cv.higlasso {higlasso}

Cross Validated Hierarchical Integrative Group LASSO

Description

Does k-fold cross-validation for higlasso, and returns optimal values for lambda1 and lambda2.

Usage

cv.higlasso(
  Y,
  X,
  Z,
  method = c("aenet", "gglasso"),
  lambda1 = NULL,
  lambda2 = NULL,
  nlambda1 = 10,
  nlambda2 = 10,
  lambda.min.ratio = 0.05,
  nfolds = 5,
  foldid = NULL,
  sigma = 1,
  degree = 2,
  maxit = 5000,
  tol = 1e-05
)

Arguments

Y

A length n numeric response vector

X

A n x p numeric matrix

Z

A n x m numeric matrix

method

Type of initialization to use. Possible choices are gglasso for group LASSO and aenet for adaptive elastic net. Default is aenet

lambda1

A numeric vector of main effect penalties on which to tune By default, lambda1 = NULL and higlasso generates a length nlambda1 sequence of lambda1s based off of the data and min.lambda.ratio

lambda2

A numeric vector of interaction effects penalties on which to tune. By default, lambda2 = NULL and generates a sequence (length nlambda2) of lambda2s based off of the data and min.lambda.ratio

nlambda1

The number of lambda1 values to generate. Default is 10, minimum is 2. If lambda1 != NULL, this parameter is ignored

nlambda2

The number of lambda2 values to generate. Default is 10, minimum is 2. If lambda2 != NULL, this parameter is ignored

lambda.min.ratio

Ratio that calculates min lambda from max lambda. Ignored if 'lambda1' or 'lambda2' is non NULL. Default is 0.05

nfolds

Number of folds for cross validation. Default is 10. The minimum is 3, and while the maximum is the number of observations (ie leave one out cross validation)

foldid

An optional vector of values between 1 and max(foldid) identifying what fold each observation is in. Default is NULL and cv.higlasso will automatically generate foldid based off of nfolds

sigma

Scale parameter for integrative weights. Technically a third tuning parameter but defaults to 1 for computational tractability

degree

Degree of bs basis expansion. Default is 2

maxit

Maximum number of iterations. Default is 5000

tol

Tolerance for convergence. Defaults to 1e-5

Details

There are a few things to keep in mind when using cv.higlasso

• higlasso uses the strong heredity principle. That is, X_1 and X_2 must included as main effects before the interaction X_1 X_2 can be included.

• While higlasso uses integrative weights to help with estimation, higlasso is more of a selection method. As a result, cv.higlasso does not output coefficient estimates, only which variables are selected.

• Simulation studies suggest that higlasso is a very conservative method when it comes to selecting interactions. That is, higlasso has a low false positive rate and the identification of a nonlinear interaction is a good indicator that further investigation is worthwhile.

• cv.higlasso can be slow, so it may may be beneficial to tweak some of its settings (for example, nlambda1, nlambda2, and nfolds) to get a handle on how long the method will take before running the full model.

As a side effect of the conservativeness of the method, we have found that using the 1 standard error rule results in overly sparse models, and that lambda.min generally performs better.

Value

An object of type cv.higlasso with 7 elements

lambda

An nlambda1 x nlambda2 x 2 array containing each pair (lambda1, lambda2) pair.

lambda.min

lambda pair with the lowest cross validation error

lambda.1se

cvm

cross validation error at each lambda pair. The error is calculated from the mean square error.

cvse

standard error of cvm at each lambda pair.

higlasso.fit

higlasso output from fitting the whole data.

call

The call that generated the output.

Author(s)

Alexander Rix

References

A Hierarchical Integrative Group LASSO (HiGLASSO) Framework for Analyzing Environmental Mixtures. Jonathan Boss, Alexander Rix, Yin-Hsiu Chen, Naveen N. Narisetty, Zhenke Wu, Kelly K. Ferguson, Thomas F. McElrath, John D. Meeker, Bhramar Mukherjee. 2020. arXiv:2003.12844

Examples

library(higlasso)

X <- as.matrix(higlasso.df[, paste0("V", 1:7)])
Y <- higlasso.df$Y
Z <- matrix(1, nrow(X))


# This can take a bit of time

fit <- cv.higlasso(Y, X, Z)

print(fit)