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.


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



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

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.


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.