Hi
I have to identify the moderation effect of one latent variable on other two latent variables. Can I use the regression based factor scores (z score) obtained in SPSS to calculate the latent variable scores.
I tried the data imputation in AMOS but that is not working for my SEM . I was thinking of using the factor scores obtained from AMOS and multiplying with the z scores of the observed variables to obtain the second order latent variable score. Is it right to use this?
In the attached model, I am looking for a latent variable score for Mooring , so I was planning to use the factor scores obtained from AMOS and multiplying that with individual z scores of the observed variables and getting a latent variable score.
Please let me know if this is good way.
Dear,
I suggest to estimate before a measurement model employing a CFA approach (it seems to me that you have a structured theory to test) evaluating if the hypothesised measurement model fits the data well. Only after you tested that the measurement model holds I suggest to add the structural relationships between latent variables.
Take also into account the nature of the variables, if they are continuous, ordinal or categorical. You need to use different estimators according to the items.
Please, consider also that if you are going to compare groups (cultures, countries, etc.) or your sample has a nested structure, you need to test for measurement invariance, otherwise you cannot compare the latent means.
Best,
Gianmaria
Dear Reema,
as I pointed out in my response to your other posting, specifying a second-order factor with only two primary factor is not such a good idea.
With regard to factor scores for investigating moderaton, there is some limited research, for instance
Yang-Wallentin, F., Schmidt, P., Davidov, E., & Bamberg, S. (2004). Is there any interaction effect between intention and perceived behavioral control? Methods of Psychological Research Online, 8(2), 127-157.
The problem however is that a factor score is not error-free because it is estimated from the data (the so called factor indeterminacy). Hence, I would propose to the following
If your CFA fits cleanly, and a following interaction model with manifest variables results in a moderator effect far from significant, a latent interaction model will probably not give you any thing. If it is significant, the problem is solved anyway (unless a manifest interaction increases the chance to find spurious interaction effects, but I am not aware of studies that show this). If you p-value of the interaction however, is around p = .10, than spending the effort to run a full interaction model can be beneficial as measurement error (from with the manifest interaction model suffers a lot) may have turned an actual interaction into a non-significant one.
If AMOS does not allow treating missing data properly, switch to R and the lavaan package (www.lavaan.org). There are some swithing costs but after spending 1-2 day on it, it works. In lavaan, you can use the FIML estimator to treat missing data.
I apologize for self-advertisement, but in this paper we demonstrated the options how to model a latent interaction effect.
Steinmetz, H., Davidov, E., & Schmidt, P. (2011). Three approaches to estimate latent interaction effects: Intention and perceived behavioral control in the theory of planned behavior. Methodological Innovations Online, 6(1), 95-110.
HTH
Holger
I agree with above. But while not ideal I'm pretty sure you could use those EFA factor scores to estimate a latent variable. EFA and CFA both try to find factors or latent traits.
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