lava (version 1.8.2)

closed_testing: Closed testing procedure

Description

Given p hypotheses H1, ..., Hp all 2^p-1 intersection hypotheses are calculated and adjusted p-values are obtained for Hj is calculated as the max p-value of all intersection hypotheses containing Hj. Example, for p=3, the adjusted p-value for H1 will be obtained from {(H1, H2, H3), (H1,H2), (H1,H3), (H1)}.

Usage

closed_testing(object, test = test_wald, ...)

Arguments

object

`estimate` object

test

function that conducts hypothesis test. See details below.

...

Additional arguments passed to `test`

Details

The function `test` should be a function `function(object, index, ...)` which as its first argument takes an `estimate` object and and wit an argument `index` which is a integer vector specifying which subcomponents of `object` to test. The ellipsis argument can be any other arguments used in the test function. The function test_wald is an example of valid test function (which has an additional argument `null` in reference to the above mentioned ellipsis arguments).

References

Marcus, R; Peritz, E; Gabriel, KR (1976). "On closed testing procedures with special reference to ordered analysis of variance". Biometrika. 63 (3): 655–660.

Examples

m <- lvm()
regression(m, c(y1,y2,y3,y4)~x) <- c(0, 0.25, 0, 0.25)
regression(m, to=endogenous(m), from="u") <- 1
variance(m,endogenous(m)) <- 1
set.seed(1)
d <- sim(m, 200)
l1 <- lm(y1~x,d)
l2 <- lm(y2~x,d)
l3 <- lm(y3~x,d)
l4 <- lm(y4~x,d)

(a <- merge(l1, l2, l3, l4, subset=2))
if (requireNamespace("mets",quietly=TRUE)) {
   alpha_zmax(a)
}
adj <- closed_testing(a)
adj
adj$p.value
summary(adj)