Bayesian inference for GLMs with group-specific coefficients that have unknown covariance matrices with flexible priors.
stan_glmer(formula, data = NULL, family = gaussian, subset, weights,
na.action = getOption("na.action", "na.omit"), offset, contrasts = NULL,
..., prior = normal(), prior_intercept = normal(),
prior_aux = exponential(), prior_covariance = decov(), prior_PD = FALSE,
algorithm = c("sampling", "meanfield", "fullrank"), adapt_delta = NULL,
QR = FALSE, sparse = FALSE)stan_lmer(formula, data = NULL, subset, weights,
na.action = getOption("na.action", "na.omit"), offset, contrasts = NULL,
..., prior = normal(), prior_intercept = normal(),
prior_aux = exponential(), prior_covariance = decov(), prior_PD = FALSE,
algorithm = c("sampling", "meanfield", "fullrank"), adapt_delta = NULL,
QR = FALSE)
stan_glmer.nb(formula, data = NULL, subset, weights,
na.action = getOption("na.action", "na.omit"), offset, contrasts = NULL,
link = "log", ..., prior = normal(), prior_intercept = normal(),
prior_aux = exponential(), prior_covariance = decov(), prior_PD = FALSE,
algorithm = c("sampling", "meanfield", "fullrank"), adapt_delta = NULL,
QR = FALSE)
Same as for glmer. We
strongly advise against omitting the data argument. Unless
data is specified (and is a data frame) many post-estimation
functions (including update, loo, kfold) are not
guaranteed to work properly.
Same as glm.
Same as glm, but rarely
specified.
The prior distribution for the regression coefficients.
prior should be a call to one of the various functions provided by
rstanarm for specifying priors. The subset of these functions that
can be used for the prior on the coefficients can be grouped into several
"families":
| Family | Functions |
| Student t family | normal, student_t, cauchy |
| Hierarchical shrinkage family | hs, hs_plus |
| Laplace family | laplace, lasso |
| Product normal family | product_normal |
See the priors help page for details on the families and
how to specify the arguments for all of the functions in the table above.
To omit a prior ---i.e., to use a flat (improper) uniform prior---
prior can be set to NULL, although this is rarely a good
idea.
Note: Unless QR=TRUE, if prior is from the Student t
family or Laplace family, and if the autoscale argument to the
function used to specify the prior (e.g. normal) is left at
its default and recommended value of TRUE, then the default or
user-specified prior scale(s) may be adjusted internally based on the
scales of the predictors. See the priors help page and the
Prior Distributions vignette for details on the rescaling and the
prior_summary function for a summary of the priors used for a
particular model.
The prior distribution for the intercept.
prior_intercept can be a call to normal, student_t or
cauchy. See the priors help page for details on
these functions. To omit a prior on the intercept ---i.e., to use a flat
(improper) uniform prior--- prior_intercept can be set to
NULL.
Note: If using a dense representation of the design matrix
---i.e., if the sparse argument is left at its default value of
FALSE--- then the prior distribution for the intercept is set so it
applies to the value when all predictors are centered. If you prefer
to specify a prior on the intercept without the predictors being
auto-centered, then you have to omit the intercept from the
formula and include a column of ones as a predictor,
in which case some element of prior specifies the prior on it,
rather than prior_intercept.
The prior distribution for the "auxiliary" parameter (if
applicable). The "auxiliary" parameter refers to a different parameter
depending on the family. For Gaussian models prior_aux
controls "sigma", the error
standard deviation. For negative binomial models prior_aux controls
"reciprocal_dispersion", which is similar to the
"size" parameter of rnbinom:
smaller values of "reciprocal_dispersion" correspond to
greater dispersion. For gamma models prior_aux sets the prior on
to the "shape" parameter (see e.g.,
rgamma), and for inverse-Gaussian models it is the
so-called "lambda" parameter (which is essentially the reciprocal of
a scale parameter). Binomial and Poisson models do not have auxiliary
parameters.
prior_aux can be a call to exponential to
use an exponential distribution, or normal, student_t or
cauchy, which results in a half-normal, half-t, or half-Cauchy
prior. See priors for details on these functions. To omit a
prior ---i.e., to use a flat (improper) uniform prior--- set
prior_aux to NULL.
Cannot be NULL; see decov for
more information about the default arguments.
A logical scalar (defaulting to FALSE) indicating
whether to draw from the prior predictive distribution instead of
conditioning on the outcome.
A string (possibly abbreviated) indicating the
estimation approach to use. Can be "sampling" for MCMC (the
default), "optimizing" for optimization, "meanfield" for
variational inference with independent normal distributions, or
"fullrank" for variational inference with a multivariate normal
distribution. See rstanarm-package for more details on the
estimation algorithms. NOTE: not all fitting functions support all four
algorithms.
Only relevant if algorithm="sampling". See
adapt_delta for details.
A logical scalar defaulting to FALSE, but if TRUE
applies a scaled qr decomposition to the design matrix,
\(X = Q^\ast R^\ast\), where \(Q^\ast = Q \sqrt{n-1}\) and \(R^\ast = \frac{1}{\sqrt{n-1}} R\). The coefficients relative to \(Q^\ast\) are obtained and then
premultiplied by the inverse of \(R^{\ast}\) to obtain coefficients
relative to the original predictors, \(X\). These transformations do not
change the likelihood of the data but are recommended for computational
reasons when there are multiple predictors. Importantly, while the columns
of \(X\) are almost always correlated, the columns of \(Q^\ast\)
are uncorrelated by design, which often makes sampling from the posterior
easier. However, because when QR is TRUE the prior
argument applies to the coefficients relative to \(Q^\ast\) (and
those are not very interpretable), setting QR=TRUE is only
recommended if you do not have an informative prior for the regression
coefficients.
For more details see the Stan case study The QR Decomposition For Regression Models at http://mc-stan.org/users/documentation/case-studies/qr_regression.html.
A logical scalar (defaulting to FALSE) indicating
whether to use a sparse representation of the design (X) matrix.
If TRUE, the the design matrix is not centered (since that would
destroy the sparsity) and likewise it is not possible to specify both
QR = TRUE and sparse = TRUE. Depending on how many zeros
there are in the design matrix, setting sparse = TRUE may make
the code run faster and can consume much less RAM.
For stan_glmer.nb only, the link function to use. See
neg_binomial_2.
A stanreg object is returned
for stan_glmer, stan_lmer, stan_glmer.nb.
The stan_glmer function is similar in syntax to
glmer but rather than performing (restricted) maximum
likelihood estimation of generalized linear models, Bayesian estimation is
performed via MCMC. The Bayesian model adds priors on the
regression coefficients (in the same way as stan_glm) and
priors on the terms of a decomposition of the covariance matrices of the
group-specific parameters. See priors for more information
about the priors.
The stan_lmer function is equivalent to stan_glmer with
family = gaussian(link = "identity").
The stan_glmer.nb function, which takes the extra argument
link, is a wrapper for stan_glmer with family =
neg_binomial_2(link).
Gelman, A. and Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge, UK. (Ch. 11-15)
stanreg-methods and
glmer.
The vignette for stan_glmer and the Hierarchical
Partial Pooling vignette.
# NOT RUN {
# see help(example_model) for details on the model below
if (!exists("example_model")) example(example_model)
print(example_model, digits = 1)
# }
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