blm_bc: Bayesian linear model with a Box-Cox transformation

Description

MCMC sampling for Bayesian linear regression with a (known or unknown) Box-Cox transformation. A g-prior is assumed for the regression coefficients.

Usage

blm_bc(
  y,
  X,
  X_test = X,
  psi = length(y),
  lambda = NULL,
  sample_lambda = TRUE,
  nsave = 1000,
  nburn = 1000,
  nskip = 0,
  verbose = TRUE
)

Value

a list with the following elements:

coefficients the posterior mean of the regression coefficients
fitted.values the posterior predictive mean at the test points X_test
post_theta: nsave x p samples from the posterior distribution of the regression coefficients
post_ypred: nsave x n_test samples from the posterior predictive distribution at test points X_test
post_g: nsave posterior samples of the transformation evaluated at the unique y values
post_lambda nsave posterior samples of lambda
post_sigma nsave posterior samples of sigma
model: the model fit (here, blm_bc)

as well as the arguments passed in.

Arguments

y: n x 1 vector of observed counts
X: n x p matrix of predictors
X_test: n_test x p matrix of predictors for test data; default is the observed covariates X
psi: prior variance (g-prior)
lambda: Box-Cox transformation; if NULL, estimate this parameter
sample_lambda: logical; if TRUE, sample lambda, otherwise use the fixed value of lambda above or the MLE (if lambda unspecified)
nsave: number of MCMC iterations to save
nburn: number of MCMC iterations to discard
nskip: number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
verbose: logical; if TRUE, print time remaining

Details

This function provides fully Bayesian inference for a transformed linear model via MCMC sampling. The transformation is parametric from the Box-Cox family, which has one parameter lambda. That parameter may be fixed in advanced or learned from the data.

Examples

Run this code

# Simulate some data:
dat = simulate_tlm(n = 100, p = 5, g_type = 'step')
y = dat$y; X = dat$X # training data
y_test = dat$y_test; X_test = dat$X_test # testing data

hist(y, breaks = 25) # marginal distribution

# Fit the Bayesian linear model with a Box-Cox transformation:
fit = blm_bc(y = y, X = X, X_test = X_test)
names(fit) # what is returned
round(quantile(fit$post_lambda), 3) # summary of unknown Box-Cox parameter