SEM with Multiple Imputation
Message/Author
 TD posted on Friday, August 24, 2007 - 7:17 pm
Hello -

I would like to run an SEM on 5 data sets that I imputed using Gary King's AMELIA. But I needed clarification regarding Mplus' SEM capabilities with imputed data.

1) Is it correct that Mplus does not provide standardized coefficients with TYPE=IMPUTATION?

2) Is is also correct that Mplus does not provide total and total indirect effects with TYPE=IMPUTATION?

Thank you.
 Linda K. Muthen posted on Saturday, August 25, 2007 - 8:58 am
Standardized coefficients are available with TYPE=IMPUTATION. MODEL INDIRECT is not.
 TD posted on Saturday, August 25, 2007 - 2:07 pm
Thank you Dr. Muthen. Other than calculating the indirect effects by hand, do you have any suggestions?
 Linda K. Muthen posted on Saturday, August 25, 2007 - 6:27 pm
This would be a bit of a bother to do. You would need to use MODEL CONSTRAINT to estimate the indirect effect and its standard error for each imputed data set. Then you would have to calculate the standard error of the indirect effect using the formula in Schafer.
 TD posted on Sunday, August 26, 2007 - 7:29 am
Yes. I have had to do something similar with HLM estimates with the imputed data sets. Thank you for your help Dr. Muthen!
 Alex Buff posted on Wednesday, September 23, 2009 - 9:03 am
Dear Dr. Muthen

I also wanted to calculate indirect effects, but realized that MODEL INDIRECT is not supported with imputed data.

As far as I understand the discussion above, I have to run five analyses with my five datasets and then combine the five results - raw (unstandardized) regression coefficients and their standard errors - according the formula of Rubin/Schaffer (for example in NORM). The resulting combined regression coefficient and its standard error is then to be used the usual way. Correct?

What I don’t understand is that you wrote: “ … need to use MODEL CONSTRAINT to …” What exactly do you mean by that?
I have just a simple path model with observed variables (but imputed data).

 Linda K. Muthen posted on Wednesday, September 23, 2009 - 10:27 am
You need to use MODEL CONSTRAINT to define the indirect effects. See MODEL CONSTRAINT in the user's guide to see how it works.
 Dorothee Durpoix posted on Wednesday, December 09, 2009 - 2:04 pm
Following from the messages above, I am not sure either why one would need to use MODEL CONSTRAINT. Could not one use MODEL INDIRECT with each of the imputed dataset and then combine the results using Rubin/Schafer formula?
 Linda K. Muthen posted on Wednesday, December 09, 2009 - 5:56 pm
MODEL CONSTRAINT is recommended to define the indirect effect because MODEL INDIRECT is not available with IMPUTATION. You could analyze each data set separately and use Rubin/Schafer.
 Dorothee Durpoix posted on Thursday, December 10, 2009 - 12:49 pm
Just a precision:
If we analyze each imputed dataset separately, is it mathematically sound to treat these datasets like 'normal' datasets, and hence, not specifying IMPUTATION and use MODEL INDIRECT on each of them, for, later, combining the results following Schafer formula?
 Linda K. Muthen posted on Thursday, December 10, 2009 - 2:50 pm
It's no different applying the rules to the indirect effects than to the regular estimates.
 HZ posted on Friday, February 26, 2010 - 6:43 pm
Hello, I have 5 imputed data and use Type=Imputation to do the analysis. In the first step, I want to create one latent variable based on several observed variables. I tried to use "savedata" command to save the factor scores, but it did not work. Can you tell me how I can save factor scores in the multiple imputed data?
Below are the commands I used:

savedata:
file is F:\Mplus\imputfactor.dat;
save=fscores;

I guess this will give me the same factor scores for these 5 imputed data. Are these factor scores just the average of 5 sets of factor scores based on these 5 imputed data? Another related question is if I want to do other analyses by using other software, should I do these analyses based on the same factor scores for these 5 imputed data, or should I do CFA for each imputed data seperately and get 5 different sets of factor scores.

Thanks much!
 Linda K. Muthen posted on Saturday, February 27, 2010 - 10:02 am
Factor scores are not available with TYPE=IMPUTATION.
 songthip ounpraseuth posted on Monday, February 07, 2011 - 9:20 am
Dr. Muthen -

I am still fairly new to Mplus. Currently, I am using version 6.1. Does Mplus provide a way the pool fit indices such as RMSEA, CFI, and TLI? If not, do you have any suggestions or references I may look into for further investigation?
 Tihomir Asparouhov posted on Monday, February 07, 2011 - 2:29 pm
Yes - when using the ML estimator.
 fritz posted on Wednesday, March 02, 2011 - 7:29 am

Would it be alright to save factor scores for each imputed data set seperatly and use newly created data files including factor scores for further analyses with "TYPE=IMPUTATION" (meaning that analyses based on these factor scores will be combined)?

