Factor Score and Parameter Estimation in Nonlinear Dynamical Systems Models

This chapter presents the key aspects of a nonlinear Kalman filter technique. This technique is suited for fitting nonlinear dynamical systems models as well as for estimating longitudinal factor scores. The chapter summarizes several alternative techniques that are used primarily to capture complex nonlinear dynamics using time series data. In some of the early modelling approaches, reparameterized versions of the integral solutions of a set of differential equations were fitted as linear regression or structural equations models without the appropriate nonlinear constraints. One advantage of the joint estimation approach utilized is that it provides researchers with a more flexible way of representing the dynamics of time-varying parameters in conjunction with the dynamics of the state variables. Much of the work in fitting nonlinear models in psychology was instigated by the work of D. A. Kenny and C. M. Judd, who highlighted some issues in fitting a specific cross-sectional model with interaction between two latent variables.