iprior: An R Package for Regression Modelling using I-priors

TL;DR

The iprior R package provides a unified framework for regression modeling using I-priors, enabling flexible parametric and nonparametric analysis with competitive predictive performance.

Contribution

This paper introduces the iprior package that implements I-prior methodology for diverse regression models, simplifying estimation and inference processes.

Findings

I-prior models perform comparably or better than state-of-the-art models.

Estimation using I-priors is straightforward and computationally efficient.

The package effectively handles various data types, including multilevel, longitudinal, and functional data.

Abstract

This is an overview of the R package iprior, which implements a unified methodology for fitting parametric and nonparametric regression models, including additive models, multilevel models, and models with one or more functional covariates. Based on the principle of maximum entropy, an I-prior is an objective Gaussian process prior for the regression function with covariance kernel equal to its Fisher information. The regression function is estimated by its posterior mean under the I-prior, and hyperparameters are estimated via maximum marginal likelihood. Estimation of I-prior models is simple and inference straightforward, while small and large sample predictive performances are comparative, and often better, to similar leading state-of-the-art models. We illustrate the use of the iprior package by analysing a simulated toy data set as well as three real-data examples, in particular, a multilevel data set, a longitudinal data set, and a dataset involving a functional covariate.