Fit Bayesian generalized (non-)linear multivariate multilevel models using Stan for full Bayesian inference. A wide range of distributions and link functions are supported, allowing users to fit -- among others -- linear, robust linear, count data, survival, response times, ordinal, zero-inflated, hurdle, and even self-defined mixture models all in a multilevel context. Further modeling options include non-linear and smooth terms, auto-correlation structures, censored data, meta-analytic standard errors, and quite a few more. In addition, all parameters of the response distributions can be predicted in order to perform distributional regression. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with posterior predictive checks and leave-one-out cross-validation.
brm(
formula,
data,
family = gaussian(),
prior = NULL,
autocor = NULL,
data2 = NULL,
cov_ranef = NULL,
sample_prior = "no",
sparse = NULL,
knots = NULL,
drop_unused_levels = TRUE,
stanvars = NULL,
stan_funs = NULL,
fit = NA,
save_pars = getOption("brms.save_pars", NULL),
save_ranef = NULL,
save_mevars = NULL,
save_all_pars = NULL,
init = NULL,
inits = NULL,
chains = 4,
iter = 2000,
warmup = floor(iter/2),
thin = 1,
cores = getOption("mc.cores", 1),
threads = getOption("brms.threads", NULL),
opencl = getOption("brms.opencl", NULL),
normalize = getOption("brms.normalize", TRUE),
control = NULL,
algorithm = getOption("brms.algorithm", "sampling"),
backend = getOption("brms.backend", "rstan"),
future = getOption("future", FALSE),
silent = 1,
seed = NA,
save_model = NULL,
stan_model_args = list(),
file = NULL,
file_compress = TRUE,
file_refit = getOption("brms.file_refit", "never"),
empty = FALSE,
rename = TRUE,
...
)An object of class formula,
brmsformula, or mvbrmsformula (or one that can
be coerced to that classes): A symbolic description of the model to be
fitted. The details of model specification are explained in
brmsformula.
An object of class data.frame (or one that can be coerced
to that class) containing data of all variables used in the model.
A description of the response distribution and link function to
be used in the model. This can be a family function, a call to a family
function or a character string naming the family. Every family function has
a link argument allowing to specify the link function to be applied
on the response variable. If not specified, default links are used. For
details of supported families see brmsfamily. By default, a
linear gaussian model is applied. In multivariate models,
family might also be a list of families.
One or more brmsprior objects created by
set_prior or related functions and combined using the
c method or the + operator. See also default_prior
for more help.
(Deprecated) An optional cor_brms object
describing the correlation structure within the response variable (i.e.,
the 'autocorrelation'). See the documentation of cor_brms for
a description of the available correlation structures. Defaults to
NULL, corresponding to no correlations. In multivariate models,
autocor might also be a list of autocorrelation structures.
It is now recommend to specify autocorrelation terms directly
within formula. See brmsformula for more details.
A named list of objects containing data, which
cannot be passed via argument data. Required for some objects
used in autocorrelation structures to specify dependency structures
as well as for within-group covariance matrices.
(Deprecated) A list of matrices that are proportional to the
(within) covariance structure of the group-level effects. The names of the
matrices should correspond to columns in data that are used as
grouping factors. All levels of the grouping factor should appear as
rownames of the corresponding matrix. This argument can be used, among
others to model pedigrees and phylogenetic effects.
It is now recommended to specify those matrices in the formula
interface using the gr and related functions. See
vignette("brms_phylogenetics") for more details.
Indicate if draws from priors should be drawn
additionally to the posterior draws. Options are "no" (the
default), "yes", and "only". Among others, these draws can
be used to calculate Bayes factors for point hypotheses via
hypothesis. Please note that improper priors are not sampled,
including the default improper priors used by brm. See
set_prior on how to set (proper) priors. Please also note
that prior draws for the overall intercept are not obtained by default
for technical reasons. See brmsformula how to obtain prior
draws for the intercept. If sample_prior is set to "only",
draws are drawn solely from the priors ignoring the likelihood, which
allows among others to generate draws from the prior predictive
distribution. In this case, all parameters must have proper priors.
(Deprecated) Logical; indicates whether the population-level
design matrices should be treated as sparse (defaults to FALSE). For
design matrices with many zeros, this can considerably reduce required
memory. Sampling speed is currently not improved or even slightly
decreased. It is now recommended to use the sparse argument of
brmsformula and related functions.
Optional list containing user specified knot values to be used
for basis construction of smoothing terms. See
gamm for more details.
Should unused factors levels in the data be
dropped? Defaults to TRUE.
