DESIGN DEFECT. The scale should be uniform for the variables. The problem may be caused by the differences in scales among the variables. You might consider pre-treat the data so that it is converted into the same scale and then run your testing or modeling.

I think you can also influence the drafting of indicators and the proposal consistent with the theoretical model, if you have 4 VI can raise common cause model, mediation or moderation considering that your model does not fit.

Omid, it is not really clear how your (misfitting) model looks like. I guess you did a CFA with 5 latent variables?

If yes, you have to understand what "misfit" means in a factor model (or SEM in general): A model in which a set of indicators is fitted to a single latent variable has a set of implications which must hold if the model is correct. That is, a) the indicators correlate (because they reflect the factor) and b) these correlations vanish when you statistically control the latent variable. THIS is what is tested in a factor model (it is called local independence). Hence, if your model does not fit, this essential set of assumptions fail and one or more pairs of indicators still have some correlations even after considering the factor. These residual correlations (like any other correlation) may stem from

a) two indicators share a further, but omitted common influence

b) one indicator causes the other ("serial effects")

c) The one-factor assumption is imply wrong and the set of indicators is causally diverse and they measure different latent variables.

Unfortunately, the data does not tell you what explanation holds.

Hence, you have to first understand which pairs of indicators cause the problem and than return to the "drawing board" and reconsider the theoretically appropriate causal structure. Of course it is most easy to simply add (an) error covariance but this may mask possible deeper problems with your proposed structure.

For the diagnostic phase (i.e., finding out where the problem lies), most software packages print the "standardized residuals" which are the differences between the empirical correlations and those correlations which your presumed factor structure implies. Hence, find out how to print them. I guess you use AMOS and as far as I know, AMOS does not do that. If that's true, I recommend, switching to the lavaan package in R.

Don't worry about your indicators having different metrics. IF your model is correct and indicators loading on one factor have different metrics will not result in misfit. In some cases, if one indicator has a metric implying a very large variance (and covariances), the model may not converge but this does not seem to be the case in your model.

Best,

Holger

Dear Holger Steinmetz

Thank you very much for your comments. Yes, you guessed it right I use Amos and I have five latent variables

Hey Dr Holger Steinmetz

Do you recommend any paper that have discussed this issue? thank you.

Hello Jawad,

here is a thread that I linked a recent study where I had to test a CFA model which did not fit. Luckily the reviewers were ok with me describing the diagnostics and some re-specification attempts. The R markdown file with the annotated R code is also there:

https://www.researchgate.net/post/Model_fit_measures_in_CB_SEM

All the best,

Holger

Hey Dr Holger Steinmetz

Thank you so much for sharing this. Just to clarify, in your paper, and based on the logic of Herting and Costner (200), it is permissible to delete some of the indicators. however, in my model, some constructs are not meeting the discriminate validity test. This is due to having some of the indicators to be loaded in more than one constructs. The constructs that are not meeting the discrimination validity are not part of the initial theory (I am using the technology acceptance model theory and I have added some external variables to the model). These constructs are added to my initial theory to help in predicting the intention of the users.

However, since I am unable to meet the discriminant validity, I have tried to merge some of the indicators with other constructs, and sometimes I have tried to merge some of the constructs together. I am still not able to pass the discriminant validity so I have deleted the external constructs.

In my new model, which contains the initial theory with one external variable, is meeting the construct validity and reliability, and the model fit indices are indicating that the model have a close fit to the data. My question is, do I have the right to delete an entire construct based on the logic of Herting and Costner (200) ? Thank you.

regards,

Jawad

Hi Jawad,

the fact that a indicator has a double loading creates no harm for the model / estimates as long as you stay in the latent variable framework. I know that some field have these strange AVE rules, hence you have to see in how far you can violate these. This however is a political / strategic question not a scientific one. If you have several indicators, eliminating the double-loading-affected will not be problematic either. And by the way: The discriminant validity issue concerns the indicators. Whether the latents themselves are invalid is a question that you should by means of the test of the model structure (i.e., the chisquare test). Again. If modeling two latent variables adhers to reality, a double loading is neither a counterevidence nor leads to bias.

"Merging indicators to other constructs" however, sounds strange. This is no process that you can control. If these indicators don't measure these other constructs, you create a misspecification.

If the above was not clear enough, perhaps, you can become more specific wrt the overall model structure and question wordings of the indicators. Many discussions on researchgate are overly complicated because people don't provide enough information. That's why I created this posting:

https://www.researchgate.net/post/Netiquette_proposal_for_questions_on_structural_equation_modeling

HTH

Holger