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cobin:R package for cobin and micobin regression models

Cobin and micobin regression models are scalable and robustalternative 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:2504.15269https://arxiv.org/abs/2504.15269

A dedicated Github repository for reproducing the analysis in thepaper is available athttps://github.com/changwoo-lee/cobin-reproduce. This Rpackage repository contains the functions for the cobin and micobinregression models, as well as sampler for Kolmogorov-Gamma randomvariables.

Install the package from GitHub:

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

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

vignette

Comparisonof cobin and beta density

Comparisonof micobin and beta density

Please seeMMIdata analysis code corresponding to the Section 6 of the paper(https://arxiv.org/abs/2504.15269). More detailedexamples TBA.

Code structure

Basic functions

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

Cobin / Micobinregression (Bayesian, cobit link)

• 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 micobinGLMM

Spatialcobin / micobin regression (Bayesian, cobit link)

• 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 randomeffect
• spmicobinreg.R:
  • micobinreg(): fit Bayesian cobin GLM or GLMM
  • └── fit_micobin_spatial.R: backend function with GP randomeffect
  • └── fit_micobin_spatial_NNGP.R: backend function with NNGP randomeffect

Helper functions

• CB.R:
  • qcb(),rcb(): quantile and random variategeneration of continuous Bernoulli
• IH.R:
  • dIH(): density of Irwin-Hall distribution
• varfunctions.R: collection of functions related to variance functionof 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 linkfunction
  • bftprimeprime(),bftprimeprimeprime():\(B''(x)\) and\(B'''(x)\)
  • bftprimeinv(): inverse of\(B'(x)\), corresponding to cobit linkfunction
  • Vft():\(B''((B')^{-1}(\mu))\), variancefunction of cobin
• cobinfamily.R:
  • cobinfamily(): a list of functions and expressionsneeded to fit cobin GLM

cobin regression(non-Bayesian)

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