I'd think so, but just want to make it sure. Thanks in Advance!
 Bengt O. Muthen posted on Wednesday, March 02, 2011 - 10:43 am
If you are interested in working with factor scores in this context you should consider using "plausible values" instead. See the paper on our web site:

Asparouhov, T. & Muthén, B. (2010). Plausible values for latent variables using Mplus. Technical Report.

See also the UG for how to obtain plausible values - example 11.6.
 thomas schmidt posted on Monday, May 09, 2011 - 9:34 am
Dear Dr. Muthen,

I am planning to use plausible values for successive analyses. Referring to the Skrondal (2001). Regression among factor scores - article my understanding is, that unbiased structural parameters can only be obtained, if the factor scores for exogeneous variables are generated using the regression method, factor scores for endogeneous variables using the Bartlett-method. Can you tell me whether using the mean of plausible values for exogeneous as well as endogeneous variables generates unbiased results? Are there alternative ways, given that the convential approach of using FScores does not work due to the number of missing values?

Thank you very much in advance.
 Bengt O. Muthen posted on Monday, May 09, 2011 - 10:24 am
You can use the Mplus Bayes estimator to generate plausible values for both exogenous and endogenous factors and then do path analysis on those data sets with the factors treated as observed variables. See the UG ex 11.6 for how to get plausible values. See Section 4.2 of

Asparouhov, T. & Muthén, B. (2010). Plausible values for latent variables using Mplus. Technical Report.

for a simulation showing the superiority of plausible values over factor scores. This paper also gives references that discuss the properties of the plausible values.
 thomas schmidt posted on Thursday, June 23, 2011 - 3:13 am
Dear Dr. Muthen,
I have a further question regarding the plausible values I could not find an answer for in the MPlus user guide: When I generate a summary file using the "PLAUSIBLE"-command one part of the output file consists of the within-level and between-level plausible values for factors specified in the MODEL part. Additionally for all variables in the model, the same variable names followed by an asterisk (*) or prefaced by "B_" are included in the output (variable* and B_variable). Can you please clarify for me, what the meaning of those variables is? Thank you once again very much for your help.
 Linda K. Muthen posted on Thursday, June 23, 2011 - 11:29 am
* - within-level underlying latent response variables for categorical observed variables

B for observed variables - random intercepts
B for latent variables - between-level factors
 Andrea Hildebrandt posted on Wednesday, November 02, 2011 - 9:50 am
I try to run a model on 5 inputed data sets and receive the following error message:

THE CHI-SQUARE COULD NOT BE COMPUTED. THIS MAY BE DUE TO AN INSUFFICIENT NUMBER OF IMPUTATIONS OR A LARGE AMOUNT OF MISSING DATA.

If I run the model for each dataset separately it works well.

Do you have any suggestion about what the problem could be?

Many thanks!

Andrea
 Linda K. Muthen posted on Thursday, November 03, 2011 - 11:45 am
The calculation that has the problem is the calculation of the imputed chi-square as described in the following Technical Appendix:

Chi-Square Statistics with Multiple Imputation

You can try more imputed data sets to see if that helps.
 Andrea Hildebrandt posted on Tuesday, November 15, 2011 - 12:42 pm
Thank you for your suggestion. I tried 40 imputed data sets and still doesn't work. Do you have another suggestion what the Problem could be?

Thank you!
Andrea
 Linda K. Muthen posted on Wednesday, November 16, 2011 - 2:23 pm
If the individual files run fine and get chi-square values, send your input, a few data sets, your output, and your license number to support@statmodel.com.
 sailor cai posted on Thursday, March 08, 2012 - 2:46 am
A quick question:Are plausible values calculated using Mplus analogies of IRT scores? If so, 1PL-IRT or 2PL? Thanks!
 sailor cai posted on Thursday, March 08, 2012 - 2:52 am
Adding up to my last posting: Can I use Mplus to compute 2PL-IRT plausible values? Either with binary variables or ordered variables? Anyone can give some sample Mplus Syntax? Many thanks!
 Linda K. Muthen posted on Thursday, March 08, 2012 - 12:34 pm
Plausible values are estimates using the 2 parameter normal ogive model. Bayes uses probit regression. See Example 11.6 in the user's guide.