higlasso: Hierarchical Integrative Group LASSO
In umich-cphds/higlasso: Hierarchical Integrative Group LASSO

Description Usage Arguments Details Value Author(s) References Examples

View source: R/higlasso.R

HiGLASSO is a regularization based selection method designed to detect non-linear interactions between variables, particularly exposures in environmental health studies.

higlasso(
  Y,
  X,
  Z,
  method = c("aenet", "gglasso"),
  lambda1 = NULL,
  lambda2 = NULL,
  nlambda1 = 10,
  nlambda2 = 10,
  lambda.min.ratio = 0.05,
  sigma = 1,
  basis.function = splines::bs,
  maxit = 5000,
  tol = 1e-05
)

`Y`	A length n numeric response vector
`X`	A n x p numeric matrix of covariates to basis expand
`Z`	A n x m numeric matrix of non basis expanded and non regularized covariates
`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
`sigma`	Scale parameter for integrative weights. Technically a third tuning parameter but defaults to 1 for computational tractability
`basis.function`	Function that performs a basis expansion on each variable. The default is `bs`, from the 'splines' package
`maxit`	Maximum number of iterations. Default is 5000
`tol`	Tolerance for convergence. Default is 1e-5

There are a few things to keep in mind when using 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, 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.
higlasso can be slow, so it may may be beneficial to tweak some of its settings (for example, nlambda1 and nlambda2) to get a handle on how long the method will take before running the full model.

An object of type "higlasso" with 4 elements:

lambda: An nlambda1 x nlambda2 x 2 array containing each pair (lambda1, lambda2) pair.
selected: An nlambda1 x nlambda2 x ncol(X) array containing higlasso's selections for each lambda pair.
df: The number of nonzero selections for each lambda pair.
call: The call that generated the output.

Alexander Rix

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

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

You can specify alternate basis expansions by changing 'basis.function'
bf = function(x) splines::bs(x, df = 4)
higlasso.fit <- higlasso(Y, X, Z, basis.function = bf)