README.md
In cobin: Cobin and Micobin Regression Models for Continuous Proportional Data

cobin: R package for cobin and micobin regression models

Cobin and micobin regression models are scalable and robust alternative to beta regression model for continuous proportional data. See the following paper for more details:

Lee, C. J., Dahl, B. K., Ovaskainen, O., Dunson, D. B. (2025). Scalable and robust regression models for continuous proportional data. arXiv preprint arXIV:2504.15269 https://arxiv.org/abs/2504.15269

A dedicated Github repository for reproducing the analysis in the paper is available at https://github.com/changwoo-lee/cobin-reproduce. This R package repository contains the functions for the cobin and micobin regression models, as well as sampler for Kolmogorov-Gamma random variables.

Install the package from GitHub:

# install.packages("devtools")
devtools::install_github("changwoo-lee/cobin")

Glossaries: GLM: generalized linear model; GLMM: generalized linear mixed model; GP: Gaussian process; NNGP: nearest neighbor Gaussian process; cobin: continuous binomial; micobin: mixture of continuous binomial;

Comparison of cobin and beta density

Comparison of micobin and beta density

Please see MMI data analysis code corresponding to the Section 6 of the paper(https://arxiv.org/abs/2504.15269). More detailed examples TBA.

cobin.R:
dcobin(x, theta, lambda): Density of $\mathrm{cobin}(\theta, \lambda^{-1})$ at x
rcobin(n, theta, lambda): Random variate generation from $\mathrm{cobin}(\theta, \lambda^{-1})$
micobin.R:
dmicobin(x, theta, psi): Density of $\mathrm{micobin}(\theta, \psi)$ at x
rmicobin(n, theta, psi): Random variate generation from $\mathrm{micobin}(\theta, \psi)$

cobinreg.R:
cobinreg(): fit Bayesian cobin GLM or GLMM
└── fit_cobin_fixedeffect.R: backend function for cobin GLM
└── fit_cobin_mixedeffect.R: backend function for cobin GLMM
micobinreg.R:
micobinreg(): fit Bayesian micobin GLM or GLMM
└── fit_micobin_fixedeffect.R: backend function for micobin GLM
└── fit_micobin_mixedeffect.R: backend function for micobin GLMM

spcobinreg.R:
cobinreg(): fit spatial cobin regresson
└── fit_cobin_spatial.R: backend function with GP random effect
└── fit_cobin_spatial_NNGP.R: backend function with NNGP random effect
spmicobinreg.R:
micobinreg(): fit Bayesian cobin GLM or GLMM
└── fit_micobin_spatial.R: backend function with GP random effect
└── fit_micobin_spatial_NNGP.R: backend function with NNGP random effect

CB.R:
qcb(), rcb(): quantile and random variate generation of continuous Bernoulli
IH.R:
dIH(): density of Irwin-Hall distribution
varfunctions.R: collection of functions related to variance function of cobin, with numerically stable computation
bft(): $B(x) = \log((\exp(x)-1)/x)$, cumulant (log partition) function
bftprime(): $B'(x) = 1/(1-\exp(-x))-1/x$, corresponding to inverse of cobit link function
bftprimeprime(), bftprimeprimeprime(): $B''(x)$ and $B'''(x)$
bftprimeinv(): inverse of $B'(x)$, corresponding to cobit link function
Vft(): $B''((B')^{-1}(\mu))$, variance function of cobin
cobinfamily.R:
cobinfamily(): a list of functions and expressions needed to fit cobin GLM

glm.cobin.R:
glm.cobin(): fit cobin GLM using iteratively reweighted least squares (stats::glm.fit). Supports link functions “cobit”, “logit”, “probit”, “cloglog”, “cauchit”.