I am currently at the beginning stages of learning Mplus (version 4.1 [a friend is letting me use his computer while he is on holidays])to analyze some data. I am testing a path analysis and want to test for moderation. I see on page 481 in the manual, that I should use the define command. If I were doing a latent variable analysis, I would have the following:
Analysis: Type = random; Algorithm =integration. (1)Is this what I should type for my model?
(2)Do I simply muliply my two variables to create the interaction?
(3)I have 5 possible moderators. Do I test five different models or one model with the five?
Any help is appreciated. I am a PhD student and am just learning this program. Thanks.
If the interaction is between two observed variables, you would multiply them together. If one of the variables is a latent variable, you would use the XWITH command. See the user's guide on the website for further information.
As you see there is an interaction term in Eq.2 that contains y1. When I substitute (Eq.1) in (Eq.2), x2 is correlated with the error term, which causes an endogeneity problem. I found a friend of mine who has Mplus program. The program does not seem to support a model I suggested. Being less familiar with SEM literature, I haven't been able to find a correct way of estimating beta22. 2SLS wouldn't work either due to non-linearity. Could someone help me on this issue?
I don't think that there are any problems in estimating beta22. In fact you don't need equation 1 at all. You can simply estimate equation 2 directly and ML will give you the consistent estimates.
If you choose to substitute Y1 in the second equation and then estimate beta22 from the combined equation you can still get consistent estimates if you specify that [E with X2] is a free parameter, but you need to specify the correct parameter constraint for this parameter with Mplus Model Constraint which will also involve gamma11.
Maybe I am asking a totally trivial question, but it is not immediately clear to me how the Model Constraint command can resolve the endogeneity problem that becomes visible when I substitute (Eq.1) into (Eq.2). Doesn't this command just specify relationship among parameters?
You can specify the correlation between the covariate and the residual as part of model constraint, but again ... you should not substitute (Eq.1) into (Eq.2) for the sole purpose of obtaining unbiased parameter estimates of that model.
See Example 5.23 in the user's guide for how to use model constraints to build a model with varying variance (Y2 variance) and varying correlation (Y2 with X2).