I have a question about using LCA to test the effects of an intervention on the slope. Earlier work by Curran and Muthen (American journal of Community Psychology, 1999) proposed a technique in which the model is first fit for the control group. This is followed by the model for treatment group and another latent factor for treatment slope. This is shown in figure 1 on page 579. Curran and Muthen demonstrate in figure 2 on page 583 that this method is more powerful that more standard analyses such as ANCOVA.
My question is” “How is this technique different from an LCA in which we fit the model for both groups and regress the slope onto a binary variable indicating treatment condition?”
The Curran and Muthen analysis uses multiple group analysis where the groups are known -- treatment and control. I'm not sure how latent class analysis comes into play here. In LCA, the classes are unobserved.
My appolgies for not being clear By LCA I meant Latent Curve Analysis. In this model we are aware of the treatment group assignment but are fitting the growth curve model as a Latent variable model. The treatment condtion X will be included in the model as a time invariant covariate.
Thus, we would fit the model for all cases and then regress the slope onto the binary TX vs Control variable, or with a three group design use X1 and X2 as dummy variables.
There are two differences. The first is that with multiple group analysis, you can see the difference between more parameters than when you use the grouping variable as a covariate where only mean shifts can be examined.
The second specific to the Muthen/Curran paper, is that the extra treatment factor represents development beyond that of the control group. It is a type of value-added analysis. It is development above what would be expected without a treatment.