pqrBayes {pqrBayes}

fit a regularized Bayesian quantile varying coefficient model

Description

fit a regularized Bayesian quantile varying coefficient model

Usage

pqrBayes(
  g,
  y,
  u,
  e = NULL,
  quant = 0.5,
  iterations = 10000,
  kn = 2,
  degree = 2,
  sparse = TRUE,
  hyper = NULL,
  debugging = FALSE
)

Arguments

g

the matrix of predictors (subject to selection) without intercept.

y

the response variable. The current version only supports the continuous response.

u

a vector of effect modifying variable of the quantile varying coefficient model.

e

a matrix of clinical covariates not subject to selection.

quant

the quantile level specified by users. The default value is 0.5.

iterations

the number of MCMC iterations.

kn

the number of interior knots for B-spline.

degree

the degree of B-spline basis.

sparse

logical flag. If TRUE, spike-and-slab priors will be used to shrink coefficients of irrelevant covariates to zero exactly.

hyper

a named list of hyperparameters.

debugging

logical flag. If TRUE, progress will be output to the console and extra information will be returned.

Details

The model described in "data" is:

Y_{i}=\sum_{k=1}^{q} E_{ik} \beta_k +\sum_{j=0}^{p}\gamma_j(V_i)X_{ij} +\epsilon_{i},

where \beta_k's are the regression coefficients for the clinical covariates and \gamma_j's are the varying coefficients for the intercept and predictors (e.g. genetic factors).

When sparse=TRUE (default), spike–and–slab priors are adopted. Otherwise, Laplacian shrinkage will be used. Users can modify the hyper-parameters by providing a named list of hyper-parameters via the argument ‘hyper’. The list can have the following named components

• a0, b0: shape parameters of the Beta priors (\pi^{a_{0}-1}(1-\pi)^{b_{0}-1}) on \pi_{0}.

• c1, c2: the shape parameter and the rate parameter of the Gamma prior on \nu.

Please check the references for more details about the prior distributions.

Value

an object of class "pqrBayes" is returned, which is a list with components:

posterior

posterior samples from the MCMC

coefficients

a list of posterior estimates of coefficients

References

Zhou, F., Ren, J., Ma, S. and Wu, C. (2023). The Bayesian regularized quantile varying coefficient model. Computational Statistics & Data Analysis, 107808 doi:10.1016/j.csda.2023.107808

Ren, J., Zhou, F., Li, X., Ma, S., Jiang, Y. and Wu, C. (2023). Robust Bayesian variable selection for gene-environment interactions. Biometrics, 79(2), 684-694 doi:10.1111/biom.13670

Ren, J., Zhou, F., Li, X., Chen, Q., Zhang, H., Ma, S., Jiang, Y. and Wu, C. (2020) Semi-parametric Bayesian variable selection for gene-environment interactions. Statistics in Medicine, 39: 617– 638 doi:10.1002/sim.8434

Examples

data(data)
g=data$g
y=data$y
u=data$u
e=data$e

## default method
fit1=pqrBayes(g,y,u,e,quant=0.5)
fit1



## non-sparse
sparse=FALSE
fit2=pqrBayes(g,y,u,e,quant=0.5,sparse = sparse)
fit2