Mplus Discussion > Structural Equation Modeling >
 Anonymous posted on Sunday, May 01, 2005 - 10:11 am
Quick question. When I'm mimic modeling in the two step format (i.e., measurement model and structural model), do I retain the mimic factors on the measurement part of the model when I am examining the structural model? New to this and have a short hang up.
 Anonymous posted on Sunday, May 01, 2005 - 10:14 am
Oh one other thing. When I'm using a random slopes model, how can I write the syntax so that I can mimic my factors on the interaction term?

Thanks in advance for addressing these two questions.
 bmuthen posted on Sunday, May 01, 2005 - 4:52 pm
Re the first question, yes you want to retain the measurement model when you add the rest of the model.

Re your second question, I am not sure what you mean by "mimic my factors on the interaction term"; please clarify.
 Anonymous posted on Tuesday, May 03, 2005 - 4:21 am
Re the second question, I want to regress a measure of race (x1) on my interaction term
(f1xf2 | f1 XWITH f2). How may I be able to do this?
 Linda K. Muthen posted on Tuesday, May 03, 2005 - 6:14 am
x1 ON f1xf2;
 Anonymous posted on Tuesday, May 03, 2005 - 7:57 am
Thank you linda, but I need race to be the independent variable and not the dependent variable. So, it makes more sense to me that f1xf2 on x1. However, Mplus will not allow this argument in the program. Your syntax will give me the desired regression?
 bmuthen posted on Tuesday, May 03, 2005 - 9:42 am
Interactions are products of 2 or more variables used to better predict a dependent variable. Interactions are not used as dependent variables. Perhaps you intend for race to give different effects of the interaction on the dependent variable? If so, you can interact race with the interaction, giving a 3-way interaction.
 Anonymous posted on Tuesday, May 03, 2005 - 3:14 pm
Yes, this is exactly what I'm wanting to do. Will Linda's syntax provide that?
 bmuthen posted on Tuesday, May 03, 2005 - 3:20 pm
You get the 3-way interaction using the 2 statements:

f1xf2 | f1 xwith f2;

rf1xf2 | r xwith f1xf2;

where "r" is the race variable. And then you get the regression using:

y on rf1xf2;

where y is your dependent variable.
 Anonymous posted on Tuesday, May 03, 2005 - 4:00 pm
Thank you
 Anonymous posted on Thursday, May 05, 2005 - 8:29 pm
I'm comparing the fit of a MIMIC model with a common factor model. The two models for comparison are non-nested, and I want to select the model most consistent with the data. I know people often use information indices, AIC etc, is there any reason rmsea can't also be used?
 Linda K. Muthen posted on Friday, May 06, 2005 - 7:13 am
I think the problem with comparing non-nested models is that there is no way to assess whether one fit statistic is significantly better than another. So RMSEA would have that same problem.
 Paul A.Tiffin posted on Saturday, December 12, 2009 - 6:13 am
Dear Mplus Team,
I have a quick question about a MIMIC model I am working on. I have categorical dependent variables that make up the well fitting basic CFA model with 2 factors and 19 ordinal indicators but I wanted to add in two covariates (to create a MIMIC model); one which is continuous, if significantly skew (i.e. non-normal) and one binary variable. When specifying the model I note only dependent variables can be defined as categorical. How should you approach covariates that are either categorical or non-normal continuous? In the latter case should I just attempt a transformation (e.g. log) to obtain normally distributed variable?
Your help as always is appreciated and I am continuing to very much enjoy using Mplus.
 Bengt O. Muthen posted on Saturday, December 12, 2009 - 9:06 am
Covariates need not be normally distributed. Binary covariate are treated as "continuous" as in regular regression, that is, they influence the intercept of the dependent variable when they change from say 0 to 1.

I would only transform a skewed covariate if I believed that this would make the linearity assumption more plausible.
 Paul A.Tiffin posted on Saturday, December 12, 2009 - 9:09 am
Thanks for your swift response Professor Muthen. Your help is much appreciated.
 Johannes Bauer posted on Thursday, August 30, 2012 - 7:54 am
I am trying to run a MIMIC model with two covariates that is similar to the one on slide 184 in the Topic 1 handout: A dichotomous (school type) and a continuous (SES) observed variable predict several continuous latent variables. School type and SES are correlated (manifest r ~ .5).

