State Space Modeling in an Open Source, Modular, Structural Equation Modeling Environment

REFERENCES

• Anderson, T. W. (1963). The use of factor analysis in the statistical analysis of multiple time series. Psychometrika, 28, 1–25. doi:10.1007/BF02289543
   Web of Science ®Google Scholar
• Åström, K. J., & Murray, R. M. (2010). Feedback systems: An introduction for scientists and engineers (Version v2.10c ed.). Princeton, NJ: Princeton University Press.
   Google Scholar
• Boker, S. M., Neale, M. C., & Rausch, J. (2004). Latent differential equation modeling with multivariate multi-occassion indicators. In K. Van Montfort, H. Oud, & A. Satorra (Eds.), Recent developments on structural equation models: Theory and applications (pp. 151–174). Dordrecht, Netherlands: Kluwer Academic. doi:10.1007/978-1-4020-1958-6_9
   Google Scholar
• Boker, S. M., & Nesselroade, J. R. (2002). A method for modeling the intrinsic dynamics of intraindividual variability: Recovering the parameters of simulated oscillators in multi-wave panel data. Multivariate Behavioral Research, 37, 127–160.
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (alt) models: A synthesis of two traditions. Sociological Methods & Research, 32, 336–383. doi:10.1177/0049124103260222
   Web of Science ®Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation approach. Hoboken, NJ: Wiley.
   Google Scholar
• Browne, M. W., & Nesselroade, J. R. (2005). Representing psychological processes with dynamic factor models: Some promising uses and extensions of autoregressive moving average models. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary psychometrics: A festschrift for Roderick P. McDonald (pp. 415–452). Mahwah, NJ: Erlbaum.
   Google Scholar
• Dolan, C. V. (2005). MKFM6: Multi-group, multi-subject stationary time series modeling based on the Kalman filter [Computer software manual]. Retrieved from http://users/fmg.uva.nl/cdolan/
   Google Scholar
• Driver, C. C., Oud, J. H. L., & Voelkle, M. C. (2017). Continuous time structural equation modelling with R package ctsem. Journal of Statistical Software, 77, 1–35.
   Web of Science ®Google Scholar
• Duncan, O. D. (1969). Some linear models for two-wave, two-variable panel analysis. Psychological Bulletin, 72, 177–182. doi:10.1037/h0027876
   Web of Science ®Google Scholar
• Durbin, J., & Koopman, S. J. (2001). Time series analysis by state space methods. New York, NY: Oxford University Press.
   Google Scholar
• Fahrmeir, L. (1992). Posterior mode estimation by extended Kalman filtering for multivariate dynamic generalized linear models. Journal of the American Statistical Association, 87, 501–509. doi:10.1080/01621459.1992.10475232
   Web of Science ®Google Scholar
• Fahrmeir, L., & Wagenpfeil, S. (1997). Penalized likelihood estimation and iterative Kalman smoothing for non-Gaussian dynamic regression models. Computational Statistics & Data Analysis, 24, 295–320. doi:10.1016/S0167-9473(96)00064-3
   Web of Science ®Google Scholar
• Fisher, R. A. (1925). Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society, 22, 700–725.
   Google Scholar
• Gates, K. M., Molenaar, P. C. M., Hillary, F. G., & Slobounov, S. (2011). Extended unified SEM approach for modeling event-related fMRI data. NeuroImage, 54, 1151–1158. doi:10.1016/j.neuroimage.2010.08.051
   PubMed Web of Science ®Google Scholar
• Gilbert, D. P. (2006). Brief user’s guide: Dynamic systems estimation [Computer software manual]. Retrieved from http://cran.r-project.org/web/packages/dse/vignettes/Guide.pdf
   Google Scholar
• Grewal, M. S., & Andrews, A. P. (2001). Kalman filtering: Theory and practice using MATLAB (2nd ed.). New York, NY: Wiley.
   Google Scholar
• Grewal, M. S., & Andrews, A. P. (2008). Kalman filtering: Theory and practice using MATLAB (3rd ed.). Hoboken, NJ: Wiley.
   Google Scholar
• Gu, F., Preacher, K. J., Wu, W., & Yung, Y.-F. (2014). A computationally efficient state space approach to estimating multilevel regression models and multilevel confirmatory factor models. Multivariate Behavioral Research, 49, 119–129. doi:10.1080/00273171.2013.866537
   PubMed Web of Science ®Google Scholar
• Hamaker, E. L., Dolan, C. V., & Molenaar, P. C. M. (2005). Statistical modeling of the individual: Rationale and application of multivariate time series analysis. Multivariate Behavioral Research, 40, 207–233. doi:10.1207/s15327906mbr4002_3
   PubMed Web of Science ®Google Scholar
• Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20, 102–116. doi:10.1037/a0038889
   PubMed Web of Science ®Google Scholar
• Hamerle, A., Nagl, W., & Singer, H. (1991). Problems with the estimation of stochastic differential equations using structural equations models. Journal of Mathematical Sociology, 16, 201–220.
