# posterior_predict.stanreg

##### 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.

##### Usage

```
# 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`

.- newdata
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.- draws
An integer indicating the number of draws to return. The default and maximum number of draws is the size of the posterior sample.

- re.form
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.- fun
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.- seed
An optional

`seed`

to use.- offset
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.- m
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.

##### See Also

`pp_check`

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

##### Examples

```
# NOT RUN {
if (!exists("example_model")) example(example_model)
yrep <- posterior_predict(example_model)
table(yrep)
# }
# NOT RUN {
# 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)
# }
# NOT RUN {
# }
```

*Documentation reproduced from package rstanarm, version 2.17.4, License: GPL (>= 3)*