REBayes: An R Package for Empirical Bayes Mixture Methods

Abstract

Models of unobserved heterogeneity, or frailty as it is commonly known in survival analysis, can often be formulated as semiparametric mixture models and estimated by maximum likelihood as proposed by Robbins (1950) and elaborated by Kiefer and Wolfowitz (1956). Recent developments in convex optimization, as noted by Koenker and Mizera (2014b), have led to dramatic improvements in computational methods for such models. In this vignette we describe an implementation contained in the R package REBayes with applications to a wide variety of mixture settings: Gaussian location and scale, Poisson and binomial mixtures for discrete data, Weibull and Gompertz models for survival data, and several Gaussian models intended for longitudinal data. While the dimension of the nonparametric heterogeneity of these models is inherently limited by our present gridding strategy, we describe how additional fixed parameters can be relatively easily accommodated via profile likelihood. We also describe some nonparametric maximum likelihood methods for shape and norm constrained density estimation that employ related computational methods.

Shifts in Soybean Yield, Nutrient Uptake, and Nutrient Stoichiometry: A Historical Synthesis‐Analysis

“…The SMATR package (Warton et al, 2015) from the R program (R Core Team, 2017) was used to test for common slopes. Envelopes portraying maximum and minimum boundaries (0.99 and 0.01 quantile lines, respectively) for yieldto-nutrient content and nutrient ratios were calculated using the "quantreg" package in R software (Koenker, 2005(Koenker, , 2017. The upper boundary of the envelope represents the maximum nutrient dilution, and the lower boundary represents the maximum nutrient accumulation (Janssen et al, 1990;Witt et al, 1999).…”

Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data

“…All computational results of this paper can be reproduced with the R packages REBayes Koenker and Gu (2015) and Rmosek (Friberg, 2012), and code available from the authors on request. The Rmosek package provides a convenient R interface to the Mosek optimization language of Andersen (2010).…”

Using quantile regression to create baseline norms for neuropsychological tests

“…All analyses were carried out using R 3.1.1. The quantreg package [13] was used for quantile regression, and the lmtest package [14] was used for the Breusch-Pagan test; otherwise, calculations were implemented using the base software.…”