Hello Mustafa,

Are you using item parcel / summated scores for the 12 variables, or are you genuinely trying this model as a measurement and structural model (with the 51 observed scores loading onto 12 factors, and 11 of the factors influencing the EP (12th) factor? In my experience, showing good model-data fit is usually easier in the first approach than in the second (though technically less rigorous).

The second question has to do with the correlations mentioned; I presume these are the estimated relationships between the 11 factors (e.g., RA, PU) and the 12th (EP). If so, then yes, it is possible that a "better" model-data fit could be attained by respecification of the model, typically by adding relationships (rather than eliminating relationships). Sometimes, this respecification may be pretty much benign, such as allowing errors of sets of the variables to correlate. Of course, your theory would be critical for judging whether such amendments are defensible.

Finally, consider as well the possibility that you have as good a capture of the relationships as possible, given the set of 51 observed scores used as indicators of the latent variables/factors. In other words, the structural model might not be inherently improved unless you find better indicators/observed scores.

Good luck with your work!

Hello David Morse ,

Thanks for taking the time to replay.

For now, i running the model as it is, i heard that Item parcel could be useful in such cases, but i don't know is my data suitable for that or not? How I can figure that out?

Another question is, how many allowed covariances can be applied? As i have around 20 theoretically based covariances.

Thanks again.

Mustafa

Hello Mustafa,

1. Using item parcels/summated scores vs. measurement & structural models is a matter of choice. As I said, the latter approach is more rigorous (but, offers more ways for misfit to be identified).

2. How many covariances? If you mean, to what degree does it make sense to have error terms that correlate, the answer depends on your theory and characterization of the latent variables involved. You'll have to use good judgment.

At the extreme, if you end up with a model in which every variable links to every other variable (fully saturated), then the model-data fit is artificially perfect, and cannot be assessed as for over-identified models.

Hello David Morse ,

Now i'm using the parcels tech. However, having 11 IVs and 1 DV, how many variables can I parcel? Is there a limit to that? I've parceled items of 8 IVs separately, is this OK?

Thanks again for your great comments.

Best regards,

Mustafa

Hello Mustafa,

No; the parcels refer to the observed scores used to estimate the 11 IVs and 1 DV, not to combining sets of the latent variables/factors.

One final point: You can still have low correlations/loadings/path coefficients among the latent variables and obtain superb model-data fit, if those (low) coefficients work well to reproduce the observed relationships in the data set. In other words, the model could be an accurate portrayal of relatively modest relationships among the constructs of interest.

Good luck with your work.

Thanks David Morse for the replays.

Hi Mustafa

You asked "....Are these low correlations? If so, are they going to affect the model fitness and low CFI? ". I think the answer is Yes. Many years ago Jeremy Miles and I ran some simulations to work out if the magnitude of the parameter estimates in a model influenced the fit statistics. We examine the GFI (an old index from the early LISREL days) and incremental fit indices. What we found was that when the sample correlations were low, and the resultant factor loadings were low, then there was insufficient power for the models to be rejected. This led to the strange conclusion - " Our primary conclusion is simple. If you wish your model to fit, according to the proposed criteria, ensure that your measures are unreliable.".

So if your model is not fitting then you need to think about finding alternative measures that produce less reliable scores. Maybe you could reword the items to make them more difficult to understand, or use measures in an entirely inappropriate sample, or even introduce lots of random coding errors. That should help in the process of model fitting. The consequence of these actions will be that you have a well-fitting model that doesn't mean anything. Of course, I'm being facetious with these suggestions, but I'm also trying to make the point that the traditional SEM fit indices, and how we interpret then, do not operate exactly as we'd want them to across all types of models. At a very minimum we need to think about overall model fit, but also try to understand which parts of our model may not be fitting well (and understand why), and how well our model fits compared to other alternative, or competing, models. Maybe an even more difficult task is to try to get journal reviewers to be more accommodating to a more nuanced evaluation of model fit rather than relying on >.90 is good and