Question about Bayesian analysis for likelihood ratio test or goodness of fit

 In classic statistic method (SPSS), we have a goodness of fit or likelihood ratio test before the model estimate. And we can know whether have differences between the reduced model (only have residual) and final model via likelihood ratio chi-square and p value.
 But now, when i replaced it with bayesian analysis, i didn't find some evidence like p value. so, anyone knows which methods can replace the goodness of fit in multinomial logistic regression or which packages in R can solve this issue.   (the method need provide a BF value to support the null hypothsis that the two models were not different).
 Thank you !