   Web of Science ®Google Scholar
• Hamilton, J. D. (1994). State-space models. In R. F. Engle & D. L. McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 3039–3080). New York, NY: Elsevier. Retrieved from http://www-stat.wharton.upenn.edu/stine/stat910/
   Google Scholar
• Hartikainen, J., Solin, A., & Särkkä, S. (2011). Optimal filtering with Kalman filters and smoothers. Espoo, Finland: Department of Biomedica Engineering and Computational Sciences, Aalto University School of Science.
   Google Scholar
• Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Helske, J. (2016a). KFAS: Exponential family state space models in R. Journal of Statistical Software, 1–38
   Web of Science ®Google Scholar
• Helske, J. (2016b). KFAS: Kalman filter and smoother for exponential family state space models [Computer software manual]. Retrieved from http://cran.r-project.org/package=KFAS (R package version 1.2.1)
   Google Scholar
• Holmes, E. E., Ward, E. J., & Wills, K. (2012). MARSS: Multivariate autoregressive state-space models for analyzing time-series data. The R Journal, 4(1), 30.
   Google Scholar
• Horn, J. L., & McArdle, J. J. (1980). Perspectives on mathematical/statistical model building (MASMOB) in reseach on aging. In L. W. Poon (Ed.), Aging in the 1980’s: Selected contemporary issues in the psychology of aging (pp. 503–541). Washington, DC: American Psychological Association. doi:10.1037/10050-037
   Google Scholar
• Jones, R. H. (1993). Longitudinal data with serial correlation: A state-space approach. Berlin, Germany: Springer. doi: 10.1007/978-1-4899-4489-4
   Google Scholar
• Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Basic Engineering, 82, 35–45. doi:10.1115/1.3662552
   Google Scholar
• Kalman, R. E., & Bucy, R. S. (1961). New results in linear filtering and prediction theory. Transactions of the ASME, Series D, Journal of Basic Engineering, 83, 95–108. doi:10.1115/1.3658902
   Google Scholar
• Kim, J., Zhu, W., Chang, L., Bentler, P. M., & Ernst, T. (2007). Unified structural equation modeling approach for the analysis of multisubject, multivariate functional MRI data. Human Brain Mapping, 28, 85–93. doi:10.1002/hbm.20259
   PubMed Web of Science ®Google Scholar
• King, A. A., Nguyen, D., & Ionides, E. L. (n.d.). Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software, 69(12), 1–43. doi:10.18637/jss.v069.i12
   Web of Science ®Google Scholar
• Kitagawa, G. (1977). An algorithm for solving the matrix equation X = FXFT + S. International Journal of Control, 25, 745–753. doi:10.1080/00207177708922266
   Web of Science ®Google Scholar
• Koopman, S. J., Shephard, N., & Doornik, J. A. (1999). Statistical algorithms for models in state space using SsfPack 2.2. Econometrics Journal, 2(1), 113–166. doi:10.1111/1368-423X.00023
   Google Scholar
• MacCallum, R. C., & Ashby, F. G. (1986). Relationships between linear systems theory and covariance structure modeling. Journal of Mathematical Psychology, 30, 1–27. doi:10.1207/S15327906MBR3801_5
   Web of Science ®Google Scholar
• MATLAB. (2014). Version 8.3 (r2014a). Natick, MA: The MathWorks.
   Google Scholar
• McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110–133.
   PubMed 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. doi:10.1007/BF02294246
   Web of Science ®Google Scholar
• Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement, 2, 201–218. doi:10.1207/s15366359mea0204_1
   Google Scholar
• Muthén, B. O., & Curran, P. J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2, 371–402. doi:10.1037/1082-989X.2.4.371
   Web of Science ®Google Scholar
• Muthén, B. O., & Satorra, A. (1995). Technical aspects of Muthén’s LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60, 489–503. doi:10.1007/BF02294325
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2014). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Neale, M. C., Hunter, M. D., Pritikin, J. N., Zahery, M., Brick, T. R., Kirkpatrick, R. M., … Boker, S. M. (2016). OpenMx 2.0: Extended structural equation and statistical modeling. Psychometrika, 80, 535–549. doi:10.1007/s11336-014-9435-8
   Web of Science ®Google Scholar
• Neale, M. C., & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113–120. doi:10.1023/a:1025681223921
   PubMed Web of Science ®Google Scholar
• Nesselroade, J. R., McArdle, J. J., Aggen, S. H., & Meyers, J. M. (2002). Dynamic factor analysis models for representing process in multivariate time-series. In D. S. Moskowitz & S. L. Hershberger (Eds.), Modeling intraindividual variability with repeated measures data: Methods and applications (pp. 235–265). Mahwah, NJ: Erlbaum.
