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I am estimating latent curve models (btw, this is my first time using LCM) for multiple indices (n = 6) taken from the same sample of research subjects. For some of these indices, the fit measures TFI and IFI are indicating that the model is overfitted (TFI > 1.2 & IFI > 1.2), but for other indices they are telling me the model fit is quite good (TFI and IFI around 1.0). Also, none of the conditional models (predictors n = 3) indicate overfitting.

Can someone explain why, for some indices, the model is overfitted, yet for others it is not, even though the sample size nor the number of parameters does not change?

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It's not overfit (necessarily). I've never heard people describe these indicators as overfitting.

Some fit indices can go over 1, others can't. You seem to have a typo in your question, as you report IFI being 1.0 and also being 1.2. I presume that by TFI you mean TLI - it's also called the NNFI, which stands for Non-Normed Fit Index - it's not normed because it can go over 1.

Check the equations for the indices - if your chi-square is lower than df, the the indices might go over 1 (or might be equal to 1).

I'm not sure what you mean by multiple indices.

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  • $\begingroup$ In Bollen & Curran (2005), they state that TLI (sorry for the typo) and IFI scores "much greater than 1 (e.g. 1.2) suggest the possibility of overfitting the data or having a model with too many parameters" (p. 46). For my study, I am creating multiple models for different indices (e.g. word frequency, word range, concreteness) taken from the same sample of subjects. The models for some of these indices are returning TLI and IFI values that are what Bollen and Curran (2006) claim to be evidence of overfitting. Models for some of the other indices, are not. Thanks. I'll check my equations. $\endgroup$
    – user145250
    Mar 14, 2017 at 10:40
  • $\begingroup$ Thanks. I didn't remember that (and I've read that book!) $\endgroup$
    – Jeremy Miles
    Mar 14, 2017 at 15:34
  • $\begingroup$ I suspect your model has very few df - is that the case? $\endgroup$
    – Jeremy Miles
    Mar 14, 2017 at 15:35
  • $\begingroup$ The models returning TLI and IFI scores at or above 1.2 all have df = 8. I don't remember (from what I've read) if that's considered "very few". $\endgroup$
    – user145250
    Mar 15, 2017 at 16:49
  • $\begingroup$ It's on the lower side. But it's not bad for LCMs that don't have anything complicated going on. $\endgroup$
    – Jeremy Miles
    Mar 15, 2017 at 23:49

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