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.

# S3 method for stanreg
posterior_predict(object, newdata = NULL,
draws = NULL, re.form = NULL, fun = NULL, seed = NULL,
offset = NULL, ...)

# S3 method for stanmvreg
posterior_predict(object, m = 1, newdata = NULL,
draws = NULL, re.form = NULL, fun = NULL, seed = NULL, ...)

## Arguments

object A fitted model object returned by one of the rstanarm modeling functions. See stanreg-objects. Optionally, a data frame in which to look for variables with which to predict. If omitted, the model matrix is used. If newdata is 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 newdata argument 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. If object contains group-level parameters, a formula indicating which group-level parameters to condition on when making predictions. re.form is 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 NA or ~0. The newdata argument 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. fun is found by a call to match.fun and so can be specified as a function object, a string naming a function, etc. An optional seed to use. A vector of offsets. Only required if newdata is specified and an offset argument was specified when fitting the model. For stanmvreg objects, argument m can be specified indicating the submodel for which you wish to obtain predictions. Integer specifying the number or name of the submodel

## Value

A draws by 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.

## Note

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 successes and failures must be in newdata. The particular values of successes and failures in 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 both trials and successes would need to be in newdata, probably with successes set to 0 and trials specifying the number of trials. See the Examples section below and the How to Use the rstanarm Package for examples.

For models estimated with stan_clogit, the number of successes per stratum is ostensibly fixed by the research design. Thus, when doing posterior prediction with new data, the data.frame passed to the newdata argument must contain an outcome variable and a stratifying factor, both with the same name as in the original data.frame. Then, the posterior predictions will condition on this outcome in the new data.

pp_check for graphical posterior predictive checks. Examples of posterior predictive checking can also be found in the rstanarm vignettes and demos.

predictive_error and predictive_interval.

## Examples

if (!exists("example_model")) example(example_model)
yrep <- posterior_predict(example_model)
table(yrep)#> yrep
#>     0     1     2     3     4     5     6     7     8     9    10    11    12
#> 10068  7250  4129  2354  1349   784   584   422   302   185   170   103    98
#>    13    14    15    16    17    18    19    20    21    22
#>    63    51    23    17    17    13    11     2     2     3
# \donttest{
# Using newdata
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
dat <- data.frame(counts, treatment, outcome)
fit3 <- stan_glm(
counts ~ outcome + treatment,
data = dat,
prior = normal(0, 1, autoscale = FALSE),
prior_intercept = normal(0, 5, autoscale = FALSE),
refresh = 0
)
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))#> [1] 500   3
ytilde <- data.frame(
count = c(ytilde),
outcome = rep(nd$outcome, each = 500) ) ggplot2::ggplot(ytilde, ggplot2::aes(x=outcome, y=count)) + ggplot2::geom_boxplot() + ggplot2::ylab("predicted count") # Using newdata with a binomial model. # example_model is binomial so we need to set # the number of trials to use for prediction. # This could be a different number for each # row of newdata or the same for all rows. # Here we'll use the same value for all. nd <- lme4::cbpp print(formula(example_model)) # cbind(incidence, size - incidence) ~ ...#> cbind(incidence, size - incidence) ~ size + period + (1 | herd)nd$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, refresh = 0)
ytilde <- posterior_predict(fit, fun = exp)
# }