Latent Differential Equation Models for Binary and Ordinal Data

REFERENCES

• Achen, C. H. (1991). A polychotomous linear probability model. Berkeley, CA: Political Methodology Society.
   Google Scholar
• Berkson, J. (1944). Application of the logistic function to bio-assay. Journal of the American Statistical Association, 39, 357–365.
   Web of Science ®Google Scholar
• Berry, W. D. (1993). Understanding regression assumptions. Thousand Oaks, CA: Sage.
   Google Scholar
• Bisconti, T. L., Bergeman, C. S., & Boker, S. M. (2004). Emotional well-being in recently bereaved widows: A dynamical systems approach. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 59, 158–167. doi:10.1093/geronb/59.4.P158
   PubMed Web of Science ®Google Scholar
• Bliss, C. I. (1934). The method of probits. Science, 79, 38–39. doi:10.1126/science.79.2037.38
   PubMed Web of Science ®Google Scholar
• Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51. doi:10.1007/BF02291411
   Web of Science ®Google Scholar
• Boker, S. M. (2002). Consequences of continuity: The hunt for intrinsic properties within parameters of dynamics in psychological processes. Multivariate Behavioral Research, 37, 405–422. doi:10.1207/S15327906MBR3703_5
   PubMed Web of Science ®Google Scholar
• Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2009). Generalized local linear approximation of derivatives from time series. In S. M. Chow & E. Ferrar (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 161–178). New York, NY: Taylor & Francis.
   Google Scholar
• Boker, S. M., & Graham, J. (1998). A dynamical systems analysis of adolescent substance abuse. Multivariate Behavioral Research, 33, 479–507. doi:10.1207/s15327906mbr3304_3
   PubMed Web of Science ®Google Scholar
• Boker, S. M., Neale, M. C., Maes, H., Wilde, M., Spiegel, M., Brick, T., … Fox, J. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76, 306–317. doi:10.1007/s11336-010-9200-6
   PubMed Web of Science ®Google Scholar
• Boker, S. M., Neale, M. C., & Rausch, J. R. (2003). Latent differential equation modeling with multivariate multi-occasion indicators. In H. O. K. Van Montfort & A. Satorra (Eds.), Recent developments on structural equation models: Theory and applications (pp. 151–174). Amsterdam, The Netherlands: Kluwer.
   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. doi:10.1207/S15327906MBR3701_06
   PubMed Web of Science ®Google Scholar
• Boker, S. M., Staples, A. D., & Hu, Y. (2016). Dynamics of change and change in dynamics. Journal for Person-Oriented Research, 2(1–2), 34–55. doi:10.17505/jpor
   PubMedGoogle Scholar
• Butner, J., Amazeen, P. G., & Mulvey, G. M. (2005). Multilevel modeling of two cyclical processes: Extending differential structural equation modeling to nonlinear coupled systems. Psychological Methods, 10, 159–177. doi:10.1037/1082-989X.10.2.159
   PubMed Web of Science ®Google Scholar
• Cattel, R. B. (1959). The dynamic calculus: Concepts and crucial experiments. In M. R. Jones (Ed.), The Nebraska symposium on motivation (pp. 84–134). Lincoln, NE: University of Nebraska Press.
   Google Scholar
• Chow, S.-M., Hamaker, E. L., Fujita, F., & Boker, S. M. (2009). Representing time-varying cyclic dynamics using multiple-subject state-space models. British Journal of Mathematical and Statistical Psychology, 62, 683–716. doi:10.1348/000711008X384080
   PubMed Web of Science ®Google Scholar
• Duncan, T. E., Duncan, S. C., Strycker, A. L., Li, F., & Alpert, A. (1999). An introduction to latent variable growth curve modeling: Concepts, issues, and applications. Mahwah, NJ: Erlbaum.
   Google Scholar
• Finan, P. H., Hessler, E. E., Amazeen, P. G., Butner, J., Zautra, A. J., & Tennen, H. (2010). Oscillations in daily pain prediction accuracy. Nonlinear Dynamics, Psychology, and Life Sciences, 14(1), 27–46.
   PubMed Web of Science ®Google Scholar
• Genz, A. (1991). Subregion adaptive algorithms for multiple integrals. Contemporary Mathematics (Statistical Numerical Integration), 115, 23–31.
   Google Scholar
• Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387–404. doi:10.1007/BF00152012
   Web of Science ®Google Scholar
• Lee, S. Y., Poon, W. Y., & Bentler, P. (1990). Full information likelihood analysis of structural equations models with polytomous variables. Statistics and Probability Letters, 9, 91–97. doi:10.1016/0167-7152(90)90100-L
   Web of Science ®Google Scholar
• Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 140, 1–55.
   Google Scholar
• Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
   Web of Science ®Google Scholar
• Magee, J. C., & Teachman, B. A. (2007). Why did the white bear return? Obsessive–compulsive symptoms and attributions for unsuccessful thought suppression. Behaviour Research and Therapy, 45, 2884–2898. doi:10.1016/j.brat.2007.07.014
   PubMed Web of Science ®Google Scholar
• McArdle, J. J., & Hamagami, F. (1992). Modeling incomplete longitudinal and cross-sectional data using latent growth structural models. Experimental Aging Research, 18, 145–166. doi:10.1080/03610739208253917
   PubMed Web of Science ®Google Scholar
• Muthén, B. O. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132. doi:10.1007/BF02294210
   Web of Science ®Google Scholar
• Odgers, L. C., Mulvey, E. P., Skeem, J. L., Gardner, W., Lidz, C. W., & Schubert, C. (2009). Capturing the ebb and flow of psychiatric symptoms with dynamical systems models. The American Journal of Psychiatry, 166, 575–582. doi:10.1176/appi.ajp.2008.08091398
   PubMed Web of Science ®Google Scholar
• Oud, J. H. L., & Jansen, R. A. (2000). Continuous time state space modeling of panel data by means of SEM. Psychometrica, 65, 199–215. doi:10.1007/BF02294374
   Web of Science ®Google Scholar
• Ryff, C. D., Seeman, T., & Weinstein, M. (2013). National Survey of Midlife Development in the United States (MIDUS II): Biomarker project, 2004–2009 (ICPSR29282-v6). Ann Arbor, MI: Inter-university Consortium for Political and Social Research. doi:10.3886/ICPSR29282.v6
   Google Scholar
• Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, 34, 100–114.
   Web of Science ®Google Scholar
• Singer, H. (1993). Continuous-time dynamical systems with sampled data, errors of measurement and unobserved components. Journal of Time Series Analysis, 14, 527–545. doi:10.1111/j.1467-9892.1993.tb00162.x
   Google Scholar
• Soetaert, K., Petzoldt, T., & Setzer, R. W. (2010). Solving differential equations in R: Package deSolve. Journal of Statistical Software, 33(9), 1–25. doi:10.18637/jss.v033.i09
   PubMed Web of Science ®Google Scholar
• Takane, Y., & De Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408. doi:10.1007/BF02294363
   Web of Science ®Google Scholar
• Von Oertzen, T., & Boker, S. M. (2010). Time delay embedding increases estimation precision of models of intraindividual variability. Psychometrika, 75, 158–175. doi:10.1007/s11336-009-9137-9
   PubMed Web of Science ®Google Scholar
• Weare, B. C., & Nasstrom, J. S. (1982). Examples of extended empirical orthogonal function analyses. Monthly Weather Review, 110, 481–485. doi:10.1175/1520-0493(1982)110<0481:EOEEOF>2.0.CO;2
   Web of Science ®Google Scholar