We are examining whether the experience of trauma affects the underlying latent variable structure of a big five personality measure. We have shown that that there is little variance in the latent variable structures from pre-trauma to post-trauma. Now we want to see if the degree to which participants were exposed affects the extent of invariance between pre and post-trauma. We could always divide participants into high and low trauma, and rerun separate invariance tests. But does anyone know how to achieve this sort of thing with a continuous measure of trauma?
You have the Mplus option of CONSTRAINT = trauma; in the VARIABLE command which is illustrated in UG ex 5.23. This way, the trauma score can influence measurement parameters continuously. A simple variation on this theme is the alternative of MIMIC modeling where a trauma covariate influences certain items directly, allowing for measurement intercept non-invariance. This can be done effectively using BSEM (see my talk handouts and 2012 Psych Meth article).
But isn't low (or zero) trauma the same as pre-trauma? And you found no measurement differences between pre- and post-trauma. Perhaps you are saying that post-trauma can encompass substantially different degrees of trauma.
Thanks for your kind reply. The participants completed a big five measure before and after a tornado. As you guessed, they reported varying degrees of exposure to the tornado. Thus we want to test whether the degree of model (in)variance is associated with the degree to which they were exposed. We are hoping to find that even at high levels of exposure the big five measure is measuring the same constructs in the same way that it is operating for low exposure subjects.
I will look at the examples that ou have pointed out.
Below is the measurement model for time1 and time2 big five personality data. "prop" is a continuous measure of trauma experienced during a tornado that occurred between those time points. How do we model the effects of that exposure variable on the invariance of the models across the two time points.
As a starting point, why don't you first do a MIMIC model for one of the time points with prop as a covariate. Then look for direct effects - that is, evidence of non-invariance as a function of prop - as in our teaching in our Day 1 short course; see the Topic 1 handout and video on our website.