Iprior: an R Package for Regression Modelling Using I-Priors
iprior: An R Package for Regression Modelling using I-priors Haziq Jamil Wicher Bergsma Universiti Brunei Darussalam London School of Economics 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 regres- sion 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. Keywords: Gaussian, process, regression, objective, prior, empirical, Bayes, RKHS, kernel, EM, algorithm, Nystr¨om, random, effects, multilevel, longitudinal, functional, I-prior, R. 1. Introduction For subject i 2 f1; : : : ; ng, assume a real-valued response yi has been observed, as well as a row vector of p covariates xi = (xi1; : : : ; xip), where each xik belongs to some set Xk, k = 1; : : : ; p. To describe the dependence of the yi on the xi, we consider the regression model yi = α + f(xi) + i (1) iid −1 i ∼ N(0; ) where f is some regression function to be estimated, and α is an intercept.
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