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I analyzed my data by using maximum likelihood estimation and a Bayesian approach. Now, I want to see which model has a better fit. How could I do this using either plots or numbers? Please be specific if possible.

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Welcome to the site. You should know that it's going to be a challenge for anyone to really help you without more information on your research question and especially your methods. –  rolando2 Jan 13 '13 at 13:22
    
My methods are basic linear models (y = Xbeta + e). I conducted a regression analysis for my data by using a maximum likelihood estimation approach in R and a bayesian approach in winbugs from R and calculated the parameters and the fitted values. Now, I want to see which approach has a better fit. –  Günal Jan 13 '13 at 13:34
    
I don't know as much as I would like to about Baysean methods, but is there a reason why you can't just compare AIC values? You need not be a Baysean to get a likelihood, and you know the number of parameters... Also, if you're just running OLS, shouldn't you be getting identical results from the Baysean stuff, unless you specify some non-flat prior? Again, I don't know as much about Baysean as I'd like, so that question might be a bit naive. –  ACD Jan 13 '13 at 17:54
    
As far as I know, I cannot calculate AIC values for a Bayesian model, but BIC values and I am not sure I can compare AICs with BICs. Can I? –  Günal Jan 13 '13 at 18:56
    
AIC = 2k - 2ln(L), BIC = -2ln(L) +k(ln(N)) why can't you get a AIC or BIC for either model? (L=likelihood, k=number of parameters, N = sample size) –  ACD Jan 13 '13 at 19:01

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