Conferences

In the structural equation modelling (SEM) literature, two models for the analysis of longitudinal data become very popular in the past: autoregressive (AR) cross-lagged models and latent trajectory (LT) models. Curran and Bollen (2001) and Bollen and Curran (2004), however, argued that, theoretically, there are many instances when both the processes described by the AR model and the processes described by the LT model are plausible. They proposed the autoregressive latent trajectory (ALT) model, which captures features of both. The discrete-time approach in the ALT model has been criticized by Delsing and Oud (2008), who proposed a continuous time version of the ALT model, using stochastic differential equations, called “continuous time autoregressive latent trajectory” (CALT) model. In the paper, the linear component appearing in both the ALT and the CALT models will be criticized on several counts. It is shown that most of the problems associated with the linear component are solved by a second-order stochastic differential equation model.

References:

Bollen, K.A., and Curran, P.J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.
Curran, P.J. and Bollen, K.A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In A. Sayer and L. Collins (Eds.), New methods for the analysis of change (pp. 107-135). Washington, DC: American Psychological Association.
Delsing, M.J.M.H., & Oud, J.H.L. (2008). Analyzing reciprocal relationships by means of the continuous-time autoregressive latent trajectory model. Statistica Neerlandica, 62, 58-82.