I'm fitting a MIMIC model using categorical indicators and MLR. The model includes an interaction between a continuous random latent variable (theta) and an observed causal indicator (z) defined using XWITH and |.
It seems that by default the covariances between the interaction and theta and the interaction and z are 0. Is it possible to estimate these covariances?
I'm having difficulty finding documentation describing the methods implemented for the latent variable interactions. Is there a technical appendix?
We found something that said procedures were in line with Klein & Moosbrugger (2000). But Marsh et al. (2004) says that LMS method was superseded by the QML method in Klein & Muthen (2002) -- is that in Mplus? Either way, is it possible to get that unpublished paper?
Another question about this same project. I'm trying to keep track of the assumptions made by LMS. Are we assuming the 2 variables involved in the interaction are continuous, latent, and bivariate normal? I am interacting one continuous latent with one observed binary.
Is there also an assumption that the observed indicators of those latent variables are continuous and normal? So it's not good to be using LMS with categorical observed data (even though I'm using "categorical" and MLR)?
Is there something about the "different algorithm" for LMS that would make it OK to do what I'm doing? Seems like I'm violating 2 by using LMS with this model.
This means that you can use XWITH or multiple group analysis to test the interaction between an observed categorical variable and a continuous latent variable. With multiple group analysis, you use the observed categorical variable as a grouping variable.
Luke W. Hyde posted on Thursday, February 10, 2011 - 7:52 am
Dear Drs. Muthen,
I'm running an SEM with two interactions using the XWITH command. One of the interactions involves a binary observed variable and a continuous latent variable. The binary variable itself is essentially exogenous - it only predicts other variables and is not predicted by variables in the model. Should this variable be signified to the model as categorical? Given its involvement in an interaction is the variable technically an independent or dependent variable?
I have run the model with the variable specified as categorical or and also without this specification. When the variable is specified as categorical, the model runs and terminates normally. When it is not specified as categorical, the model cannot terminate normally and has various not-positive definite errors (and even when changing other terms to fix the error, another error comes up). I was initially assuming the problem running the model was multicolinearity with 2 interaction terms.Is that possible?
So my main questions are: 1. Should I specify this categorical variable as categorical in the model? 2. If I shouldn't, are there anyways to decrease multicolinearity with 2 interactions (involving 2 continous, 1 categorical variable) within the same model?