| Decades of methodological advancements have oriented psychometricians toward comparing alternative models within a confirmatory framework. Nonlinear dynamical systems analyses, by contrast, capitalize heavily on the notion of a "model-free", exploratory approach. The lack of more practical tools for fitting nonlinear dynamical models to observed phenomena suggests the need for more research in this area. In this dissertation, I present and compare the robustness of three Kalman filter approaches for fitting nonlinear dynamic models, namely, the extended Kalman filter (EKF), the square-root unscented Kalman filter (SRUKF), and the square-root central difference Kalman filter (SRCDKF). The strengths and weaknesses of these three approaches were evaluated using three models, including (1) a linear damped oscillator model, (2) the classical predator-prey model, and (3) Kenny and Judd's (1984) level-based model with interaction between two latent variables. Whereas the EKF yielded a high percentage of non-convergent cases, the SRUKF and SRCDKF, if tuned appropriately, were able to recover parameter estimates very accurately, even under high noise conditions (e.g., with 50% measurement noise). However, standard errors were consistently underestimated. Potential approaches for dealing with this problem, and other issues associated with the Kalman filter approaches are discussed in relation to current applications in psychology. |
