I'm currently using Mplus 7 (demo version) to perform an Actor Partner Interdependence Mediation Model. The fit indices for my model are good, in fact they are too good. I'm quite new to Mplus and I don't really know why they are so over the top.
Number of Free Parameters 27
H0 Value -3062.519 H0 Scaling Correction Factor 1.0254 for MLR H1 Value -3062.519 H1 Scaling Correction Factor 1.0254 for MLR
Akaike (AIC) 6179.039 Bayesian (BIC) 6269.920 Sample-Size Adjusted BIC 6184.364 Value 0.000* Degrees of Freedom 0 P-Value 0.0000 Scaling Correction Factor 1.0000 for MLR Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.000
CFI 1.000 TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model Value 217.002 Degrees of Freedom 14 P-Value 0.0000
I have the same problem with my path models. CFI is exactly 1 and the TLI is greater than 1. SRMR = 0.005, RMSEA = 0.00 However, The chi-square test of model fit indicates a value of 1.523 with 2 degrees of freedom and the number of free parameters is 25.
But does these high values of CFI/TLI indicate that there are problems with my model? I don't get any errors and the findings are highly in line with the theoretical expectations.
What can I do about this? Do you have any references about TLI greater than 1? or having such good indices?
TLI can be greater than 1 but that should simply be considered as 1, that is, perfect fit according to TLI. This situation of a very well-fitting model can arise when the sample size is low and/or when the correlations are low. Also check on SEMNET.
Thank you for your answer Bengt and reference to SEMNET. The sample size was quite ok, 82 clusters with 494 observations. Indeed many of the correlations were low, is that bad? What I am concerned about is if there is overfit in my model? In this sense, I would be worry about my estimates being of use or value. Additionally, if I can say that the results can be generalised to the outside population?
I appreciate the response! Good to hear is not bad Do you have citations about this last part you mentioned by any chance? --> "less power to reject the model. A chi-square value less than the degrees of freedom is sometimes an indication of overfit."
I can't think of references for this off hand. The power issue is well known and probably has many articles on it and is perhaps also in Bollen's SEM book - ask on SEMNET. The overfitting part is just my own undocumented experience/hunch.