A model for case-control studies with optional prior distributions for the coefficients, intercept, and auxiliary parameters.
stan_clogit(formula, data, subset, na.action = NULL, ..., strata,
prior = normal(), prior_covariance = decov(), prior_PD = FALSE,
algorithm = c("sampling", "optimizing", "meanfield", "fullrank"),
adapt_delta = NULL, QR = FALSE, sparse = FALSE)Same as for glmer,
except that any intercept included in the formula will be dropped. 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.
Further arguments passed to the function in the rstan
package (sampling, vb, or
optimizing), corresponding to the estimation method
named by algorithm. For example, if algorithm is
"sampling" it is possibly to specify iter, chains,
cores, refresh, etc.
A factor indicating the groups in the data where the number of
successes (possibly one) is fixed by the research design. It may be useful
to use interaction or strata to
create this factor. However, the strata argument must not rely on
any object besides the data data.frame.
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.
Cannot be NULL when lme4-style group-specific
terms are included in the formula. See decov for
more information about the default arguments. Ignored when there are no
group-specific terms.
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.
A stanreg object is returned
for stan_clogit.
The stan_clogit function is mostly similar in syntax to
clogit but rather than performing maximum
likelihood estimation of generalized linear models, full Bayesian
estimation is performed (if algorithm is "sampling") via
MCMC. The Bayesian model adds priors (independent by default) on the
coefficients of the GLM.
The data.frame passed to the data argument must be sorted by
the variable passed to the strata argument.
The formula may have group-specific terms like in
stan_glmer but should not allow the intercept to vary by the
stratifying variable, since there is no information in the data with which
to estimate such deviations in the intercept.
stanreg-methods and
clogit.
The vignette for Bernoulli and binomial models.
# NOT RUN {
post <- stan_clogit(case ~ spontaneous + induced + (1 | education),
strata = stratum,
data = infert[order(infert$stratum), ],
subset = parity <= 2,
QR = TRUE,
chains = 2, iter = 500) # for speed only
nd <- infert[infert$parity > 2, c("case", "spontaneous", "induced",
"education", "stratum")]
# next line would fail without case and stratum variables
pr <- posterior_linpred(post, newdata = nd, transform = TRUE)
all.equal(rep(sum(nd$case), nrow(pr)), rowSums(pr)) # not a random variable
# }
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