posterior_predictive {bpr} | R Documentation |

## Compute Posterior Predictive Distribution

### Description

This function is a method for class `poisreg`

. Compute the posterior predictive distribution and summary statistics for
posterior check of the model;
optionally, it also computes
the predictive distribution with new values of the explanatory variables.

### Usage

```
posterior_predictive(object, new_X = NULL)
```

### Arguments

`object` |
object of class " |

`new_X` |
(optional) a data frame in which to look for variables with which to predict. |

### Value

The call to this function returns an object of S3 class `posterior_check`

. The object is a list with the following elements:

`data`

: the component from `object`

(list with covariates `X`

and response variable `y`

).

`y_pred`

: matrix of dimension `[n, iter]`

(with `n`

sample size), each column is a draw from the posterior predictive distribution.

`y_MAP_pred`

: vector of length `n`

containing a draw from the posterior distribution obtained using the maximum a posteriori estimates (MAP) of the parameters.

`diagnostics`

: list containing 2 elements: `CPO`

, i.e. the Conditional Predictive Ordinate (Gelfand et al. 1992); and `LPML`

, i.e.
the logarithm of the pseudo-marginal likelihood (Ibrahim et al. 2014).

`newdata`

: if the matrix `new_X`

of new values of the covariates is provided, list of three elements:

`new_X`

: the provided matrix of explanatory variables;`y_newdata`

: a matrix of dimension`[nrow(new_X), iter]`

, each column is a draw from the posterior predictive distribution using`new_X`

;`y_MAP_newdata`

: vector of length`nrow(new_X)`

containing a draw from the posterior distribution obtained using the MAP estimate of the parameters, computed on the new data`new_X`

.

`perc_burnin`

: the component from `object`

.

### References

Gelfand, A., Dey, D. and Chang, H. (1992), Model determination using predictive distributions with implementation via sampling-based-methods (with discussion),
in ‘Bayesian Statistics 4’, University Press.

Ibrahim, J. G., Chen, M.H. and Sinha, D. (2014), Bayesian Survival Analysis, American Cancer Society.

*bpr*version 1.0.8 Index]