cobin (version 1.0.1.3)

micobinreg: micobin generalized linear (mixed) models

Description

Fit Bayesian micobin regression model under canonical link (cobit link) with Markov chain Monte Carlo (MCMC). It supports both fixed-effect only model $$ y_i \mid x_i \stackrel{ind}{\sim} micobin(x_i^T\beta, \psi), $$ for \(i=1,\dots,n\), and random intercept model (v 1.0.x only supports random intercept), $$ y_{ij} \mid x_{ij}, u_i \stackrel{ind}{\sim} micobin(x_{ij}^T\beta + u_i, \psi), \quad u_i\stackrel{iid}{\sim} N(0, \sigma_u^2) $$ for \(i=1,\dots,n\) (group), and \(j=1,\dots,n_i\) (observation within group). See dmicobin for details on micobin distribution.

Usage

micobinreg(
  formula,
  data,
  link = "cobit",
  contrasts = NULL,
  priors = list(beta_intercept_scale = 100, beta_scale = 100, beta_df = Inf),
  nburn = 1000,
  nsave = 1000,
  nthin = 1,
  psi_fixed = NULL
)

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

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

psi_fixed

logical, fixing psi; 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_max, Default 70, upper bound for lambda (integer)

• psi_ab, Default c(2,2), beta shape parameters for \(\psi\) (length 2 vector).

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

Examples

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

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

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