CFI changes with " test - mean.var.adjusted " included (CFA with categorical data, estimator = "WLSMV")

[Christopher Runyon]

Hi Group,

I have a 2-factor model with 8 items loading onto each factor, and the response scale ranges from 0-3 for each item. According to what I know, I should be using estimator = "WLSMV" and test = "mean.var.adjusted" due to the fact that my data is categorical (e.g., Finney and DiStefano, 2006).

When using the above syntax, the CFI is much lower than the TLI:

User Model versus Baseline Model:

 

  Comparative Fit Index (CFI)                    0.970       0.552

  Tucker-Lewis Index (TLI)                       0.965       0.915

When I omit test = "mean.var.adjusted", the CFI / TLI values are closer to one another, and the CFI is higher than the TLI (as I thought should always be the case):

User Model versus Baseline Model:

 

  Comparative Fit Index (CFI)                    0.970       0.819

  Tucker-Lewis Index (TLI)                       0.965       0.789

Can someone help me with what's happening here? Is it due to the scaling correction factor, shift parameter, or something else? Which test statistic should I use / report? Or, more broadly, please correct me if I'm using the wrong estimator and/or test for my categorical data. 

I noticed the following "bug" reported in Version 0.5-21, so it may be related to that:

"Bugs/glitches discovered after the release:

• the (new) robust CFI/TLI/RMSEA values as printed in the summary() output of version 0.5-21 (only) are wrong if (and only if) the test statistic is “mean.var.adjusted” or “scaled.shifted” (the latter is used when estimator = “WLSMV”, the default estimator in the categorical case)"

Thank you all for your help.

[Edward Rigdon]

I can only answer part of this. TLI is not normed, so it can vary outside the 0-1 range. Thus, TLI can be larger than CFI, which *is* confined to 0-1. I believe TLI will be > 1 whenever chi-square < its degrees of freedom.

In other circumstances, strange behaviour of fit indices is tied to changes in how the mean vector is treated in the baseline model. I wonder if that is the case here. Perhaps you can ask for more information about the baseline model that lavaan is running?

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[Terrence Jorgensen]

According to what I know, I should be using estimator = "WLSMV" and test = "mean.var.adjusted" due to the fact that my data is categorical (e.g., Finney and DiStefano, 2006).

That's a dated reference, published around the time that Mplus implemented a more efficient robust test ("scaled.shifted"), which has been their default for years, as well as lavaan's.

 

I noticed the following "bug" reported in Version 0.5-21, so it may be related to that:

"Bugs/glitches discovered after the release:

• the (new) robust CFI/TLI/RMSEA values as printed in the summary() output of version 0.5-21 (only) are wrong if (and only if) the test statistic is “mean.var.adjusted” or “scaled.shifted” (the latter is used when estimator = “WLSMV”, the default estimator in the categorical case)"

No, it has nothing to do with that.  

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

 

[Christopher Runyon]

Great! Thank you so much for your help. I'm glad to know that this was just a user error on my end, and I will update my references and analyses to use the "scaled.shifted" test.