# What is the difference between mixed-effects modelling in the RStan and lme4 packages?

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?

• Stan is used to perform a Bayesian analysis, lme4 is used to perform a frequentist analysis. – Glen Jun 8 '18 at 19:47
• 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. – Ben Bolker Jun 8 '18 at 20:03
• 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. – Edward Tyler Jun 8 '18 at 20:06

lme4 is fully frequentist, 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
• 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