spcobinreg: spatial cobin regression model

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

spatial cobin regression model

Description

Fit Bayesian spatial cobin regression model under canonical link (cobit link) with Markov chain Monte Carlo (MCMC).

y(s_{i}) \mid x(s_{i}), u(s_i) \stackrel{ind}{\sim} cobin(x(s_{i})^T\beta + u(s_i), \lambda^{-1}), \quad u(\cdot)\sim GP

for i=1,\dots,n. See dcobin for details on cobin distribution. It currently only supports mean zero GP with exponential covariance

cov(u(s_i), u(s_j)) = \sigma_u^2\exp(-\phi_u d(s_i,s_j))

where \phi_u corresponds to inverse range parameter.

Usage

spcobinreg(
  formula,
  data,
  link = "cobit",
  coords,
  NNGP = FALSE,
  contrasts = NULL,
  priors = list(beta_intercept_scale = 10, beta_scale = 2.5, beta_df = Inf),
  nngp.control = list(n.neighbors = 15, ord = order(coords[, 1])),
  nburn = 1000,
  nsave = 1000,
  nthin = 1
)

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.
coords	a n x 2 matrix of Euclidean coordinates
NNGP	logical, if TRUE, use NNGP prior for the spatial random effects; see spNNGP
contrasts	an optional list. See the contrasts.arg of model.matrix.default.
priors	a list of prior hyperparameters. See Details
nngp.control	a list of control parameters for NNGP prior (only when NNGP = TRUE). This should be a named list of n.neighbors and ord, with default of 15 and first coordiate-based ordering. See spNNGP for 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

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).

• logprior_sigma.sq, Default half-Cauchy on the sd(u) =\sigma_u, log prior of var(u)=\sigma_u^2

• phi_lb, lower bound of uniform prior of \phi_u (inverse range parameter of spatial random effect). Can be same as phi_ub

• phi_ub, lower bound of uniform prior of \phi_u (inverse range parameter of spatial random effect). Can be same as phi_lb

Value

Returns list of

post_save	a matrix of posterior samples (coda::mcmc) with nsave rows
post_u_save	a matrix of posterior samples (coda::mcmc) of random effects, 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
coords	a n x 2 matrix of Euclidean coordinates

if NNGP = TRUE, also returns

nngp.control	a list of control parameters for NNGP prior
spNNGPfit	an "NNGP" class with empty samples, placeholder for prediction

Examples

 # Please see https://github.com/changwoo-lee/cobin-reproduce

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