Constructs projection based test statistics that can be used to control FDR along with intervals for a penalized regression model.
intervals(
fit,
lambda,
sigma,
level = 0.95,
posterior = TRUE,
relaxed = FALSE,
adjust_projection = FALSE,
X = NULL
)An data.frame containing the following columns:
colnames(X)
The original estimates at the specified parameters (lambda, gamma, alpha)
The debiased estimates.
The standard errors.
The PIPE / Relaxed Lasso / LQA test statistics
Interval lower bounds
Intervals upper bounds
The unadjusted p-value
The Benhamini and Hochberg corrected p-value
The penalty used.
The lambda value the test statistics and intervals were constructed at.
The gamma value the test statistics and intervals were constructed at (for MCP/SCAD).
The alpha value the test statistics and intervals were constructed at.
The confidence level set for interval construction.
The standard deviation used for constructing the test statistis and intervals.
An optional fit of class ncvreg or cv.ncvreg. If supplied,
X should only be supplied if fit does not contain it.
The penalty at which the tests and intervals are to be constructed. If left unspecified, will be selected using cross validation.
Standard deviation estimate used to compute test statistic and intervals. If left unspecified (default) it will be estimated using the recommendation from Reid et al. (2016)
the confidence level required.
whether the intervals returned should be posterior intervals
(default) or debiased intervals (if FALSE). Posterior
intervals are constructed from distributions where the
coefficient estimates are the is the posterior mode. Debiased
intervals are constructed around the estimates.
whether the relaxed lasso based statistic / intervals should
be used. Default is FALSE in which case PIPE based intervals
are constructed (recommended). This affects the estimate.
whether a Local Quadratic Approximation should be
used in the projection for determining variance of the PIPE
based test statistic. Default is FALSE as more research has
been done without this adjustment, however without this
adjustment, statistics and intervals may be over conservative in
the presence of correlation. This affects the SE.
The original design matrix supplied to fit. Required if fit
does not contain X.
Logan Harris, Patrick Breheny, and Biyue Dai
The function constructs test statistics and intervals based off an approximate projection onto the column space of the active features. The test statistic can be used to control FDR and the intervals generally have good coverage. However, both tend to be conservative with the introduction of correlation.
The intervals produced can either be biased (like the point estimates) or
debiased by setting the parameter posterior accordingly. The resulting
behavior is quite different. See references for more details.
Harris L and Breheny P. (2025) A new perspective on high dimensional confidence intervals. arXiv preprint, arXiv:2508.03504. https://arxiv.org/abs/2508.03504
Harris L and Breheny P. (2025) Alternative Likelihood Approximations for High-Dimensional Intervals for Lasso. arXiv preprint, arXiv:2509.14971. https://arxiv.org/abs/2509.14971
Dai B. (2019) Projection-based inference and model selection for penalized regression. PhD dissertation, University of Iowa, Iowa City, IA. tools:::Rd_expr_doi("10.17077/etd.005250")
# Linear regression (SCAD-Net penalty, PIPE intervals, pass ncvreg object)
fit <- ncvreg(Prostate$X, Prostate$y, penalty = "SCAD", alpha = 0.9)
intervals(fit) |> head()
# Logistic regression (lasso penalty, LQA intervals, pass cv.ncvreg object)
data(Heart)
cv_fit <- cv.ncvreg(Heart$X, Heart$y, family="binomial", penalty = "lasso")
intervals(cv_fit, adjust_projection = TRUE) |> head()
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