   Google Scholar
• Olsson, U., & Bergman, L. R. (1977). A longitudinal factor model for studying change in ability structure. Multivariate Behavioral Research, 12, 221–241. doi:10.1207/s15327906mbr1202_8
   PubMed Web of Science ®Google Scholar
• Ou, L., Hunter, M. D., & Chow, S. (2017). What’s for dynr: A package for linear and nonlinear dynamic modeling in R. Journal of Statistical Software.
   Google Scholar
• Oud, J. H. L. (2002). Continuous time modeling of the cross-lagged panel design. Kwantitatieve Methoden, 69, 1–27.
   Google Scholar
• Pek, J., & Wu, H. (2015). Profile likelihood-based confidence intervals and regions for structural equation models. Psychometrika, 80, 1123–1145. doi:10.1007/s11336-015-9461-1
   PubMed Web of Science ®Google Scholar
• Petris, G. (2010). An R package for dynamic linear models. Journal of Statistical Software, 36(12), 1–16.
   Web of Science ®Google Scholar
• Priestley, M., & Subba Rao, T. (1975). The estimation of factor scores and Kalman filtering for discrete parameter stationary processes. International Journal of Control, 21, 971–975. doi:10.1080/00207177508922050
   Web of Science ®Google Scholar
• Pritikin, J. N., Hunter, M. D., & Boker, S. M. (2015). Modular open-source software for item factor analysis. Educational and Psychological Measurement, 75, 458–474. doi:10.1177/0013164414554615
   PubMed Web of Science ®Google Scholar
• Pritikin, J. N., Hunter, M. D., Von Oertzen, T., Brick, T. R., & Boker, S. M. (2017). Many-level multilevel structural equation modeling: An efficient evaluation strategy. Structural Equation Modeling, 24, 684–698. doi:10.1080/10705511.2017.1293542
   Web of Science ®Google Scholar
• Pritikin, J. N., Rappaport, L. M., & Neale, M. C. (2017). Likelihood-based confidence intervals for a parameter with an upper or lower bound. Structural Equation Modeling, 24, 395–401. doi:10.1080/10705511.2016.1275969
   PubMed Web of Science ®Google Scholar
• Rauch, H. E., Tung, F., & Striebel, C. T. (1965). Maximum likelihood estimates of linear dynamic systems. American Institute of Aeronautics and Astronautics Journal, 3, 1445–1450. doi:10.2514/3.3166
   Google Scholar
• Singer, H. (2011). Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms. Advances in Statistical Analysis (Asta), 95, 375–413. doi:10.1007/s10182-011-0172-3
   Web of Science ®Google Scholar
• Smith, G. L., Schmidt, S. F., & McGee, L. A. (1962). Application of statistical filter theory to the optimal estimation of position and velocity on board a circumlunar vehicle. Washington, DC: National Aeronautics and Space Administration.
   Google Scholar
• Sörbom, D. (1989). Model modification. Psychometrika, 54, 371–384. doi:10.1007/bf02294623
   Web of Science ®Google Scholar
• Voelkle, M. C., & Oud, J. H. L. (2015). Relating latent change score and continuous time models. Structural Equation Modeling, 22, 366–381. doi:10.1080/10705511.2014.935918
   Web of Science ®Google Scholar
• Voelkle, M. C., Oud, J. H., Von Oertzen, T., & Lindenberger, U. (2012). Maximum likelihood dynamic factor modeling for arbitrary N and T using SEM. Structural Equation Modeling, 19, 329–350. doi:10.1080/10705511.2012.687656
   Web of Science ®Google Scholar
• West, M., & Harrison, P. (1997). Bayesian forecasting and dynamic models. New York, NY: Springer.
   Google Scholar
• Wu, H., & Neale, M. C. (2012). Adjusted confidence intervals for a bounded parameter. Behavior Genetics, 42, 886–898. doi:10.1007/s10519-012-9560-z
   PubMed Web of Science ®Google Scholar
• Yang, M., & Chow, S. (2010). Using state-space model with regime switching to represent the dynamics of facial electromyography (EMG) data. Psychometrika, 75, 744–771. doi:10.1007/s11336-010-9176-2
   Web of Science ®Google Scholar