inference {GGMncv}

Statistical Inference for Regularized Gaussian Graphical Models

Description

Compute p-values for each relation based on the de-sparsified glasso estimator (Jankova and Van De Geer 2015).

Usage

inference(object, method = "fdr", alpha = 0.05, ...)

significance_test(object, method = "fdr", alpha = 0.05, ...)

Arguments

object

An object of class ggmncv

method

Character string. A correction method for multiple comparison (defaults to fdr). Can be abbreviated. See p.adjust.

alpha

Numeric. Significance level (defaults to 0.05).

...

Currently ignored.

Value

• Theta De-sparsified precision matrix

• adj Adjacency matrix based on the p-values.

• pval_uncorrected Uncorrected p-values

• pval_corrected Corrected p-values

• method The approach used for multiple comparisons

• alpha Significance level

Note

This assumes (reasonably) Gaussian data, and should not to be expected to work for, say, polychoric correlations. Further, all work to date has only looked at the graphical lasso estimator, and not de-sparsifying nonconvex regularization. Accordingly, it is probably best to set penalty = "lasso" in ggmncv.

Further, whether the de-sparsified estimator provides nominal error rates remains to be seen, at least across a range of conditions. For example, the simulation results in Williams (2021) demonstrated that the confidence intervals can have (severely) compromised coverage properties (whereas non-regularized methods had coverage at the nominal level).

References

Jankova J, Van De Geer S (2015). “Confidence intervals for high-dimensional inverse covariance estimation.” Electronic Journal of Statistics, 9(1), 1205–1229.

Williams DR (2021). “The Confidence Interval that Wasn't: Bootstrapped "Confidence Intervals" in L1-Regularized Partial Correlation Networks.” PsyArXiv. doi: 10.31234/osf.io/kjh2f.

Examples

# data
Y <- GGMncv::ptsd[,1:5]

# fit model
fit <- ggmncv(cor(Y), n = nrow(Y),
              progress = FALSE,
              penalty = "lasso")


# statistical inference
inference(fit)

# alias
all.equal(inference(fit), significance_test(fit))