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 Timothy Lim posted on Thursday, May 17, 2012 - 6:54 am
Dear Dr. Muthen,

I have attempted to run latent interactions with the XWITH command, but this gives me a fatal error saying I do not have enough memory on my system to run it. I am unable to obtain a new computer in my workplace as of yet. As an alternative, I have done the following:

1) Exported the factor scores from my model without the interaction effect in the ON statement (Model 1), and manually created the interaction term from the factor scores.

2) Created a new MPlus input file including the "hand-calculated" interaction term.

3) Re-run the model, and include the interaction term in the ON statement. (Model 2) I have run this model both letting the factor loadings be freely estimated, and constraining the factor loadings to be equal to Model 1.

Both of the new models with the interaction term run, and fit well. The model with factor loadings constrained to be the same as Model 1 fit better than when factor loadings are freely estimated.

What I need is your expert opinion on whether this method is mathematically sound (i.e. no significant error introduced and parameter estimates reliable), as an interim method of modelling an interaction effect to present preliminary findings while I am searching for a machine capable of running it with the XWITH command.

Thank you very much for your time and input on this.
 Linda K. Muthen posted on Thursday, May 17, 2012 - 10:58 am
Creating an interaction term using factors is not the same as using XWITH unless factor determinacy is one which it almost never is.

If you had a model with more than one XWITH statement, I would suggest running them one at a time. It is unlikely that they are all significant.
 Timothy Lim posted on Saturday, May 19, 2012 - 7:04 pm
Thank you for your reply Dr. Muthen. I have managed to find a machine which I am able to run the interaction effects on. It runs fine at the between level. However, I am unable to run the XWITH command for the within level of my data.

It gives me an error "The resulting covariance matrix cannot be inverted. Please check your data or change your model." What would be the likely cause of this problem?
My model looks something like this at the within level:

int | x1 XWITH x2 ;
y ON x1 x2 int ;

It gives me the error even if I run it as a single level model only at the within level.

Thank you again.
 Linda K. Muthen posted on Sunday, May 20, 2012 - 10:33 am
Please send your output and license number to
 caroline masquillier posted on Tuesday, April 02, 2013 - 8:43 am
Dear Prof. Muthen,
I am running a latent cross-lagged model with an interaction term. This interaction term is between a latent factor (W1_faci) and a time-invariant dichotomous variable (fintervention_master). This is done on two waves of data. The outcome variable is hope at two waves (W1=wave1; W2=wave2). The latent factors (W_Faci; W_hope) are full metric invariant over time.
W1_supp_faci | W1_faci XWITH fintervention_master;
W2_supp_faci | W2_faci XWITH fintervention_master;
W1_hope on W1_supp_faci W1_faci fintervention_master;
W2_hope on W1_supp_faci W2_supp_faci W1_faci W2_faci fintervention_master ;
--> The SEM model without interaction showed a good fit. In the model with interaction term using the XWITH option, W2_supp_faci was significant on W2_hope.

As a second strategy, we tried to apply the same statistical procedure as aforementioned (with factor scores calculating an interaction term). The interaction term W2_supp_faci was also significant on W2_hope. However, the model fit was not good. The same model without interaction has a good model fit. How could it be possible that adding a significant path (interaction term W2_supp_faci ) decreases the fit of the model with factorscores a lot?

Is it better to use the XWITH statement or the factorscores method? What is the difference between both methods?
Thank you very much in advance,
 Linda K. Muthen posted on Tuesday, April 02, 2013 - 9:35 am
Factors in the model and factor scores can be very different unless factor score determinacy is extremely high which is usually not the case. I would use XWITH.
 caroline masquillier posted on Wednesday, April 03, 2013 - 4:25 am
Dear Prof. Muthen,

Thank you very much for your quick answer. I will continue using the XWITH statement. But could it be possible to clarify why this method is better than using the 'factor scores method'?

Thank you very much,
Kind regards,
 Linda K. Muthen posted on Wednesday, April 03, 2013 - 10:17 am
The following paper describes the problems:

Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.
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