Tuesday, November 19, 2013

Cross-sectional and longitudinal: data vs. models

Gollob & Reichardt have clarified for me the issue of time (=changes) and cases (=variability, differences), and then of course McArdle has taken these explanations to another level, with analyses of changes and differences, and changes in differences, and differences in changes.
So, one can have
1. Cross-sectional Data and Cross-sectional Models
2. Longitudinal Data and Longitudinal Models 
3. Cross-sectional Data and Longitudinal Models[1: p. 82 on]

In other words, time can be built in models with cross-sectional data, see my last figure in http://evaluatehelp.blogspot.com/2013/08/placeholders.html

What I want to show here however is how time can be extracted from repeated cross-sectional data, particularly when one is interested in development and changes in the context of natural/historical development. One of the original visual introductions to this approach is in Muthen (2000) (there are certainly earlier ones...):

In the context of say students (grades 6th to 12th) surveyed every 2 years or so, one can build a dataset structured as 'repeated", i.e. with 'year' and 'cohort' fields into it, to compare changes over time as done here [4]:  http://www.getcited.org/pub/103503915 

1. Gollob, H. F., & Reichardt, C. S. (1987). Taking account of time lags in causal models. Child Development, 58(1), 80-92.
2. Gollob, H. F., & Reichardt, C. S. (1991). Interpreting and estimating indirect effects assuming time lags really matter. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change: Recent advances, unanswered questions, future directions (pp. 243-259). Washington, DC, US: American Psychological Association.
3. Muthén, B. O. (2000). Methodological issues in random coefficient growth modeling using a latent variable framework: Applications to the development of heavy drinking. In J. Rose, L. Chassin, C. Presson & J. Sherman (Eds.), Multivariate applications in substance use research (pp. 113–140). Hillsdale: Erlbaum.
4. Combining missing-by-design and mixture modeling to assess impact of a community-wide interventions. A social marketing and text messaging campaign to reduce alcohol use among high school students. E Coman, G Rots, S Suggs, S Fuxman - 2012 Modern Modeling Methods, 2012