SEM with single-indicator binary vari... PreviousNext
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 Prof. Michael Haenlein posted on Friday, May 05, 2006 - 1:51 pm
As a reply to a posting I recently did in SEMNET, I was referred to MPlus. After having read some articles on your webpage I think that your software would be perfectly suited for the analysis I plan to do, but I would like to get your confirmation (if possible) before I order it.

My model looks as follows:

I have seven latent variables, measured with 3-5 reflective indicators each (z1-z6 and x1).
The relationship between these variables are as follows:

z1 -> z2
z2, z3, z5 -> z4
z3, z6 -> x1

In addition I have three other variables. These are not latent as they are only measured by one observable indicator each. Two of them (x2, x3) are binary (0/1) and one (y) is continuous.

The model I want to estimate is:

x1, x2, x3 -> y

y (the single-item continuous variable) is hence influenced by two single-item binary variables and one multi-item continuous latent variable.

Could you please confirm that MPlus can handle single-item measures (both continuous and binary) and latent variables in one model?

Thanks,

Michael
 Linda K. Muthen posted on Friday, May 05, 2006 - 2:21 pm
Yes, models can contain both observed and latent variables and observed dependent variables can be continuous, binary, and ordered categorical. They can also be censored, count, and nominal.
 jtw posted on Thursday, December 31, 2009 - 8:03 am
Hello,
I am attempting to estimate a hybrid model in Mplus v5.21 that contains a couple of latent variables that are measured with single indicator categorical observed variables. I can estimate this model by treating these categorical variables as observed variables but I want to assess the robustness of the parameter estimates to different specifications of measurement error (as opposed to simply assuming the constructs are measured without error).

Following standard procedures for single-indicator latent variables, I fixed the factor loading to 1 to set the scale and have specified a value for the measurement error. The factor variances are free to be estimated. Using the WLSM estimator and theta parameterization, the model is not identified using the categorical single indicators. I know this procedure works fine for single indicator latent variables with continuous measures using ML estimation.

Are there unique issues with identification for models with single indicator latent variables when the indicators are categorical? Do you recommend anything as a practical approach to working around this problem? Thanks for your time and happy holidays!
 Linda K. Muthen posted on Thursday, December 31, 2009 - 9:48 am
You cannot use the approach of fixing residual variances with categorical outcomes because categorical outcomes do not have variance parameters. You would need to adjust factor loadings. We do not recommend doing this.
 Mathias Höglund posted on Friday, February 12, 2010 - 1:53 am
Hello Linda,

I am working with an mplus SEM with latent and observed (binary) variables. The model that I have works fine and gives a decent fit. However, I have a multilevel structure where 120 subsidiaries are nested within 12 MNCs. The group N = 12 pretty much rules out multilevel modeling and therefore I tried using 11 group dummies. None of my relationships in the model get any worse. However, the fit statistics seriously deteriorate. Is there any way I can use this model in an analysis? (E.g. report the model without dummies in the main analysis and report the dummy test as a post hoc analysis and comment that none of the hypothesized relationships got any worse (In fact they are even more significant.))

I would really appreciate your help.
 Linda K. Muthen posted on Friday, February 12, 2010 - 10:20 am
By controlling for clustering, it would be expected that the chi-square value would decrease. This may point to a need for direct effects from the dummy variables to the factor indicators.
 Mathias Höglund posted on Saturday, February 13, 2010 - 9:21 am
Thank you very much for your quick response!

Just to check: Do you suggest that instead of defining paths from all cluster dummies to all latent variables I would define the paths to all factor indicators in the model?

Thanks again so much for your help!
 Linda K. Muthen posted on Saturday, February 13, 2010 - 9:45 am
You cannot include all direct effects because the model would not be identified. You should look at modification indices to see if any are large for these direct effects. Say MODINDICES (ALL); in the OUTPUT command.
 Mathias Höglund posted on Monday, February 15, 2010 - 1:14 am
Thanks again Linda!

I did this by letting the dummy variables freely correlate in the model and checked the modification indices. I found a need to define paths from a couple of dummies to some factor indicators and latent variables. After having done this the chi square goes up but I lost my significance levels for my hypothesized relationships so I will need to think of an alternative model.
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