Same values of CFA and SEM model fit indices

[Danish Kirmani]

Dear Sir and group members,

I had employed CFA and SEM on my data. The values of model fit indices of CFA (Cmin, GFI, AGFI, CFI and RMSEA) are exactly equal to the respective values of model fit indices of SEM (Cmin, GFI, AGFI, CFI and RMSEA).

Is it normal to have equal values of model fit indices of CFA and SEM or is it an indication of some problem?

If it is an indication of some problem? How can it be resolved?

Thanks & Regards

Mohd Danish Kirmani

Senior Research Fellow, 

Department of Business Administration

FMSR, AMU, Aligarh, UP

Mob: 08979328986

Email: kirm...@gmail.com
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[Neeraj Kaushik]

Dear Danish

SEM consists of 2 things: Measurement model (CFA) & Structural Model (Path Analysis. You are calling it as SEM)

The purpose of CFA is to check for the 

a) Model fitness (Goodness of fit)

b) Reliability & Validity

Only the constructs, which pass these 2 tests are eligible to enter into Path Analysis. 

Path Analysis is concerned with the relational part of the constructs, hence we pay attention to:

a) Significance of each construct (IDV)

b) r2

c) Regression line

There is no point of checking for the model fitness in Path Analysis.

Best wishes

Neeraj

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[rajeev Kumar]

Respected Sir........

There is no point of checking for the model fitness in Path Analysis.

Please elaborate the above line as this created a confusion to my understanding of Structural Equation Modelling. 

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Thanks & Regards
Rajeev Kumar Malik (UGC-SRF)
Research Scholar
Faculty of Management Studies
B.H.U.,Varanasi
Mobile- +91 979 594 3341

[Neeraj Kaushik]

Dear Rajeev

First thing in SEM is to understand is that SEM is nothing but Regression (Maximum Likelihood Estimation (MLE) Method is employed here)

It consists of 2 things: 

Measurement model (CFA) & 

Structural Model (Path Analysis)

The purpose of CFA is to check for the suitability of the known constructs (but not their relations) or questionnaire (from Review of literature or expert opinion) in our target market/respondents. Hence we check the following:

a) Model fitness (Goodness of fit)

b) Reliability & Validity

So the end result of the CFA is simply to accept or reject a construct.

Now if the constructs are ok they are eligible to enter into Path Analysis. 

Path Analysis is concerned with the relational part of the constructs. Here we join the various constructs by single side arrow marking them as DV or IDV. It is just the regression, hence we pay attention to the things we see in Regression like:

a) Significance of each construct (IDV)

b) r2

c) Regression line

Though Gaskin has mentioned to check the Model fitness (CFA, GFI values etc) just for once before proceeding for Path Analysis, but if the constructs are ok then these indicators will give same values in Path Analysis too. Hence I remarked that there is no need to check these things in Path Analysis.

Plz feel free to ask for any/every doubt.

Best wishes

Neeraj

[rajeev Kumar]

Thank you sir, I was also thinking that if CFA is giving good model fit, Path analysis model fit will also be providing good model fits. 

[Danish Kirmani]

Thanks Neeraj Sir and Rajeev Sir for the discussion. It means that I only required to model fit indices for measurement model (CFA) and if it is okay than I can proceed for path analysis.