**UPG**:
Efficient Bayesian Regression Models for Binary and Categorical
Outcomes

**UPG** offers efficient Bayesian implementations of
regression models for binary and categorical data. The package can be
used to estimate Bayesian versions of probit, logit, multinomial logit
and binomial logit models. In this context, the Bayesian paradigm is
especially useful for uncertainty quantification and solving issues
related to rare events and (quasi-)perfect separation.
**UPG** allows for efficient posterior sampling in cases
with imbalanced data as the implemented algorithms are based on the
marginal data augmentation schemes developed in Frühwirth-Schnatter,
Zens, and Wagner (2020). Several functions are available for tabulating
and visualizing results as well as for predictive exercises.

## Installation

**UPG** is available on CRAN and can be installed as
follows:

## Usage

The core function for estimating models is `UPG()`

. Given
a suitable outcome vector `y`

and a suitable design matrix
`X`

, the four implemented models can be estimated using

`UPG(y, X, model = "probit")`

for probit models
`UPG(y, X, model = "logit")`

for binary logit models
`UPG(y, X, model = "mnl")`

for multinomial logit
models
`UPG(y, X, Ni, model = "binomial")`

for binomial logit
models

where binomial logit models require the number of trials
`Ni`

as additional input.

The estimation output can be analyzed using a variety of tools
implemented in **UPG**. To tabulate and visualize the
results, `summary()`

and `plot()`

are available.
Predictions can be obtained using `predict()`

. Extracting
coefficients can be done using `coef()`

and
`logLik()`

returns the log-likelihood of the model. Finally,
the user has access to a number of MCMC diagnostics via
`UPG.Diag()`

.

More details and applied examples may be found in the package
vignette.

## References

Frühwirth-Schnatter, S., Zens, G., & Wagner, H. (2020). Ultimate
Pólya Gamma Samplers - Efficient MCMC for possibly imbalanced binary and
categorical data. arXiv preprint arXiv:2011.06898.