Bayesian inference for ordinal (or binary) regression models under a proportional odds assumption.
stan_polr(formula, data, weights, ..., subset,
na.action = getOption("na.action", "na.omit"), contrasts = NULL,
model = TRUE, method = c("logistic", "probit", "loglog", "cloglog",
"cauchit"), prior = R2(stop("'location' must be specified")),
prior_counts = dirichlet(1), shape = NULL, rate = NULL,
prior_PD = FALSE, algorithm = c("sampling", "meanfield", "fullrank"),
adapt_delta = NULL, do_residuals = NULL)stan_polr.fit(x, y, wt = NULL, offset = NULL, method = c("logistic",
"probit", "loglog", "cloglog", "cauchit"), ...,
prior = R2(stop("'location' must be specified")),
prior_counts = dirichlet(1), shape = NULL, rate = NULL,
prior_PD = FALSE, algorithm = c("sampling", "meanfield", "fullrank"),
adapt_delta = NULL, do_residuals = algorithm == "sampling")
Same as polr,
but 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 polr, but
rarely specified.
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.
One of 'logistic', 'probit', 'loglog', 'cloglog' or 'cauchit',
but can be abbreviated. See polr for more details.
A call to dirichlet to specify the
prior counts of the outcome when the predictors are at their sample
means.
Either NULL or a positive scalar that is interpreted
as the shape parameter for a GammaDistribution on
the exponent applied to the probability of success when there are only
two outcome categories. If NULL, which is the default, then the
exponent is taken to be fixed at \(1\).
Either NULL or a positive scalar that is interpreted
as the rate parameter for a GammaDistribution on
the exponent applied to the probability of success when there are only
two outcome categories. If NULL, which is the default, then the
exponent is taken to be fixed at \(1\).
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 indicating whether or not to
automatically calculate fit residuals after sampling completes. Defaults to
TRUE if and only if algorithm="sampling". Setting
do_residuals=FALSE is only useful in the somewhat rare case that
stan_polr appears to finish sampling but hangs instead of returning
the fitted model object.
A design matrix.
A response variable, which must be a (preferably ordered) factor.
A numeric vector (possibly NULL) of observation weights.
A numeric vector (possibly NULL) of offsets.
A stanreg object is returned
for stan_polr.
A stanfit object (or a slightly modified
stanfit object) is returned if stan_polr.fit is called directly.
The stan_polr function is similar in syntax to
polr but rather than performing maximum likelihood
estimation of a proportional odds model, Bayesian estimation is performed
(if algorithm = "sampling") via MCMC. The stan_polr
function calls the workhorse stan_polr.fit function, but it is
possible to call the latter directly.
As for stan_lm, it is necessary to specify the prior
location of \(R^2\). In this case, the \(R^2\) pertains to the
proportion of variance in the latent variable (which is discretized
by the cutpoints) attributable to the predictors in the model.
Prior beliefs about the cutpoints are governed by prior beliefs about the
outcome when the predictors are at their sample means. Both of these
are explained in the help page on priors and in the
rstanarm vignettes.
Unlike polr, stan_polr also allows the "ordinal"
outcome to contain only two levels, in which case the likelihood is the
same by default as for stan_glm with family = binomial
but the prior on the coefficients is different. However, stan_polr
allows the user to specify the shape and rate hyperparameters,
in which case the probability of success is defined as the logistic CDF of
the linear predictor, raised to the power of alpha where alpha
has a gamma prior with the specified shape and rate. This
likelihood is called “scobit” by Nagler (1994) because if alpha
is not equal to \(1\), then the relationship between the linear predictor
and the probability of success is skewed. If shape or rate is
NULL, then alpha is assumed to be fixed to \(1\).
Otherwise, it is usually advisible to set shape and rate to
the same number so that the expected value of alpha is \(1\) while
leaving open the possibility that alpha may depart from \(1\) a
little bit. It is often necessary to have a lot of data in order to estimate
alpha with much precision and always necessary to inspect the
Pareto shape parameters calculated by loo to see if the
results are particularly sensitive to individual observations.
Users should think carefully about how the outcome is coded when using
a scobit-type model. When alpha is not \(1\), the asymmetry
implies that the probability of success is most sensitive to the predictors
when the probability of success is less than \(0.63\). Reversing the
coding of the successes and failures allows the predictors to have the
greatest impact when the probability of failure is less than \(0.63\).
Also, the gamma prior on alpha is positively skewed, but you
can reverse the coding of the successes and failures to circumvent this
property.
Nagler, J., (1994). Scobit: An Alternative Estimator to Logit and Probit. American Journal of Political Science. 230 -- 255.
stanreg-methods and
polr.
The vignette for stan_polr.
# NOT RUN {
if (!grepl("^sparc", R.version$platform)) {
fit <- stan_polr(tobgp ~ agegp, data = esoph, method = "probit",
prior = R2(0.2, "mean"), init_r = 0.1, seed = 12345,
algorithm = "fullrank") # for speed only
print(fit)
plot(fit)
}
# }
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