(1) I want to include the correlation between school type and SES in the model, but according to the error messages that seems not possible. I read elsewhere in the forum that a way to get the correlation is to replace it by a regression path (e.g., school type on ses). Can you please explain why I cannot directly include the correlation? Am I right that the model shown on slide 184 in the Topic 1 handout shows the correlation, but the subsequent mplus example do not include it?

(2) If I want to include the SES x school type interaction as a third covariate the interaction term will be correlated with the variables it is composed of. Omitting these correlations will result in bad fit.
Can I model the correlations among the three covariates using regression paths, too? If yes, how? If no, is there another possibility to handle the correlations?

Many thanks in advance
 Linda K. Muthen posted on Thursday, August 30, 2012 - 10:24 am
Although we show the correlation in the path diagram, the correlation is not estimated. In regression, the model is estimated conditioned on the observed exogenous variables. Their means, variances, and covariances are not model parameters. This does not mean the covariances are zero. To see their values, ask for descriptive statistics using TYPE=BASIC.

You can create the interaction in the DEFINE command and use it on the right-hand side of ON.
 Ryan Krone posted on Saturday, May 02, 2015 - 4:14 pm

I'm trying to replicate a World Bank study using a MIMIC model that incorporates individual observations over time.
However, I'm having a very difficult time understanding how they are specifying their model given my
understanding of MIMIC models. Their data consists of country observations over a 8 year time period,
roughly 1500 country-year observations total - trying to estimate the informal economy in each country over
the time period.

A link to the pdf of the paper is here: http://hdl.handle.net/10986/3928

The model as described in the paper and translated into Mplus code:
iecon BY currency grlaborf grgdppc;
iecon ON sizegov unemploy gdppc goveff;

I have two questions:

1) I can understand how this would work with a cross-sectional design but how would you incorporate
time in this setup? Is this a multi-level MIMIC design? - first level time, second level country? And they just haven't
articluated this in the paper?

2) What would be the difference between this model and a Latent Growth Curve Model?
 Bengt O. Muthen posted on Sunday, May 03, 2015 - 12:31 pm
It looks like they ignored the time aspect. They also don't say if country is a multi-group feature (fixed mode) or a cluster feature (random mode). With a random model approach, you could do multilevel modeling as you say, or simply Type=Complex with Cluster=country.

Since there are only 8 time points you could do a multiple-indicator growth analysis of the factor over time. This would call for scalar measurement invariance over time. That could be with country in either fixed or random mode. In fixed mode, our Alignment work is also relevant.
 Ryan Krone posted on Sunday, December 13, 2015 - 8:39 am
Drs. Muthen,

I'm working with a MIMIC model and i've specified an interaction between two continuous covariate indicators and want to observe the marginal effects or perhaps a simple slope analysis of its effects on a latent factor. Is this possible in Mplus with any of the newer versions?

 Ryan Krone posted on Saturday, January 30, 2016 - 12:08 pm
Dear Drs. Muthen

I've asked this question before but didn't get a response. Is it possible to do some sort of simple slope analysis for a MIMIC model interaction for two continuous indicators in Mplus?

 Bengt O. Muthen posted on Monday, February 01, 2016 - 10:01 am
Trying to understand the question - so you have a model like

x->f->y1, y2, ...

where f is a factor. And it sounds like you are saying that y1 and y2, for example, are interacting. I can't understand that because an interaction is typically an IV not a DV.
 Ryan Krone posted on Saturday, February 06, 2016 - 12:48 pm
Dr. Muthen,

My apologies. So I have two exogenous factors x1 and x2 and I'm interested in their interaction effect in addition to their main effects.
So I constructed a multiplicative variable of both x1 and x2, lets call x3. Using your conventions, my model would be x1, x2, x3 -> f -> y1, y2, ...
My question: is there a way to do simple slope analysis of the multiplicative term in a latent factor framework? Similar to the approach Jeremy Dawson has toward non-latent modeling (http://www.jeremydawson.co.uk/slopes.htm). I think it would be difficult to calculate because you have multiple intercepts for each y variable.
But I was just wondering if you knew a way to observe the interactive effects given levels of the continuous variables, x1 and x2 in a latent context. Thank you for your time.

Best Regards,
 Bengt O. Muthen posted on Saturday, February 06, 2016 - 4:53 pm
See the FAQ on our website:

Latent variable interaction LOOP plot

This shows how simple slopes for your "f" are looked at.
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