qpgee {geeVerse}

Quantile Penalized Generalized Estimating Equations with Auto Selected Penalty level

Description

This function automatically select the penalty level by going through a list of lambdas, and select the best level of penalty with high-dimensional BIC (HBIC) or cross-validation (CV).

Usage

qpgee(
  x,
  y,
  tau = 0.5,
  method = "HBIC",
  ncore = 1,
  nobs = rep(1, length(y)),
  correlation = "exchangeable",
  lambda = NULL,
  intercept = FALSE,
  f0 = NULL,
  betaint = NULL,
  max_it = 100,
  cutoff = 10^-1
)

Arguments

x

A matrix of predictors.

y

A numeric vector of response variables.

tau

The quantile to be estimated (default is 0.5, the median).

method

The criterion to select level of penalty. Currently it only supports "HBIC".

ncore

A numeric value specifying how many core to use.

nobs

A numeric vector indicating the number of observations per subject.

correlation

A string specifying the working correlation structure. Options include "exchangeable" (Exchangeable), "AR1" (Autoregressive), "Tri" (Tri-diagonal), and "exchangeable" (Independent).

lambda

A vector of penalty parameter for regularization. If not provided, a grid will be provided by this function.

intercept

Whether to include an intercept when estimating.

f0

estimated conditional error distributions.

betaint

Initial values for the beta coefficients. If NULL, non-longitudinal quantile regression is used for initialization.

max_it

Maximum number of iterations (default is 100).

cutoff

Threshold for coefficient shrinkage (default is 0.1).

Value

A list containing the following components:

beta

Estimated beta coefficients.

g

Fitted values of the linear predictor.

R

Estimated working correlation matrix.

X_selected

Indices of selected predictors.

mcl

Mean check loss.

hbic

Hannan-Quinn Information Criterion value.

converge

Boolean indicating whether the algorithm converged.

Examples

# Example usage:

sim_data <- generateData(nsub = 20, nobs = rep(10, 20),  p = 20,
                         beta0 = c(rep(1,5),rep(0,15)), rho = 0.1, correlation = "AR1",
                          dis = "normal", ka = 1)

X=sim_data$X
y=sim_data$y

#fit qpgee with auto selected lambda
qpgee.fit = qpgee(X,y,tau=0.5,nobs=rep(10, 20),ncore=1)
qpgee.fit$beta