Our next topic is longitudinal SEM, actually a particular type of longitudinal design called a panel study, where the same respondents are followed up over time (longitudinal panel studies should not be confused with online/consumer panels). An example of a longitudinal panel study is the University of Michigan's Panel Study of Income Dynamics. Within the longitudinal panel design, we will learn about autoregressive and cross-lagged paths. Equality constraints will play a major role here.
One of the major purposes of longitudinal panel studies is to get a good approximation of causality. Short of actual experimentation, a longitudinal panel study is probably as good a design as there is for inferring causation. A couple of lecture modules from my methods course (here and here) may be helpful, along with a 2009 article from Child Development.
The following article by Albert Farrell should also be helpful. We will go over sections of it in class.
Farrell, A.D. (1994). Structural equation modeling with longitudinal data: Strategies for examining group differences and reciprocal relationships. Journal of Consulting and Clinical Psychology, 62, 477-487.
The article actually covers both longitudinal-panel models and multiple-group models. The two are separate topics; a study can have one of these aspects and not the other. We'll also use the Farrell article to discuss multiple-group modeling, but later on.
This PowerPoint slideshow by Patrick Sturgis is also helpful.
UPDATE (April 13, 2011): I've made some new graphics to illustrate two modeling conventions associated with panel SEM.
The correlated residuals are sometimes known as the "fountain effect" for their visual appearance. The fountain at Las Vegas's Bellagio Hotel nicely illustrates this, as seen below (from GoVegas.about.com).
UPDATE (March 18, 2010): Cameron McIntosh sent a list of references on longitudinal/panel analysis to the SEMNET listserv discussion group. The list, which I've lightly edited, may be helpful for students seeking to pursue the topic in greater detail.
Little, T.D., Preacher, K.J., Selig, J.P., & Card, N.A. (2007). New developments in latent variable panel analyses of longitudinal data. International Journal of Behavioral Development, 31, 357-365. [Copy available on Dr. Preacher's publications page; see heading "Longitudinal factorial invariance."]
Collins, L.M. (2006). Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review of Psychology, 57, 505-528.
Phillips, J.A., & Greenberg, D.F. (2007). A comparison of methods for analyzing criminological panel data. Journal of Quantitative Criminology, 24, 51-72.
Preacher, K.J., Wichman, A.L., MacCallum, R.C., & Briggs, N.E. (2008). Latent growth curve modeling (part of the series Quantitative Applications in the Social Sciences, vol. 157). Thousand Oaks, CA: Sage.
Bollen, K.A., & Brand, J.E. (2008). Fixed and random effects in panel data using structural equation models. Los Angeles, CA: California Center for Population Research, UCLA (online).
Wu, A.D., Liu, Y., Gadermann, A.M., & Zumbo, B.D. (2009). Multiple-indicator multilevel growth model: A solution to multiple methodological challenges in longitudinal studies. Social Indicators Research (published online).
More advanced:
Curran, P.J., & Bollen, K.A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L.M. Collins & A.G. Sayer (Eds.), New methods for the analysis of change (pp. 105-136). Washington, DC: American Psychological Association.
Bollen, K.A., & Curran, P.J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.
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.
Oud, J.H.L. (2002). Continuous time modeling of the cross-lagged panel design. Kwantitatieve Methoden 69, 1-26.
Hamaker, E.L. (2005). Conditions for the equivalence of the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances. Sociological Methods and Research, 33, 404-416.
Voelkle, M. C. (2008). Reconsidering the use of autoregressive latent trajectory (ALT) models. Multivariate Behavioral Research, 43,564-591.
