Package 'LassoGEE'

Cross-validation for LassoGEE.

Description

Does k-fold cross-validation for LassoGEE to select tuning parameter value for longitudinal data with working independence structure.

Usage

cv.LassoGEE(
  X,
  y,
  id,
  family,
  method = c("CGD", "RWL"),
  scale.fix,
  scale.value,
  fold,
  lambda.vec,
  maxiter,
  tol
)

Arguments

X	A design matrix of dimension (nm) * p.
y	A response vector of length m * n.
id	A vector for identifying subjects/clusters.
family	A family object: a list of functions and expressions for defining link and variance functions. Families supported here is same as in PGEE which are binomial, gaussian, gamma and poisson.
method	The algorithms that are available. "CGD" represents the I-CGD algorithm, and "RWL" represents re-weighted least square algorithm.
scale.fix	A logical variable; if true, the scale parameter is fixed at the value of scale.value. The default value is TRUE.
scale.value	If scale.fix = TRUE, this assignes a numeric value to which the scale parameter should be fixed. The default value is 1.
fold	The number of folds used in cross-validation.
lambda.vec	A vector of tuning parameters that will be used in the cross-validation.
maxiter	The number of iterations that is used in the estimation algorithm. The default value is 50.
tol	The tolerance level that is used in the estimation algorithm. The default value is 1e^-3.

Value

An object class of cv.LassoGEE.

References

Li, Y., Gao, X., and Xu, W. (2020). Statistical consistency for generalized estimating equation with $L_1$ regularization.

See Also

LassoGEE

---

Information Criterion for selecting the tuning parameter.

Description

Information Criterion for a fitted LassoGEE object with the AIC, BIC, or GCV criteria.

Usage

IC(obj, criterion = c("BIC", "AIC", "GCV", "AICc", "EBIC"))

Arguments

obj	A fitted LassoGEE object.
criterion	The criterion by which to select the regularization parameter. One of "AIC", "BIC", "GCV", "AICc", or "EBIC"; default is "BIC".

Value

IC	The calculated model selection criteria

References

Gao, X., and Yi, G. Y. (2013). Simultaneous model selection and estimation for mean and association structures with clustered binary data. Stat, 2(1), 102-118.

---

Function to fit penalized GEE by I-CGD algorithm.

Description

This function fits a $L_1$ penalized GEE model to longitudinal data by I-CGD algorithm or re-weighted least square algorithm.

Usage

LassoGEE(
  X,
  y,
  id,
  family = binomial("probit"),
  lambda,
  corstr = "independence",
  method = c("CGD", "RWL"),
  beta.ini = NULL,
  R = NULL,
  scale.fix = TRUE,
  scale.value = 1,
  maxiter = 50,
  tol = 0.001,
  silent = TRUE,
  Mv = NULL,
  verbose = TRUE
)

Arguments

X	A design matrix of dimension (nm) * p.
y	A response vector of length m * n.
id	A vector for identifying subjects/clusters.
family	A family object representing one of the built-in families. Families supported here are the same as in PGEE, e.g, binomial, gaussian, gamma and poisson, and the corresponding link functions are supported, e.g, identity, and probit.
lambda	A user supplied value for the penalization parameter.
corstr	A character string that indicates the correlation structure among the repeated measurements of a subject. Structures supported in LassoGEE are "AR1", "exchangeable", "unstructured", and "independence". The default corstr type is "independence".
method	The algorithms that are available. "CGD" represents the I-CGD algorithm, and "RWL" represents re-weighted least square algorithm.
beta.ini	User specified initial values for regression parameters. The default value is NULL.
R	User specified correlation matrix. The default value is NULL.
scale.fix	A logical variable. The default value is TRUE, then the value of the scale parameter is fixed to scale.value.
scale.value	If scale.fix = TRUE, a numeric value will be assigned to the fixed scale parameter. The default value is 1.
maxiter	The maximum number of iterations used in the algorithm. The default value is 50.
tol	The tolerance level used in the algorithm. The default value is 1e-3.
silent	A logical variable; if false, the iteration counts at each iteration of CGD are printed. The default value is TRUE.
Mv	If either "stat_M_dep", or "non_stat_M_dep" is specified in corstr, then this assigns a numeric value for Mv. Otherwise, the default value is NULL.
verbose	A logical variable; Print the out loop iteration counts. The default value is TRUE.

Value

A list containing the following components:

betaest	return final estimation
beta_all_step	return estimate in each iteration
inner.count	iterative count in each stage
outer.iter	iterate number of outer loop

References

Li, Y., Gao, X., and Xu, W. (2020). Statistical consistency for generalized estimating equation with $L_1$ regularization.

See Also

cv.LassoGEE

Examples

# required R package
library(mvtnorm)
library(SimCorMultRes)
#
set.seed(123)
p <- 200
s <- ceiling(p^{1/3})
n <- ceiling(10 * s * log(p))
m <- 4
# covariance matrix of p number of continuous covariates
X.sigma <- matrix(0, p, p)
{
  for (i in 1:p)
    X.sigma[i,] <- 0.5^(abs((1:p)-i))
}

# generate matrix of covariates
X <- as.matrix(rmvnorm(n*m, mean = rep(0,p), X.sigma))

# true regression parameter associated with the covariate
bt <- runif(s, 0.05, 0.5) # = rep(1/s,s)
beta.true <- c(bt,rep(0,p-s))
# intercept
beta_intercepts <- 0
# unstructure
tt <- runif(m*m,-1,1)
Rtmp <- t(matrix(tt, m,m))%*%matrix(tt, m,m)+diag(1,4)
R_tr <- diag(diag(Rtmp)^{-1/2})%*%Rtmp%*%diag(diag(Rtmp)^{-1/2})
diag(R_tr) = round(diag(R_tr))

# library(SimCorMultRes)
# simulation of clustered binary responses
simulated_binary_dataset <- rbin(clsize = m, intercepts = beta_intercepts,
                                 betas = beta.true, xformula = ~X, cor.matrix = R_tr,
                                 link = "probit")
lambda <- 0.2* s *sqrt(log(p)/n)
data = simulated_binary_dataset$simdata
y = data$y
X = data$X
id = data$id

ptm <- proc.time()
nCGDfit = LassoGEE(X = X, y = y, id = id, family = binomial("probit"),
                 lambda = lambda, corstr = "unstructured")
proc.time() - ptm
betaest <- nCGDfit$betaest

---

print a cross-validated LassoGEE object

Description

Print a summary of the results of cross-validation for a LassoGEE model.

Usage

## S3 method for class 'cv.LassoGEE'
print(x, digits = NULL, ...)

Arguments

x	fitted 'cv.LassoGEE' object
digits	significant digits in printout
...	additional print arguments

Details

A summary of the cross-validated fit is produced. print.cv.LassoGEE(object) will print the summary for a sequence of lambda.

References

Li, Y., Gao, X., and Xu, W. (2020). Statistical consistency for generalized estimating equation with $L_1$ regularization.

See Also

LassoGEE, and cv.LassoGEE methods.

---

print a LassoGEE object

Description

Print a summary of the results of a LassoGEE model.

Usage

## S3 method for class 'LassoGEE'
print(x, digits = NULL, ...)

Arguments

x	fitted 'LassoGEE' object
digits	significant digits in printout
...	additional print arguments

Details

A summary of the cross-validated fit is produced. print.cv.LassoGEE(object) will print the summary includes Working Correlation and Returned Error Value.

References

Li, Y., Gao, X., and Xu, W. (2020). Statistical consistency for generalized estimating equation with $L_1$ regularization.

See Also

LassoGEE, and cv.LassoGEE methods.

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