An optional stanvars object generated by function
stanvar to define additional variables for use in
Stan's program blocks.
(Deprecated) An optional character string containing
self-defined Stan functions, which will be included in the functions
block of the generated Stan code. It is now recommended to use the
stanvars argument for this purpose instead.
An instance of S3 class brmsfit derived from a previous
fit; defaults to NA. If fit is of class brmsfit, the
compiled model associated with the fitted result is re-used and all
arguments modifying the model code or data are ignored. It is not
recommended to use this argument directly, but to call the
update method, instead.
An object generated by save_pars controlling
which parameters should be saved in the model. The argument has no
impact on the model fitting itself.
(Deprecated) A flag to indicate if group-level effects for
each level of the grouping factor(s) should be saved (default is
TRUE). Set to FALSE to save memory. The argument has no
impact on the model fitting itself.
(Deprecated) A flag to indicate if draws of latent
noise-free variables obtained by using me and mi terms should
be saved (default is FALSE). Saving these draws allows to better
use methods such as predict with the latent variables but leads to
very large R objects even for models of moderate size and complexity.
(Deprecated) A flag to indicate if draws from all
variables defined in Stan's parameters block should be saved
(default is FALSE). Saving these draws is required in order to
apply the methods bridge_sampler, bayes_factor, and
post_prob. Can be set globally for the current R session via the
"brms.save_pars" option (see options).
Initial values for the sampler. If NULL (the default) or
"random", Stan will randomly generate initial values for parameters
in a reasonable range. If 0, all parameters are initialized to zero
on the unconstrained space. This option is sometimes useful for certain
families, as it happens that default random initial values cause draws to
be essentially constant. Generally, setting init = 0 is worth a try,
if chains do not initialize or behave well. Alternatively, init can
be a list of lists containing the initial values, or a function (or
function name) generating initial values. The latter options are mainly
implemented for internal testing but are available to users if necessary.
If specifying initial values using a list or a function then currently the
parameter names must correspond to the names used in the generated Stan
code (not the names used in R). For more details on specifying initial
values you can consult the documentation of the selected backend.
(Deprecated) Alias of init.
Number of Markov chains (defaults to 4).
Number of total iterations per chain (including warmup; defaults to 2000).
A positive integer specifying number of warmup (aka burnin)
iterations. This also specifies the number of iterations used for stepsize
adaptation, so warmup draws should not be used for inference. The number
of warmup should not be larger than iter and the default is
iter/2.
Thinning rate. Must be a positive integer. Set thin > 1 to
save memory and computation time if iter is large.
Number of cores to use when executing the chains in parallel,
which defaults to 1 but we recommend setting the mc.cores option to
be as many processors as the hardware and RAM allow (up to the number of
chains). For non-Windows OS in non-interactive R sessions, forking is used
instead of PSOCK clusters.
Number of threads to use in within-chain parallelization. For
more control over the threading process, threads may also be a
brmsthreads object created by threading. Within-chain
parallelization is experimental! We recommend its use only if you are
experienced with Stan's reduce_sum function and have a slow running
model that cannot be sped up by any other means. Can be set globally for
the current R session via the "brms.threads" option (see
options).
The platform and device IDs of the OpenCL device to use for
fitting using GPU support. If you don't know the IDs of your OpenCL device,
c(0,0) is most likely what you need. For more details, see
opencl. Can be set globally for the current R session via
the "brms.opencl" option
Logical. Indicates whether normalization constants should
be included in the Stan code (defaults to TRUE). Setting it
to FALSE requires Stan version >= 2.25 to work. If FALSE,
sampling efficiency may be increased but some post processing functions
such as bridge_sampler will not be available. Can be
controlled globally for the current R session via the `brms.normalize`
option.
A named list of parameters to control the sampler's
behavior. It defaults to NULL so all the default values are used.
The most important control parameters are discussed in the 'Details'
section below. For a comprehensive overview see
stan.
Character string naming the estimation approach to use.
Options are "sampling" for MCMC (the default), "meanfield" for
variational inference with independent normal distributions,
"fullrank" for variational inference with a multivariate normal
distribution, or "fixed_param" for sampling from fixed parameter
values. Can be set globally for the current R session via the
"brms.algorithm" option (see options).
Character string naming the package to use as the backend for
fitting the Stan model. Options are "rstan" (the default) or
"cmdstanr". Can be set globally for the current R session via the
"brms.backend" option (see options). Details on the
rstan and cmdstanr packages are available at
https://mc-stan.org/rstan/ and https://mc-stan.org/cmdstanr/,
respectively. Additionally a "mock" backend is available to make
testing brms and packages that depend on it easier.
