Tuesday, August 20, 2013

Can you get more latents than me?

Output of a Latent Change Score model with Growth Modeling elements and measurement error

Can you beat my 10/2 ratio latent/observed variables? Here's a simple example of a model looking at changes in 1 observed outcome only, from Y1 to Y2. The Latent Change Score setup [see an excellent intro here] allows one to answer this question in a paired t-test kind of way, but can also accommodate growth modeling elements [intercept=initial level and slope=constant additive change factor]; plus, one can incorporate measurement error, i.e. strip the true measures of unreliability (assumed to be a 10% for example). This leads to the output above [this is an application using the data mentioned here under 'The paired t-test as a simple latent change score model']

*** By the way, in case you wonder about the meaning of each of those latent variables, here's a similar example of such a struggle to find the hidden side of reality, or what's behind the observed facts:

Tuesday, August 6, 2013

Illustrations of single- and multi-group models with some variables missing/unobserved in some groups

Fig 5.2 in
Hayduk, L. A. (1996). LISREL issues, debates, and strategies: Johns Hopkins University Press.
(Ch. 5, Stacked Models with Differing Sets of Indicator Variables_155-189).

Fig. 18.10 in
McArdle, J. J., & Nesselroade, J. R. (2003). Growth curve analysis in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Handbook of psychology (Vol. 2, pp. 447–480). New York: Pergamon.

Fig. 2 in
McArdle, J. J., & Hamagami, F. (2004). Methods for dynamic change hypotheses. In K. v. Montfort, J. Oud & A. Satorra (Eds.), Recent Developments on Structural Equation Models: Theory and Applications (Vol. 19, pp. 295-336).

Fig. 5.15 in
McArdle, J. J., & Bell, R. (2000). An introduction to latent growth models for developmental data analysis. In T. Little, K. Schnabel & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: practical issues, applied approaches, and scientific examples (pp. 69-107). Mahwah, NJ: Erlbaum.

Fig. 3.2 in
McArdle, J. J., & Hamagami, F. (2003). Longitudinal tests of dynamic hypotheses on intellectual abilities measured over sixty years. In C. S. Bergeman & S. M. Boker (Eds.), Methodological Issues in Aging Research (pp. 31-98): Lawrence Erlbaum Associates, Mahwah.

Fig. 2 in
McArdle, J. J., & Woodcock, R. W. (1997). Expanding test–retest designs to include developmental time-lag components. Psychological Methods, 2(4), 403-435. doi: 10.1037/1082-989x.2.4.403
Fig 8.3 in
Hamagami, F., & McArdle, J. J. (2001). Advanced studies of individual differences linear dynamic models for longitudinal data analysis. In G. Marcoulides & R. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 203-246).

Slide 23 in
Recapturing Time in Evaluation of Causal Relations: Illustration of Latent Longitudinal and Nonrecursive SEM Models  for Simultaneous Data. Presented at the American Evaluation Association convention, Nov. 14, 2009, Orlando FL http://comm.eval.org/eval/resources/viewdocument/?DocumentKey=5f351c13-1f91-42b7-85fe-450d19f46fca