I recently ran a 2-factor CFA model that had poor fit according to CFI (.60), but adequate fit according to RMSEA (.055).
Everything that I've come across in my research has suggested that this is a symptom of low correlations among indicators and/or low quality data. This seems correct, based on an inspection of my data. However, my question is: why would low CFI be associated with low correlations among indicators? If anyone could point me to a source that explains the math behind this, it would be very much appreciated.
Conrad,
just have a look at the formula:
CFI = 1 - (max[(chi-square_t - df_t), 0]/ (max[(chi-square_t - df_t), (chi-square_i - df_i),0]
where t is the target model, i is the independence model
If the ratio is greater than one, CFI is set to one, and if the ratio is smaller than 0, then CFI is set to zero. You can find this formula in all SEM books, and in several publications, such as:
Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures. Methods of Psychological Research Online, 8(2), 23-74.
You can find this publication on ResearchGate.
Regards, Karin
Hello,
Apart from top notch explanations from Karin, just a small addition. Did you get your indicators from literature? Do they seem to be highly correlated based on past evidence? Perhaps this is the route that will let you find some answers.
Regards, Witold
Hello again,
Just came across the article that may be useful. Please see attached PDF.
Regards, Witold
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