The "mock" backend does not actually do any fitting, it only checks
the generated Stan code for correctness and then returns whatever is passed
in an additional mock_fit argument as the result of the fit.
Logical; If TRUE, the future
package is used for parallel execution of the chains and argument
cores will be ignored. Can be set globally for the current R
session via the "future" option. The execution type is controlled via
plan (see the examples section below).
Verbosity level between 0 and 2.
If 1 (the default), most of the
informational messages of compiler and sampler are suppressed.
If 2, even more messages are suppressed. The actual
sampling progress is still printed. Set refresh = 0 to turn this off
as well. If using backend = "rstan" you can also set
open_progress = FALSE to prevent opening additional progress bars.
The seed for random number generation to make results
reproducible. If NA (the default), Stan will set the seed
randomly.
Either NULL or a character string. In the latter
case, the model's Stan code is saved via cat in a text file
named after the string supplied in save_model.
A list of further arguments passed to
rstan::stan_model for backend =
"rstan" or to cmdstanr::cmdstan_model for backend =
"cmdstanr", which allows to change how models are compiled.
Either NULL or a character string. In the latter case, the
fitted model object is saved via saveRDS in a file named
after the string supplied in file. The .rds extension is
added automatically. If the file already exists, brm will load and
return the saved model object instead of refitting the model.
Unless you specify the file_refit argument as well, the existing
files won't be overwritten, you have to manually remove the file in order
to refit and save the model under an existing file name. The file name
is stored in the brmsfit object for later usage.
Logical or a character string, specifying one of the
compression algorithms supported by saveRDS. If the
file argument is provided, this compression will be used when saving
the fitted model object.
Modifies when the fit stored via the file argument
is re-used. Can be set globally for the current R session via the
"brms.file_refit" option (see options).
For "never" (default) the fit is always loaded if it
exists and fitting is skipped. For "always" the model is always
refitted. If set to "on_change", brms will
refit the model if model, data or algorithm as passed to Stan differ from
what is stored in the file. This also covers changes in priors,
sample_prior, stanvars, covariance structure, etc. If you
believe there was a false positive, you can use
brmsfit_needs_refit to see why refit is deemed necessary.
Refit will not be triggered for changes in additional parameters of the fit
(e.g., initial values, number of iterations, control arguments, ...). A
known limitation is that a refit will be triggered if within-chain
parallelization is switched on/off.
Logical. If TRUE, the Stan model is not created
and compiled and the corresponding 'fit' slot of the brmsfit
object will be empty. This is useful if you have estimated a brms-created
Stan model outside of brms and want to feed it back into the package.
For internal use only.
Further arguments passed to Stan.
For backend = "rstan" the arguments are passed to
sampling or vb.
For backend = "cmdstanr" the arguments are passed to the
cmdstanr::sample or cmdstanr::variational method.
An object of class brmsfit, which contains the posterior
draws along with many other useful information about the model. Use
methods(class = "brmsfit") for an overview on available methods.
Fit a generalized (non-)linear multivariate multilevel model via
full Bayesian inference using Stan. A general overview is provided in the
vignettes vignette("brms_overview") and
vignette("brms_multilevel"). For a full list of available vignettes
see vignette(package = "brms").
Formula syntax of brms models
Details of the formula syntax applied in brms can be found in
brmsformula.
Families and link functions
Details of families supported by brms can be found in
brmsfamily.
Prior distributions
Priors should be specified using the
set_prior function. Its documentation
contains detailed information on how to correctly specify priors. To find
out on which parameters or parameter classes priors can be defined, use
default_prior. Default priors are chosen to be
non or very weakly informative so that their influence on the results will
be negligible and you usually don't have to worry about them. However,
after getting more familiar with Bayesian statistics, I recommend you to
start thinking about reasonable informative priors for your model
parameters: Nearly always, there is at least some prior information
available that can be used to improve your inference.
Adjusting the sampling behavior of Stan
In addition to choosing the number of iterations, warmup draws, and
chains, users can control the behavior of the NUTS sampler, by using the
control argument. The most important reason to use control is
to decrease (or eliminate at best) the number of divergent transitions that
cause a bias in the obtained posterior draws. Whenever you see the
warning "There were x divergent transitions after warmup." you should
really think about increasing adapt_delta. To do this, write
control = list(adapt_delta = <x>), where <x> should usually
be value between 0.8 (current default) and 1. Increasing
adapt_delta will slow down the sampler but will decrease the number
of divergent transitions threatening the validity of your posterior
draws.
