ABSTRACT
Longitudinal analyses by latent curves methods have become useful to model a general trajectory of behavioral responses (Rao, 1958; McArdle & Epstein, 1987; McArdle & Hamagami, 1991, 1992; Meredith & Tisak, 1990). As a methodological alternative to longitudinal data analyses, the dynamic system approach by means of difference or differential equations allows an investigation of both inter-and intravariable cause-effect relationships on the time dimension (Arminger, 1986; Beddington, Free, & Lawton, 1975; Coleman, 1968; Goldberg, 1986; McArdle, 1988; Molenaar, 1985; Nesselroade, McArdle, Aggen, & Meyers, 2001; Nesselroade & Molenaar, 1999; Tuma & Hanna, 1986; Sheinerman, 1996). In a similar vein, McArdle and Nesselroade (1994) introduced the use of latent difference scores on longitudinal factor scores derived from the multivariate longitudinal structural equation modeling (SEM) (see also McArdle, 1988). In subsequent works,McArdle and Hamagami (1995,2001) expanded the use of difference equations applied to multiple occasions, which structurally allows dynamic interpretations. Structural latent difference score models are specifically
designed to accommodate interindividual variability of initial conditions and the rate of change of the dynamic system model among different people (Nesselroade, 1991). Hamagami and McArdle (2001) demonstrated that dynamical parameters of structured latent difference score models were accurately recovered by traditional SEM under a variety of missing data situations by Monte Carlo simulations (Little & Rubin, 1987; McArdle, 1994; Schafer, 1997). Both deterministic and stochastic parameters of the dynamics system were correctly recovered using full information maximum likelihood estimation (Lange, Westlake, & Spence, 1976) using Mx program (Neale, Boker, Xie, & Maes, 2003).
