Conferences

In the structural equation modeling (SEM) literature, two models for the analysis of longitudinal data became 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. Recently, the linear component appearing in both the ALT and the CALT models has been criticized on several counts. Papers discussing applications, positive and negative experiences in the application as well as critical examinations, weaknesses, improvements and alternatives for the AR, LT, ALT and CALT models are welcome.

References:

Bollen, K.A. and P.J. Curran (2004), Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.
Curran, P.J. and K.A. Bollen (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.