I've recently begun running some multilevel/hierarchical models. Initially I was using rstan/rstanarm, but then switched to the lme4 package.

Is the difference between these two packages only in the use of Bayesian priors (as in rstan) or not, as in lme4?

  • 3
    $\begingroup$ Stan is used to perform a Bayesian analysis, lme4 is used to perform a frequentist analysis. $\endgroup$
    – Glen
    Jun 8, 2018 at 19:47
  • 2
    $\begingroup$ This question is a little too broad and/or opinion-based as written. lme4 and rstanarm are fitting essentially the same models, in different statistical frameworks (as @Glen says). Unless you have a more specific question in mind, this boils down to "are [frequentist methods] effective for [statistical analysis], or should [Bayesian methods] be used instead?", which is not an easily answerable question. $\endgroup$
    – Ben Bolker
    Jun 8, 2018 at 20:03
  • $\begingroup$ Glen's comment appears correct since looking more at the functions in each package, I'm just going to narrow down the question in case anyone else has it. $\endgroup$ Jun 8, 2018 at 20:06

1 Answer 1


lme4 is fully frequentist (technically, it is "empirical Bayesian"), while rstanarm is fully Bayesian. That means there are more differences than just whether a prior is used. For example:

  • rstanarm reports marginal medians of the posterior density for each parameter, while lme4 reports maximum likelihood estimates (approximately analogous to the maximum a posteriori (MAP) estimator, or mode of the posterior distribution, given uninformative priors - but see this CV answer for discussion of why this is a loose analogy)
  • rstanarm reports posterior intervals based on quantiles of the marginal posterior distribution (not the more classical highest posterior density intervals), lme4 reports Wald standard errors or likelihood profile confidence intervals
  • diagnostics and convergence checking procedures are radically different.

For what it's worth,

  • brms, also based on Stan, implements a broad class of GLMMs (somewhat broader than rstanarm, I think)
  • MCMCglmm implements a broad class of Bayesian mixed models (based on older MCMC approaches rather than Hamiltonian MC)
  • the blme package implements a partly Bayesian approach to mixed models that allows for weakly or strongly informative priors, but reports MAP estimates (it builds on lme4's technology)
  • the R-INLA package (not on CRAN) uses integrated nested Laplace approximations; it also allows priors and returns MAP estimates

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