Title: | Hierarchical Integrative Group LASSO |
---|---|
Description: | Environmental health studies are increasingly measuring multiple pollutants to characterize the joint health effects attributable to exposure mixtures. However, the underlying dose-response relationship between toxicants and health outcomes of interest may be highly nonlinear, with possible nonlinear interaction effects. Hierarchical integrative group least absolute shrinkage and selection operator (HiGLASSO), developed by Boss et al (2020) <arXiv:2003.12844>, is a general framework to identify noteworthy nonlinear main and interaction effects in the presence of group structures among a set of exposures. |
Authors: | Alexander Rix [aut, cre], Jonathan Boss [aut] |
Maintainer: | Alexander Rix <[email protected]> |
License: | GPL-3 |
Version: | 0.9.0 |
Built: | 2024-12-12 07:07:50 UTC |
Source: | CRAN |
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 = 5, foldid = NULL, sigma = 1, degree = 2, maxit = 5000, tol = 1e-05 )
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 )
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
|
lambda1 |
A numeric vector of main effect penalties on which to tune
By default, |
lambda2 |
A numeric vector of interaction effects penalties on which to
tune. By default, |
nlambda1 |
The number of lambda1 values to generate. Default is 10,
minimum is 2. If |
nlambda2 |
The number of lambda2 values to generate. Default is 10,
minimum is 2. If |
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
|
sigma |
Scale parameter for integrative weights. Technically a third tuning parameter but defaults to 1 for computational tractability |
degree |
Degree of |
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
An nlambda1 x nlambda2 x 2
array containing each
pair (lambda1, lambda2)
pair.
lambda pair with the lowest cross validation error
cross validation error at each lambda pair. The error is calculated from the mean square error.
standard error of cvm
at each lambda pair.
higlasso output from fitting the whole data.
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$Y Z <- matrix(1, nrow(X)) # This can take a bit of time fit <- cv.higlasso(Y, X, Z) print(fit)
library(higlasso) X <- as.matrix(higlasso.df[, paste0("V", 1:7)]) Y <- higlasso.df$Y Z <- matrix(1, nrow(X)) # This can take a bit of time fit <- cv.higlasso(Y, X, Z) print(fit)
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, degree = 2, maxit = 5000, tol = 1e-05 )
higlasso( Y, X, Z, method = c("aenet", "gglasso"), lambda1 = NULL, lambda2 = NULL, nlambda1 = 10, nlambda2 = 10, lambda.min.ratio = 0.05, sigma = 1, degree = 2, 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 |
lambda1 |
A numeric vector of main effect penalties on which to tune
By default, |
lambda2 |
A numeric vector of interaction effects penalties on which to
tune. By default, |
nlambda1 |
The number of lambda1 values to generate. Default is 10,
minimum is 2. If |
nlambda2 |
The number of lambda2 values to generate. Default is 10,
minimum is 2. If |
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 |
degree |
Degree of |
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:
An nlambda1 x nlambda2 x 2
array containing each
pair (lambda1, lambda2)
pair.
An nlambda1 x nlambda2 x ncol(X)
array containing
higlasso's selections for each lambda pair.
The number of nonzero selections for each lambda pair.
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$Y Z <- matrix(1, nrow(X)) # This can take a bit of time higlasso.fit <- higlasso(Y, X, Z)
library(higlasso) X <- as.matrix(higlasso.df[, paste0("V", 1:7)]) Y <- higlasso.df$Y Z <- matrix(1, nrow(X)) # This can take a bit of time higlasso.fit <- higlasso(Y, X, Z)
This synthetic data is taken from the linear interaction simulations from the higlasso paper. The data generating model is:
higlasso.df
higlasso.df
A data.frame with 500 observations on 11 variables:
Continuous response.
Covariates.
print.cv.higlasso
prints a fitted "cv.higlaso" object and returns it
invisibly.
## S3 method for class 'cv.higlasso' print(x, ...)
## S3 method for class 'cv.higlasso' print(x, ...)
x |
An object of type "cv.higlasso" to print |
... |
Further arguments passed to or from other methods |
The original input, x
(invisibly).