Correlations between observed and lat... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 pat berglund posted on Monday, April 30, 2007 - 7:55 pm
Hello, I would like to control if the observed and latent x vars are correlated and am not sure how to specify this. For example I have 8 obs x vars and 1 latent x var and would like to let the 8 obs x vars correlate with each other but not with f1 the latent x var. Is this possible?

Here is my setup and I see f1 correlated with the x vars by default I believe:
f1 by emp edu mar birth ;
mddh sub on f1 ;
! specify correlated observed dep vars ;
mddh with sub ;

mddh sub on us mex col bel fra ger ita net ;
stand residual sampstat ;
 Linda K. Muthen posted on Monday, April 30, 2007 - 8:38 pm
In most models in Mplus, the model is estimated conditioned on the covariates so the covariances among the observed covariates and the latent covariates are zero. You would need to send your input, data, output, and license number to for me to say more.
 gloria posted on Tuesday, June 02, 2015 - 7:46 pm
I'm trying to run a model with a mix of latent variables(teacher's self efficacy, teacher's instructional practice) and observed variables (teacher's education, whether or not the teacher is a special ed teacher, frequency of prof. development) predicting a latent variable (teacher's knowledge).

When I run the model, the exogenous latent variables are correlated by default but not the observed predictors.

Here are my questions:
1. Do the correlations between the observed predictors and the latent predictors need to be correlated only based on theory or should you recommend that I start correlating all predictors (observed and latent) and then constrained the ones that are non-significant to 0?

2. Missing data. I have different types of missing data which are MAR and I understand that MPlus uses FIML by default. However, even with FIML, the number of observations reported in the analysis is less than the entire sample. I read different posts and i found that if I add back the means of all variables using [var1 var2 var3... varx], then all observations are used in the analysis. Is this still working under FIML?? Is including back the means correct?

 Bengt O. Muthen posted on Tuesday, June 02, 2015 - 10:44 pm
1. correlate all of them - or of the observed can be seen as temporally preceding the latents, regress latents on observed.

2. Sounds like you have missing on your observed predictors. You can bring them into the model (by mentioning their means or variances or covariances) although you make extra normality assumption for them when you do so. See also our FAQ: Missing on x's
 gloria posted on Thursday, June 04, 2015 - 2:11 am
Thank you for the quick response! I have a follow-up question/clarification about the original Q1. When you say "temporally preceding", do you mean in terms of when the data were collected?

Also - as I build my model, if I allow them all to correlate as a first step, will you say is okay to constrain the non-significant correlations to zero as a second step?

With regards to the missing data question, I will check the FAQ on missing on x's.

Thank you again for your help!
 Bengt O. Muthen posted on Friday, June 05, 2015 - 3:08 pm
Q1. More in terms of causal direction.

Q2. I would not do that.
 gloria posted on Monday, June 15, 2015 - 7:09 pm
Thank you for the previous response. I came back to the analysis over the weekend and some follow-up questions emerged.

1a. I do have missing variables on my predictors (mix of dichotomous and continuous). When you set all exogenous variables to correlate this makes the analysis use all cases. This is expected since we are mentioning their correlations, correct?

1b.But since these correlations involve dichotomous variables, and I have some missing cases on those variables, mentioning their correlations will incorrectly impose the normality assumption, so this is not advisable.Right?

1c. So, I went on to impute using Mplus 7 and after trying to impute all missing predictors (continuous and dichotomous) I wasn't able to make it work. Then I just tried imputing the categorical and dichotomous variables and I was able to make it work. If I do this, what do you think about using imputation for the dichotomous/categorical predictors and then mentioning the correlations or means of the other continuous predictors and take advantage of ML?? Do you see anything wrong with this "hybrid" method?

1d. Last. I'm wondering about the interpretation of the correlations for the exogenous variables in the overall model (latent predictors and observed predictors predicting a latent outcome). Are the correlations among the predictors interpreted as partial correlations?

Thank you for your help!!
 Bengt O. Muthen posted on Monday, June 15, 2015 - 7:57 pm
1a. Right.

1b. In principle you are right. The error may not be that great, however, although imputation that acknowledges the categorical nature should be better.

1c. Try to get the run working where you have both cont and cat vbles. If needed, send problems to support.

1d. They are regular (1st-order) correlations.
 gloria posted on Monday, June 15, 2015 - 8:22 pm
Thanks for the quick response!

I will give the imputation a few more tries and if I cannot get it to work I will send it to support.

About the correlations, if they are fist-order correlations, by allowing them in the model (vs. not), we are making the statement that they are needed. Model fit improves if I added them vs. if I do not, but I wonder if that is an artifact of adding more parameters to the model. Some of them might have a casual direction (i.e. having an education major and your literacy practices in the classroom) but some might not. Do you have any suggestions in terms of readings regarding correlations of latent and manifest predictors?

 Bengt O. Muthen posted on Monday, June 15, 2015 - 9:48 pm
I don't know about readings, but I would simply correlated them all (unless WLSMV estimation is used, in which case more care in the choice of WITH and ON is needed).
 gloria posted on Tuesday, June 16, 2015 - 3:26 am
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