cobinreg: cobin generalized linear (mixed) models

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

cobin generalized linear (mixed) models

Description

Fit Bayesian cobin regression model under canonical link (cobit link) with Markov chain Monte Carlo (MCMC). It supports both fixed-effect only model

y_i \mid x_i \stackrel{ind}{\sim} cobin(x_i^T\beta, \lambda^{-1}),

for i=1,\dots,n, and random intercept model (v 1.0.x only supports random intercept),

y_{ij} \mid x_{ij}, u_i \stackrel{ind}{\sim} cobin(x_{ij}^T\beta + u_i, \lambda^{-1}), \quad u_i\stackrel{iid}{\sim} N(0, \sigma_u^2)

for i=1,\dots,n (group), and j=1,\dots,n_i (observation within group). See dcobin for details on cobin distribution.

Usage

cobinreg(
  formula,
  data,
  link = "cobit",
  contrasts = NULL,
  priors = list(beta_intercept_scale = 100, beta_scale = 100, beta_df = Inf),
  nburn = 1000,
  nsave = 1000,
  nthin = 1,
  MH = FALSE,
  lambda_fixed = NULL
)

Arguments

formula	an object of class "formula" or a two-sided linear formula object describing both the fixed-effects and random-effects part of the model; see "lmer"
data	data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.
link	character, link function (default "cobit"). Only supports canonical link function "cobit" that is compatible with Kolmogorov-Gamma augmentation.
contrasts	an optional list. See the contrasts.arg of model.matrix.default.
priors	a list of prior hyperparameters. See Details
nburn	number of burn-in MCMC iterations.
nsave	number of posterior samples. Total MCMC iteration is nburn + nsave*nthin
nthin	thin-in rate. Total MCMC iteration is nburn + nsave*nthin
MH	logical, Metropolis-Hastings; experimental
lambda_fixed	logical, fixing lambda; experimental

Details

The prior setting can be controlled with "priors" argument. Prior for regression coefficients are independent normal or t prior centered at 0. "priors" is a named list of:

• beta_intercept_scale, Default 100, the scale of the intercept prior

• beta_scale, Default 100, the scale of nonintercept fixed-effect coefficients

• beta_df, Default Inf, degree of freedom of t prior. If beta_df=Inf, it corresponds to normal prior

• lambda_grid, Default 1:70, candidate for lambda (integer)

• lambda_logprior, Default p(\lambda)\propto \lambda \Gamma(\lambda+1)/\Gamma(\lambda+5), log-prior of lambda. Default choice arises from beta negative binomial distribution; (\lambda-1)\mid \psi \sim negbin(2,\psi), \psi\sim Beta(2,2).

if random intercept model, u ~ InvGamma(a_u,b_u) with

• a_u, Default 1, first parameter of Inverse Gamma prior of u

• b_u, Default 1, second parameter of Inverse Gamma prior of u

Value

Returns list of

post_save	a matrix of posterior samples (coda::mcmc) with nsave rows
loglik_save	a nsave x n matrix of pointwise log-likelihood values, can be used for WAIC calculation.
priors	list of hyperprior information
nsave	number of MCMC samples
t_mcmc	wall-clock time for running MCMC
t_premcmc	wall-clock time for preprocessing before MCMC
y	response vector
X	fixed effect design matrix

if random effect model, also returns

post_u_save	a matrix of posterior samples (coda::mcmc) of random effects
Z	random effect design matrix

Examples

requireNamespace("betareg", quietly = TRUE)
library(betareg) # for dataset example
data("GasolineYield", package = "betareg")

# basic model 
out1 = cobinreg(yield ~ temp, data = GasolineYield, 
               nsave = 2000, link = "cobit")
summary(out1$post_save)
plot(out1$post_save)

# random intercept model
out2 = cobinreg(yield ~ temp + (1 | batch), data = GasolineYield, 
               nsave = 2000, link = "cobit")
summary(out2$post_save)
plot(out2$post_save)

cobin documentation built on Sept. 2, 2025, 1:08 a.m.