Another problem arises when the depth of the tree being evaluated in each
iteration is exceeded. This is less common than having divergent
transitions, but may also bias the posterior draws. When it happens,
Stan will throw out a warning suggesting to increase
max_treedepth, which can be accomplished by writing control =
list(max_treedepth = <x>) with a positive integer <x> that should
usually be larger than the current default of 10. For more details
on the control argument see stan.
Paul-Christian Buerkner (2017). brms: An R Package for Bayesian Multilevel
Models Using Stan. Journal of Statistical Software, 80(1), 1-28.
doi:10.18637/jss.v080.i01
Paul-Christian Buerkner (2018). Advanced Bayesian Multilevel Modeling
with the R Package brms. The R Journal. 10(1), 395–411.
doi:10.32614/RJ-2018-017
if (FALSE) {
# Poisson regression for the number of seizures in epileptic patients
fit1 <- brm(
count ~ zBase * Trt + (1|patient),
data = epilepsy, family = poisson(),
prior = prior(normal(0, 10), class = b) +
prior(cauchy(0, 2), class = sd)
)
# generate a summary of the results
summary(fit1)
# plot the MCMC chains as well as the posterior distributions
plot(fit1)
# predict responses based on the fitted model
head(predict(fit1))
# plot conditional effects for each predictor
plot(conditional_effects(fit1), ask = FALSE)
# investigate model fit
loo(fit1)
pp_check(fit1)
# Ordinal regression modeling patient's rating of inhaler instructions
# category specific effects are estimated for variable 'treat'
fit2 <- brm(rating ~ period + carry + cs(treat),
data = inhaler, family = sratio("logit"),
prior = set_prior("normal(0,5)"), chains = 2)
summary(fit2)
plot(fit2, ask = FALSE)
WAIC(fit2)
# Survival regression modeling the time between the first
# and second recurrence of an infection in kidney patients.
fit3 <- brm(time | cens(censored) ~ age * sex + disease + (1|patient),
data = kidney, family = lognormal())
summary(fit3)
plot(fit3, ask = FALSE)
plot(conditional_effects(fit3), ask = FALSE)
# Probit regression using the binomial family
ntrials <- sample(1:10, 100, TRUE)
success <- rbinom(100, size = ntrials, prob = 0.4)
x <- rnorm(100)
data4 <- data.frame(ntrials, success, x)
fit4 <- brm(success | trials(ntrials) ~ x, data = data4,
family = binomial("probit"))
summary(fit4)
# Non-linear Gaussian model
fit5 <- brm(
bf(cum ~ ult * (1 - exp(-(dev/theta)^omega)),
ult ~ 1 + (1|AY), omega ~ 1, theta ~ 1,
nl = TRUE),
data = loss, family = gaussian(),
prior = c(
prior(normal(5000, 1000), nlpar = "ult"),
prior(normal(1, 2), nlpar = "omega"),
prior(normal(45, 10), nlpar = "theta")
),
control = list(adapt_delta = 0.9)
)
summary(fit5)
conditional_effects(fit5)
# Normal model with heterogeneous variances
data_het <- data.frame(
y = c(rnorm(50), rnorm(50, 1, 2)),
x = factor(rep(c("a", "b"), each = 50))
)
fit6 <- brm(bf(y ~ x, sigma ~ 0 + x), data = data_het)
summary(fit6)
plot(fit6)
conditional_effects(fit6)
# extract estimated residual SDs of both groups
sigmas <- exp(as.data.frame(fit6, variable = "^b_sigma_", regex = TRUE))
ggplot(stack(sigmas), aes(values)) +
geom_density(aes(fill = ind))
# Quantile regression predicting the 25%-quantile
fit7 <- brm(bf(y ~ x, quantile = 0.25), data = data_het,
family = asym_laplace())
summary(fit7)
conditional_effects(fit7)
# use the future package for more flexible parallelization
library(future)
plan(multisession, workers = 4)
fit7 <- update(fit7, future = TRUE)
# fit a model manually via rstan
scode <- stancode(count ~ Trt, data = epilepsy)
sdata <- standata(count ~ Trt, data = epilepsy)
stanfit <- rstan::stan(model_code = scode, data = sdata)
# feed the Stan model back into brms
fit8 <- brm(count ~ Trt, data = epilepsy, empty = TRUE)
fit8$fit <- stanfit
fit8 <- rename_pars(fit8)
summary(fit8)
}