36. Julier, S. J., Uhlmann, J. K., & Durrant-Whyte, H. F. (1995, June). A new approach for filtering nonlinear systems. In Proceedings of the American Control Conference (pp. 1628-1632). Seattle, WA: IEEE.
37. 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.
38. Kim, C.-J., & Nelson, C. R. (1999). State-space models with regime switching: Classical and Gibbs-sampling approaches with applications. Cambridge, MA: MIT Press.
39. Koopman, S. J., Shephard, N., & Doornik, J. A. (1999). Statistical algorithms for models in state space using ssfpack 2.2. Econometrics Journal, 2, 113-166.
40. Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963-974.
41. Lawley, D. N., & Maxwell, M. A. (1971). Factor analysis as a statistical method (2nd ed.). London: Butterworths.
42. Ljung, L., & Söderström, T. (1983). Theory and practice of recursive identification. Cambridge, MA: MIT Press.
43. MacCallum, R. C., & Ashby, G. F. (1986). Relationships between linear systems theory and covariance structure modeling. Journal of Mathematical Psychology, 30(1), 1-27.
44. MacCallum, R. C., Browne, M., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130-149.
45. Mauss, I., McCarter, L., Levenson, R., Wilhelm, F., & Gross, J. (2005). The tie that binds? Coherence among emotion experience, behavior and physiology. Emotion, 5, 175-190.
46. McArdle, J. J. (1994). Structural factor analysis experiments with incomplete data. Multivariate Behavioral Research, 29,409-454.
47. McArdle, J. J., & Epstein, D. B. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110-133.
48. McArdle, J. J., & Hamagami, F. (2001). Latent difference score structural models for linear dynamic analysis with incomplete longitudinal data. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 139-175). Washington, DC: American Psychological Association.
49. McArdle, J. J., & Woodcock, R. W. (1997). Expanding test-retest design to include developmentaltime-lag components. Psychological Methods, 2, 403-435.
50. McArdle, J. J., Hamagami, F., Jones, K., Jolesz, F., Kikinis, R., Spiro, A. I., et al. (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.
51. McArdle, J. J., & 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.
52. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
53. Molenaar, P. C. M. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181-202.
54. Molenaar, P. C. M., & 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.
55. Molenaar, P. C. M., & Raijmakers, M. E. J. (1998). Fitting nonlinear dynamical models directly to observed time series. In K. M. Newell & P. C. M. Molenaar (Eds.), Applications of nonlinear dynamics to developmental process modeling (pp. 269-297). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
56. Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (1999). Mx: Statistical modeling (5th ed.). Richmond, VA: Department of Psychiatry, Virginia Commonwealth University.
57. Nesselroade, J. R., McArdle, J. J., Aggen, S. H., & Meyers, J. M. (2002). Alternative dynamic factor models for multivariate time-series analyses. In D. M. Moskowitz & S. L. Hershberger (Eds.), Modeling intraindividual variability with repeated measures data: Advances and techniques (pp. 235-265).Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
58. Otter, P. (1986). Dynamic structure systems under indirect observation: Indentifiability and estimation aspects from a system theoretic perspective. Psychometrika, 51, 415-428.
59. Oud, J. H. L., & Jansen, R. A. R. G. (2000). Continuous time state space modeling of panel data by means of SEM. Psychometrika, 65, 199-215.
60. Oud, J. H. L., van den Bercken, J. H., & Essers, R. J. (1990). Longitudinal factor score estimation using the Kalman filter. Applied Psychological Measurement, 14, 395-418.
61. Rao, C. R. (1958). Some statistical methods for the comparison of growth curves. Biometrics, 14, 1-17.
62. Satorra, A., & Saris, W. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83-90.
63. Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147-177.
64. Shumway, R. H. (2000). Dynamic mixed models for irregularly observed time series. Resenhas-Reviewsof the Institute of Mathematics and Statistics, 4, 433-456.
65. Shumway, R. H., & Stoffer, D. S. (2004). Time series analysis and its applications. New York: Springer-Verlag.
66. Singer, H. (1998). Continuous panel models with time dependent parameters. Journal of Mathematical Sociology, 23, 77-98.
67. Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19-23.
68. Van der Merwe, R. (2003). ReBEL: Recursive Baysian Estimation Library (ReBEL online documentation), Oregon Health & Science University.
69. Wood, P., & Brown, D. (1994). The study of intraindividual differences by means of dynamic factor models: Rationale, implementation, and interpretation. Psychological Bulletin, 116, 166-186.
70. Zarchan, P., & Musoff, H. (2000). Fundamentals of Kalman filtering: A practical approach. Reston, VA: American Institute of Aeronautics and Astronautics, Inc.
71. Zhang, G. (2010). Dynamic factor analysis with ordinal variables. In S.-M. Chow, E. Ferrer, & F. Hsieh, Notre Dame series on quantitative methodology (vol. 4). Statistical methods for modeling human dynamics: An interdisciplinary dialogue. New York: Taylor & Francis.
72. Zhang, Z., Hamaker, E. L., & Nesselroade, J. R. (2008). Comparison of four methods for estimating a dynamic factor model. Structural Equation Modeling, 15, 377-402.