the interpretation of the model fit indices

[Jane Li]

Hi, I conducted a CFA using lavaan, RMSEA=.067, SRMR=.043, however, CFI=.804, TLI=.707, the sample size of the data is more than 30,000. In this case, can I say the model is fairly good? 

Thank you very much! 

[Edward Rigdon]

It looks like correlations among your observed variables are generally low, which may make fit  based on Rmsea, Srmr seem better than it might. You won't find an authority endorsing such low values for CFI, TLI.

On Jun 24, 2017 9:35 PM, "Jane Li" <jane...@gmail.com> wrote:

Hi, I conducted a CFA using lavaan, RMSEA=.067, SRMR=.043, however, CFI=.804, TLI=.707, the sample size of the data is more than 30,000. In this case, can I say the model is fairly good? 

Thank you very much! 

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[Mauricio Garnier-Villarreal]

The problem is that the CFI and TLI are influenced by the null model, which in cases where the items have low correlations can lead to lower fit. Even when it shows proper fit in other index like RMSEA. This is a reason why I dont like these ones as much. In cases where CFI/TLI disagree with RMSEA/gammahat I trust more the second ones

You can use the semTools function moreFitIndices to calculate gammahat and adjusted gammahat. These as RMSEA are not related to the null model and are more reliable.

You can look at West, Taylor, Wu (2012) for a review of more fit indexes. It has become due to practice to limit the report of fit to rmsea, cfi, tli. While there are more options

West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of Structural Equation Modeling (pp. 209-231). New York, NY: Guilford.

On Saturday, June 24, 2017 at 9:58:51 PM UTC-5, Edward Rigdon wrote:

It looks like correlations among your observed variables are generally low, which may make fit  based on Rmsea, Srmr seem better than it might. You won't find an authority endorsing such low values for CFI, TLI.

On Jun 24, 2017 9:35 PM, "Jane Li" <jane...@gmail.com> wrote:

Hi, I conducted a CFA using lavaan, RMSEA=.067, SRMR=.043, however, CFI=.804, TLI=.707, the sample size of the data is more than 30,000. In this case, can I say the model is fairly good? 

Thank you very much! 

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[kma...@aol.com]

The West, Taylor and Wu (2012) chapter offers and excellent reference.  I just want to offer another perspective on incremental fit indices.

If your sample covariance matrix had only zero values off the main diagonal, that is, only variances no non-zero covariances, then you could fit any structural model by matching the variances and estimating all the structural parameters as zero.  This thought experiment illustrates the idea that data with low correlations between variables offers less power to distinguish rival hypotheses than does data with larger correlations, positive or negative.  One can think of incremental fit indices as providing a safeguard against overinterpreting low-powered results.  If you have a well fitting model that does not improve much on the null model, then you have not made a very challenging test of your model.  You should think about ways to raise the bar  by designing a more challenging test of the hypothesis.

In my informal experience experimenting with the indices using simulated data, it is not very hard to construct an example in which absolute fit indices like RMSEA look good but incremental fit indices like CFI look bad.  However, it is not as easy to construct examples in which absolute fit is poor but sufficiently better than the null model to produce a favorable values for incremental fit indices.  Your fit needs to be pretty good to remove most of the ill fit in the null model.  So, that might offer a perspective that would favor keeping incremental indices in the mix when evaluating model fit.

The fundamental point on which everyone should agree, however, is that fit is not a unidimensional construct.  Different indices measure different dimensions of fit.  This is why most sources favor a profile of different types of indices rather than selecting one index as the best measure of fit.  However, even those who favor just one number can agree with the broader point that fit measures do not reflect a single dimension of fit.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

[Jane Li]

Got it. Thanks so much, Kmarkus, Mauricio and Edward! 

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