Draw from posterior predictive distribution
The posterior predictive distribution is the distribution of the outcome implied by the model after using the observed data to update our beliefs about the unknown parameters in the model. Simulating data from the posterior predictive distribution using the observed predictors is useful for checking the fit of the model. Drawing from the posterior predictive distribution at interesting values of the predictors also lets us visualize how a manipulation of a predictor affects (a function of) the outcome(s). With new observations of predictor variables we can use the posterior predictive distribution to generate predicted outcomes.
"posterior_predict"(object, newdata = NULL, draws = NULL, re.form = NULL, fun = NULL, seed = NULL, offset = NULL, ...)
- A fitted model object returned by one of the
rstanarm modeling functions. See
- Optionally, a data frame in which to look for variables with
which to predict. If omitted, the model matrix is used. If
newdatais provided and any variables were transformed (e.g. rescaled) in the data used to fit the model, then these variables must also be transformed in
newdata. This only applies if variables were transformed before passing the data to one of the modeling functions and not if transformations were specified inside the model formula. Also see the Note section below for a note about using the
newdataargument with with binomial models.
- An integer indicating the number of draws to return. The default and maximum number of draws is the size of the posterior sample.
group-levelparameters, a formula indicating which group-level parameters to condition on when making predictions.
re.formis specified in the same form as for
predict.merMod. The default,
NULL, indicates that all estimated group-level parameters are conditioned on. To refrain from conditioning on any group-level parameters, specify
newdataargument may include new levels of the grouping factors that were specified when the model was estimated, in which case the resulting posterior predictions marginalize over the relevant variables.
- An optional function to apply to the results.
funis found by a call to
match.funand so can be specified as a function object, a string naming a function, etc.
- An optional
- A vector of offsets. Only required if
newdatais specified and an
offsetargument was specified when fitting the model.
- Currently ignored.
nrow(newdata)matrix of simulations from the posterior predictive distribution. Each row of the matrix is a vector of predictions generated using a single draw of the model parameters from the posterior distribution. The returned matrix will also have class
"ppd"to indicate it contains draws from the posterior predictive distribution.
For binomial models with a number of trials greater than one (i.e., not
Bernoulli models), if
newdata is specified then it must include all
variables needed for computing the number of binomial trials to use for the
predictions. For example if the left-hand side of the model formula is
cbind(successes, failures) then both
failures must be in
newdata. The particular values of
newdata do not matter so
long as their sum is the desired number of trials. If the left-hand side of
the model formula were
cbind(successes, trials - successes) then
successes would need to be in
successes set to
the number of trials. See the Examples section below and the
How to Use the rstanarm Package for examples.
pp_check for graphical posterior predictive checks.
Examples of posterior predictive checking can also be found in the
rstanarm vignettes and demos.
if (!exists("example_model")) example(example_model) yrep <- posterior_predict(example_model) table(yrep) # Using newdata counts <- c(18,17,15,20,10,20,25,13,12) outcome <- gl(3,1,9) treatment <- gl(3,3) fit3 <- stan_glm(counts ~ outcome + treatment, family = poisson(link="log"), prior = normal(0, 1), prior_intercept = normal(0, 5)) nd <- data.frame(treatment = factor(rep(1,3)), outcome = factor(1:3)) ytilde <- posterior_predict(fit3, nd, draws = 500) print(dim(ytilde)) # 500 by 3 matrix (draws by nrow(nd)) ytilde <- data.frame(count = c(ytilde), outcome = rep(nd$outcome, each = 500)) ggplot2::ggplot(ytilde, ggplot2::aes(x=outcome, y=count)) + ggplot2::geom_boxplot() + ggplot2::ylab("predicted count") # Using newdata with a binomial model. # example_model is binomial so we need to set # the number of trials to use for prediction. # This could be a different number for each # row of newdata or the same for all rows. # Here we'll use the same value for all. nd <- lme4::cbpp print(formula(example_model)) # cbind(incidence, size - incidence) ~ ... nd$size <- max(nd$size) + 1L # number of trials nd$incidence <- 0 # set to 0 so size - incidence = number of trials ytilde <- posterior_predict(example_model, newdata = nd) # Using fun argument to transform predictions mtcars2 <- mtcars mtcars2$log_mpg <- log(mtcars2$mpg) fit <- stan_glm(log_mpg ~ wt, data = mtcars2) ytilde <- posterior_predict(fit, fun = exp)