cv.higlasso: Cross Validated Hierarchical Integrative Group LASSO
In umich-cphds/higlasso: Hierarchical Integrative Group LASSO

Description Usage Arguments Details Value Author(s) References Examples

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

cv.higlasso(
  Y,
  X,
  Z,
  method = c("aenet", "gglasso"),
  lambda1 = NULL,
  lambda2 = NULL,
  nlambda1 = 10,
  nlambda2 = 10,
  lambda.min.ratio = 0.05,
  nfolds = 10,
  foldid = NULL,
  sigma = 1,
  degree = 3,
  maxit = 5000,
  tol = 1e-05
)

`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 3
`maxit`	Maximum number of iterations. Default is 5000
`tol`	Tolerance for convergence. Defaults to 1e-5

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.

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.

Alexander Rix

TODO

library(higlasso)

X <- as.matrix(higlasso.df[, paste0("V", 1:10)])
Y <- higlasso.df$Y
Z <- matrix(1, nrow(X))

## Not run: 
# This can take a bit of time
cv.fit <- cv.higlasso(Y, X, Z)

## End(Not run)