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According to Brown (2015), one is expected to examine and report localized areas of ill fit (e.g. modification indices (MI)) as part of the model evaluation. I have a number of questions about reporting and examining the MI’s given the following scenario

  1. Overall fit of the model being tested in CFA is good according to CFI,
    TLI, S-RMR, RMSEA
  2. However, there are simply too many modification indices that exceed the value of 10 (about the same number as the total number of indicators). For the most part, these pertained to error covariances of items that load onto the same latent variables. Therefore, it is not easy to dismiss the large MI values on the basis of substantive reasons.

Questions are:

  1. How do you interpret so many indicators of poor local fit in the presence of
    good overall model fit?

  2. Are you expected to report AND address "focal strains"?

Reference Brown, Timothy A. Confirmatory factor analysis for applied research. Guilford Publications, 2015.

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  • $\begingroup$ What's your sample size? $\endgroup$ – Jeremy Miles May 26 '16 at 16:11
  • $\begingroup$ Sample size is approx. 700. $\endgroup$ – user81715 May 26 '16 at 16:13
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I wouldn't worry about MIs of 10 in a sample size of 100. Look at the standardized expected parameter change (SEPC). Is that big enough to worry about?

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  • $\begingroup$ Thank you for your response. SEPC for the largest MI values (>20-45) range from -.17 to .17. These are for approx. 30% of the indicators. I do not have a good sense of how these indicators generally relate to the sample size (n=700) though I did note from text that more ill fit is likely to occur with larger samples. $\endgroup$ – user81715 May 26 '16 at 16:21
  • $\begingroup$ They're not huge, but they are moderate. If your fit is good, I wouldn't worry. $\endgroup$ – Jeremy Miles May 26 '16 at 16:56
  • $\begingroup$ Upvotes for answer appreciated. $\endgroup$ – Jeremy Miles May 26 '16 at 18:11
  • $\begingroup$ I remain curious about the second part of my question, which concerns the proper reporting of these results. I suppose some may choose not to draw attention to the focal strain, especially when there is no need to make changes to the model to improve the model fit. My reading of a few studies has been that studies often have various reasons for minimizing the local ill fit. $\endgroup$ – user81715 May 26 '16 at 18:25
  • $\begingroup$ I'm not sure what a focal strain is. I've not heard that term used in CFA. $\endgroup$ – Jeremy Miles May 26 '16 at 18:26

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