In structural equation, Can coefficient between covariate and indicator when controlling latent be estimated ?
In MIMIC models, can coefficient between covariate and indicator when controlling latent be estimated by direct paths from covariate to indicator? do you mind to take a look at my model attached? Thanks in advance,
Hi Ceren,
of course, you can estimate such an effect. The questions are a) what is the meaning of such an effect (as it represents a direct effect on the indicator controlling for the latent and b) on which basis you do that (if the model cleanly fits without the effect), there is little chance to get a significant one.
Besides that, I would have some doubts about the common factor structure when getting a significant effect as it undermines the idea underlying the functioning of the reflective indicators as pure and mere indicators of the latent variable. If an indicator has a special relationship with your X-variables then perhaps the whole structure of the latent variable is misspecified. This is at least an option and would prompt me to challenge the model with some other included specific predictors of the latent variable that support the idea that it is something really meaningful/existing.
HTH
Holger
Thnx Holger,
making modification controlling latent increased model fit , without those modifications my model had poor fit. (I keep in mind that modifications can make theoretical sense).
This would indicate if there is any difference in average according to the covariate with respect to the indicator, also known as DIF (differential analysis of the indicator, in this case of the indicated element), this must be taken into account that the control in the latent variable is significant, which indicates that there is not a difference or lack of invariance of the covariate.
Ceren, adding a parameter due to misfit in order to fit, CAN be reasonable in the same way that adding a double-loading or error covariance CAN be reasonable. With "reasonable" I mean that the structure was (almost) correctly specified from the beginning and just the respective parameter was falsely fixed to zero.
However, the seemingly necessity to estimate such a parameter may just signal a more fundamental problem of the overall structure. Estimating the parameter in this regard, functions like a technical system in which you open a valve to release pressure (misfit) of the system.
You could do the following: Do you have one or more variables in your data set (further X's) that should have an effect or be affected by the latent variable. If incorporating such a variable still results in a fit then this could be regarded as supporting the structure.
Best,
Holger
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