In SEM, Maximum Likelihood Method (ML) produces good results. However, while perform Bayesian estimation which gives poor results, for example, the posterior predictive p value gets value 0.00. Then how can I compare the results?
For the edification of all involved, would you please list the assumptions of each model and how you decided that your data satisfied those assumptions. Please also include the assumptions for a parametric model so that we can see why you did not choose that option. This is where I would start if the real question is something like: Why should I trust the ML approach and reject the Bayesian approach.
How did you select the prior in the Bayesian method? Might you get a "better" answer if you used a different prior, or is this something that you have already explored?
I have to agree with Prof. Ebert. You have to first map which assumptions are being violated for the results to be that different. Take a look at your assumptions for a parametric model and in that case you might even need to take a read on non-parametric SEM. Another important topic is which software are you using to run the models. Still there shouldn't be algorithms different enough to accept/reject models... Look after violations.
My data does not meet the multivariate normality. However, skew and kurtosis are with in the acceptable range. Therefore, i tried in Bayesian estimation as well. I have used AMOS 21 for both estimations.
First, check your model again using ML or MLR (robust, to non-normal distribuition). You can do this by using the indices modifiers (modindices). In fact, a low posterior predictive p-value (PPP) indicates poor fit. However, the deviance information criterion (DIC) could be used similar to AIC (Akaike) and BIC (Bayesian) in the ML estimations (low value is good). Some statistical packages does Bayesian analysis and DIC can be obtained (ex.: Mplus 7 or OpenBUGS). So, comparisions can be made using DIC and AIC information.
The problem as I understand it is that Yogarajah has a model: say crop yield = nitrogen fertilizer + potassium fertilizer + weed control. Two methods were used to fit the model: a maximum likelihood and a Bayesian approach. The two methods gave different answers (maybe ML indicated a significant relationship while Bayesian method indicated a non-significant relationship), and now we need to figure out which approach is correct.
Statistics like AIC are used when you have a dependent variable and five independent variables and you want to decide which independent variables (and interactions) are important. They are not appropriate for comparing models with different dependent variables or models where the dependent variable is transformed versus not transformed. I don't know for certain, but I think it would be inappropriate to use AIC (and similar statistics) for deciding if you should use ML versus Bayesian methods. At least that is the assumption I would start with.
I have used ML method and identified a best model for the study. The fit indices give good values in ML. However, in Bayesian, PPP value is 0.00 but the R square results between ML and Bayesian are almost similar.
So could i consider other fit indices in Bayesian ?
Depends on model selection.
Using a proper kernel (and optimizing hyperparameters) and a prior would be useful.
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