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I want to apply a multilevel model (random intercept random slope model) comparing Maximum Likelihood and Bayesian estimation. I am used to Maximum Likelihood estimation, however, the Bayesian estimation part is not perfectly clear to me.

1) Do I necessarily have to use Hierarchical Bayes estimation when I want to apply a multilevel model the Bayesian way?

2) And in turn, can I infer that a paper that has used a Hierachical Bayes estimation necessarily applied a multilevel model?

Thanks for your help!

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1.) You can fit multilevel (mixed) models in various ways. Restricted Maximum likelihood or bayesian are the most popular ones. I would recommend MCMC (bayesian) when the data set is small or you need many random or cross Level effects. E.g. check the MCMCglmm packages in R for Multilevel with MCMC.

2.) No, there are other models using hierarchical bayes which are not truly multilevel models.

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