islasso: The Induced Smoothed Lasso: A practical framework for...

In islasso: The Induced Smoothed Lasso

The Induced Smoothed Lasso: A practical framework for hypothesis testing in high dimensional regression

Description

This package implements an induced smoothed approach for hypothesis testing in Lasso regression.

Fits regression models with a smoothed L1 penalty under the induced smoothing paradigm. Supports linear, logistic, Poisson, and Gamma responses. Enables reliable standard errors and Wald-based inference.

Usage

islasso(
  formula,
  family = gaussian,
  lambda,
  alpha = 1,
  data,
  weights,
  subset,
  offset,
  unpenalized,
  contrasts = NULL,
  control = is.control()
)

Arguments

formula	A symbolic formula describing the model.
family	Response distribution. Can be gaussian, binomial, poisson, or Gamma.
lambda	Regularization parameter. If missing, it is estimated via cv.glmnet.
alpha	Elastic-net mixing parameter (0 \le \alpha \le 1).
data	A data frame or environment containing the variables in the model.
weights	Observation weights. Defaults to 1.
subset	Optional vector specifying a subset of rows to include.
offset	Optional numeric vector of offsets in the linear predictor.
unpenalized	Vector indicating variables (by name or index) to exclude from penalization.
contrasts	Optional contrasts specification for factor variables.
control	A list of parameters to control model fitting. See is.control.

Details

Package:	islasso
Type:	Package
Version:	1.6.0
Date:	2025-07-30
License:	GPL-2

islasso fits generalized linear models with an L1 penalty on selected coefficients. It returns both point estimates and full covariance matrices, enabling standard error-based inference. Related methods include: summary.islasso, predict.islasso, logLik.islasso, deviance.islasso, and residuals.islasso.

islasso.path fits regularization paths using the Induced Smoothed Lasso. It computes coefficients and standard errors across a grid of lambda values. Companion methods include: summary.islasso.path, predict.islasso.path, logLik.islasso.path, residuals.islasso.path, coef.islasso.path, and fitted.islasso.path.

The non-smooth L1 penalty is replaced by a smooth approximation, enabling inference through standard errors and Wald tests. The approach controls type-I error and shows strong power in various simulation settings.

Value

A list with components such as:

coefficients	Estimated coefficients
se	Standard errors
fitted.values	Fitted values
deviance, aic, null.deviance	Model diagnostic metrics
residuals, weights	IWLS residuals and weights
df.residual, df.null, rank	Degrees of freedom
converged	Logical; convergence status
model, call, terms, formula, data, offset	Model objects
xlevels, contrasts	Factor handling details
lambda, alpha, dispersion	Model parameters
internal	Other internal values

Author(s)

Gianluca Sottile, based on preliminary work by Vito Muggeo. Maintainer: [e-mail]

Gianluca Sottile [e-mail]

References

Cilluffo, G., Sottile, G., La Grutta, S., Muggeo, VMR (2019). *The Induced Smoothed lasso: A practical framework for hypothesis testing in high dimensional regression*, Statistical Methods in Medical Research. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0962280219842890")}

Sottile, G., Cilluffo, G., Muggeo, VMR (2019). *The R package islasso: estimation and hypothesis testing in lasso regression*. Technical Report on ResearchGate. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.13140/RG.2.2.16360.11521")}

Cilluffo G., Sottile G., La Grutta S., Muggeo V.M.R. (2019) The Induced Smoothed Lasso: A practical framework for hypothesis testing in high dimensional regression. Statistical Methods in Medical Research. DOI: 10.1177/0962280219842890

Sottile G., Cilluffo G., Muggeo V.M.R. (2019) The R package islasso: estimation and hypothesis testing in lasso regression. Technical Report. DOI: 10.13140/RG.2.2.16360.11521

See Also

summary.islasso, predict.islasso, logLik.islasso

Examples

n <- 100; p <- 100

beta <- c(rep(1, 5), rep(0, p - 5))
sim1 <- simulXy(n = n, p = p, beta = beta, seed = 1, family = gaussian())
o <- islasso(y ~ ., data = sim1$data, family = gaussian())

summary(o, pval = 0.05)
coef(o)
fitted(o)
predict(o, type="response")
plot(o)
residuals(o)
deviance(o)
AIC(o)
logLik(o)

## Not run: 
# for the interaction
o <- islasso(y ~ X1 * X2, data = sim1$data, family = gaussian())

##### binomial ######
beta <- c(c(1,1,1), rep(0, p-3))
sim2 <- simulXy(n = n, p = p, beta = beta, interc = 1, seed = 1,
                size = 100, family = binomial())
o2 <- islasso(cbind(y.success, y.failure) ~ .,
              data = sim2$data, family = binomial())
summary(o2, pval = 0.05)

##### poisson ######
beta <- c(c(1,1,1), rep(0, p-3))
sim3 <- simulXy(n = n, p = p, beta = beta, interc = 1, seed = 1,
                family = poisson())
o3 <- islasso(y ~ ., data = sim3$data, family = poisson())
summary(o3, pval = 0.05)

##### Gamma ######
beta <- c(c(1,1,1), rep(0, p-3))
sim4 <- simulXy(n = n, p = p, beta = beta, interc = -1, seed = 1,
                dispersion = 0.1, family = Gamma(link = "log"))
o4 <- islasso(y ~ ., data = sim4$data, family = Gamma(link = "log"))
summary(o4, pval = 0.05)

## End(Not run)

islasso documentation built on Aug. 9, 2025, 1:06 a.m.