mediation_test_Bayes: Bayes risk optimal testing

In achambaz/mediation.test: More Powerful Tests of the Composite Null Hypothesis Arising in Mediation Analysis

Bayes risk optimal testing

Description

Carries out the Bayes risk optimal test of the composite null "\delta_x \times \delta_y=0" against its alternative "\delta_x \times \delta_y\neq 0" based on the test statistic in the real plane.

Usage

mediation_test_Bayes(t, map, truncation = 0)

Arguments

t	A vector consisting of two numerics, the test statistic in the real plane, or a 'n x 2' matrix of such test statistics.
map	The "map" of rejection probabilities – the 'map' item of the output of function compute_map_rejection_probs.
truncation	A nonnegative numeric used to bound the rejection region away from the null hypothesis space. Defaults to 0, in which case the rejection region is minimax optimal.

Details

For details, we refer to the technical report "Optimal Tests of the Composite Null Hypothesis Arising in Mediation Analysis", by Miles & Chambaz (2024), https://arxiv.org/abs/2107.07575

Value

A list, consisting of:

t:

a vector of two numerics, the test statistic, or a 'n x 2' matrix of such test statistics;

alpha:

a numeric, the type-I error;

truncation:

a nonnegative numeric, used to bound the rejection region away from the null hypothesis space

decision:

a vector of logicals, FALSE if the null hypothesis can be rejected for the alternative at level 'alpha' and TRUE otherwise;

pval:

a vector of numerics, the p-values of the tests, 'NA' in this case;

method:

the character "Bayes";

map:

The "map" of rejection probabilities – the 'map' item of the output of function compute_map_rejection_probs.

Examples

n <- 10
x <- MASS::mvrnorm(2 * n, mu = c(0, 0), Sigma = diag(c(1, 1)))
delta <- matrix(stats::runif(4 * n, min = -3, max = 3), ncol = 2)
epsilon <- stats::rbinom(n, 1, 1/2)
delta <- delta * cbind(c(epsilon, rep(1, n)),
                       c(1 - epsilon, rep(1, n)))
x <- x + delta
(mt_01_0.05 <- mediation_test_Bayes(x, map = map_01_0.05))
plot(mt_01_0.05)
(mt_quad_0.05_0.1 <- mediation_test_Bayes(x, map = map_quad_0.05_0.1))
plot(mt_quad_0.05_0.1)

achambaz/mediation.test documentation built on Feb. 8, 2025, 1:17 p.m.