I would like to confirm that there are qualitative as well as quantitative differences in items endorsed by the respective classes in a LCA of PTSD symptoms in traumatised people, ie. that the classes not only differ along a gradient of severity, but that the different items are endorsed to different extents in the different classes.
For instance, in an article addressing a similar question, it was argued that the groups identified in the 3 class solution were qualitatively different, as the prevalence of symptoms differed substantialy between groups on one of the constructs identified in previous factor analytic work in PTSD samples ("numbing" symptoms). I was wondering whether Mplus provides a more rigorous means of confirming that groups differ qualitatively? (ques. 1)
I would like to conduct a confirmatory factor analysis to help interpret differences in symptom prevalence. Specifically, I was hoping to construct equivalent confirmatory factor analytic models for the symptomatic groups that are derived, and then compare the models for dimensional, configural, metric, strong factorial and strict factorial invariance. Is this easily accomplished in Mplus (ques. 2) and, more importantly, would this be a viable strategy in determining whether, and in identifying how, different classes differ with respect to different symptom clusters? (ques. 3)
It sounds like your questions can be answered by using factor mixture analysis. An introduction to this topic can be found in the following paper which can be downloaded from our website:
Muthén, B. (2006). Latent variable hybrids: Overview of old and new models. Forthcoming in Hancock, G. R., & Samuelsen, K. M. (Eds.). (2007). Advances in latent variable mixture models. Charlotte, NC: Information Age Publishing, Inc.
If measurement invariance holds across classes (thresholds and factor loadings the same for all classes), then factor mean differences would be a quantitative difference. If not, the classes would differ qualitatively in your terms.
Thank you for your rapid response. FMA does sound like it is what I need. I was wondering whether you could help me with something else.
I would like to use FMA on one sample, and then allocate participants from another sample in a post-hoc fashion to the classes detected in step one (without performing LSA or FMA on the second sample). Is there any agreed upon method of doing this? Can one perhaps use the conditional probability scores for this purpose?
You could analyze the second sample with all parameters fixed at the estimated parameter values from the first sample - you would then request posterior probabilities for this second sample analysis and use them for classification.