Acceptable CFI but poor TLI

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Cath Kids

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Mar 3, 2019, 1:25:26 PM3/3/19
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Hi, 

I'm working on a path analysis using lavaan. Here is my result:
Chi square: >.05
CFI: 0.94
TLI: 0.86
RMSEA: 0.05
SRMR 0.05

I'm wondering what is the reason for the poor TLI?
I know that if CFI is less than 1, TLI will always be smaller than CFI. But what explains the huge difference between them?
I have a relatively small sample size: 187. Would it be related to that? 
Please advise how I should interpret this result and whether I can still consider this model to have acceptable fit. 
Thank you! 

Edward Rigdon

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Mar 3, 2019, 6:04:42 PM3/3/19
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TLI is built (mostly) out of ratios of chi-square / degrees of freedom (DF), while CFI is built out of differences chi-square - DF. So your model's degrees of freedom probably play a role in the magnitude of the difference between TLI and CFI. "Acceptable?" If you are asking about reviewer reaction, I suggest you look at published applications of SEM in your target journal. Is there a specific statistical question that you have in mind?

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Chantel Leung

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Mar 4, 2019, 10:44:37 AM3/4/19
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Dear Dr. Rigdon, 

Thanks for your reply. From what I have observed, it seems that not all articles in my field reported TLI (but there is a growing trend of reporting both CFI and TLI). My concern is if I report both indices, then I'm not sure how to justify the difference between CFI And TLI. I read from this website: http://www.davidakenny.net/cm/fit.htm that TLI has a higher penalty for model complexity (more parameters) than CFI. Could this be the reason (I attached my model below)? Also, some of the variables in my model have low correlations, but this would affect both CFI and TLI I suppose?

Thank you!
image.png

Cath Kids

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Mar 4, 2019, 10:55:20 AM3/4/19
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Sorry I realized that attachment link was broken. Here it is. 
image.png

Christopher Bratt

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Mar 5, 2019, 2:06:47 PM3/5/19
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I don't think the relatively low TLI value is your main concern. My recommendation would be to read on SEM, or even path analysis only (only manifest variables). A good starting point is Rex Kline's book on SEM. Good luck!

Best,
Christopher
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