I have a question regarding PPP when using the Bayesian estimator. In Muthén, B. & Asparouhov, T. (2011), it says low PPP indicates poor fit but also says a PPP around 0.5 indicates an excellent-fitting model. However, in my analysis, I had a PPP about 0.99. Did this indicate a poor fit model or a good fit model? Thanks.
This would indicate good fit. You are looking for values greater than .05. A value of .5 would indicate excellent fit.
Phil Wood posted on Tuesday, November 27, 2012 - 8:35 am
Is it ever acceptable to use the ppp from a Bayesian analysis to compute a Bayes Factor between two models, or is it always preferable to use the BIC? (Assuming you have enough draws to believe it as a point estimator). I read a recent article by Meng in the Annals of Statistics which frowned on doing so, but it seems that argument is based on "using the same data twice," which we also did when using the BIC. Any thoughts from anyone?
I haven't seen any methodology on computing BF using PPP. PPP definition typically involves just 1 model while BF involves 2 models. Note also that PPP can be defined in many ways and the way it is defined in Mplus has nothing to do with what is in Meng's article. Mplus uses SEM style chi2 fit function.
If you want to compare PPP and BF testing power and quality I would recommend looking at a simulation study.
Phil Wood posted on Tuesday, December 04, 2012 - 7:25 am
I had just meant dividing the PPP from one model by the PPP from another model. Looking at just a few calculations, it doesn't sem to work very well in practice relative to using, say, the BIC. Thanks for clearing up my confusion on Meng's article, though!
I am running a second-order factor model using both ML estimation and Bayesian estimation. I have 16 subscale scores and 16 subscale scores load on four factors and the four factors load on one higher factor.
I found that Model fits from ML estimation seem to be good based on CFI(0.973) and RMSEA (0.044). However PPP from Bayesian estimation was very low. It was PPP=0.00. I don't understand why two estimation methods provide very different results in terms of model fit. Do you have any idea why this happens? (For the reference, I used default priors in bayesian estimation.)
So the p-value for the chi-square and the PPP agree as is expected. These fit statistics are less forgiving than CFI. So it isn't a matter of Bayes vs ML but a matter of which fit statistics you deem best.
Thanks a lot for your answer. I have following-up questions.
I prefer using other fit indices such as CFI and RMSEA than the chi-square when assessing the model fit. It's because the literature has demonstrated that the chi-square is sensitive to sample size.
I wonder whether PPP is also sensitive to sample size or not. If so, I wouldn't want to use PPP to assess model fit. Then my another question is that is there any other model fit indices to assess model fit in Bayesian SEM?
I don't think one should be so quick to abandon chi-square (or PPP). Instead, try to investigate why the chi-square is not good enough. What's good about the Bayes approach is that you get an interval for the fit and when you relax the model you can see how the lower limit decreases, getting closer to zero (and into the negative).
PPP is based on chi-square and therefore also has its power increase with increasing sample size. Mplus does not give any other Bayes fit measures. Note, again however that I would think you want to relax some restrictions in your model as discussed in
Muthén, B. & Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, 313-335.
If you do so, some of your key results might change.