I ran SEM model in Mplus and initially, I did not use any latent variables defined with command BY. CFI and TLI was 1.000 and X² and RMSEA of 0.000. However when I replaced one of the predictors with a latent concept (BY) then fit indices looked more ‘normal’ (e.g. X² = 936.01(10), CFI = .744, TLI = .448, RMSEA = .120). Could anyone explain why this has happened. Is it simply that because not including latent concepts in the Mplus makes it impossible to obtain RMSEA and X² , but then CFI and TLI look as perfect… Please if someone could shed some light.
If you assume that all of the variables in your model are directly observed, then you have a "path model" or "SEM with structural part only". In a simple mediation path model (without any latent variables) in which you let all of the direct and indirect effects to be freely estimated, you will always have a perfect model-data fit because your model would be just-identified. If, for the same conceptual model, you assume some or all of your variables to be latent, structural part of your model still remains just-identified but now, your model also involves a measurement part. This measurement part which indicates the hypothesized relationships among indicators and the corresponding latent variables is over-identified and that is why your overall model becomes a testable one. But the only thing you can test is the measurement aspect of the model. So, if the fit indices are not good, that means that there is a problem with your measurement instrument(s), e.g. your items are not working as they're supposed to. It does not say anything about the mediation, direct or indirect effects in your model.
It's been a while since I did mediation analysis so I might forget something.
First: a X² of 0 means your model fits the data perfectly. this is an indication of error in almost all cases of mediation. Maybe your independent variables do not distinguish between data or maybe your independent variable is dependent on the dependent variable (this can be by various ways; for example by mirroring the structure of the DV).
A X² of 0 can also be when the DV does not have any variance but this seems unlikely in your case since by adding a mediator you got some high X² values.
I'm very sceptical in mediation analysis uses in most research so if you are doing this for research and not for learning (e.g. seminar-course), please be sure you have a strong theoretical concept for your model as mediation analysis might show you some results but they are absolutelly useless as the direction of influence could be totally different.
It might be best to share the model specification so that might be examined. What was(were) the degrees of freedom in the initial model.
Dear Witold,
RMSEA comes with latent variables. If you do not include any, you have, by definition, not a SEM since it represents correlations/regressions between them. Furthermore, I am not absolutely sure what you mean when you say that your fit indices are "normal". They are "normal" in the sense that they can all be found in the output once you include the BY-command. Yet, in this case, they show that your data do not fit your model specifications.
Kind regards
Marcel
If you assume that all of the variables in your model are directly observed, then you have a "path model" or "SEM with structural part only". In a simple mediation path model (without any latent variables) in which you let all of the direct and indirect effects to be freely estimated, you will always have a perfect model-data fit because your model would be just-identified. If, for the same conceptual model, you assume some or all of your variables to be latent, structural part of your model still remains just-identified but now, your model also involves a measurement part. This measurement part which indicates the hypothesized relationships among indicators and the corresponding latent variables is over-identified and that is why your overall model becomes a testable one. But the only thing you can test is the measurement aspect of the model. So, if the fit indices are not good, that means that there is a problem with your measurement instrument(s), e.g. your items are not working as they're supposed to. It does not say anything about the mediation, direct or indirect effects in your model.
Hi there, Serkan absolutely nailed it! :D
People too often regard the fit of their structural model as a support of the causal structure of the substantial variable although it is just the measurement model that provides the fit. By the way: Your fit indices are far from being ok. But that is no reason for despair. Check the item formulations and revise the structure.
Best,
Holger
We do not know, for example, what are the relations between these variables and whether they are certainly linear. Maybe the model contains some specification errors, for example, strongly non-linear relationships, or variables makes form some sort of unorthgonal system, or are too closely related. Can you provide some information on this matter?
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