calcType1postSelection {lavaSearch2}

Compute the Type 1 Error After Selection [EXPERIMENTAL]

Description

Compute the type 1 error after selection [EXPERIMENTAL].

Usage

calcType1postSelection(
  level,
  mu,
  Sigma,
  quantile.previous,
  distribution,
  df,
  n = 10,
  correct = TRUE,
  ...
)

Arguments

level

[numeric 0-1] expected coverage.

mu

[numeric vector] the expectation of the joint distribution of the test statistics

Sigma

[matrix] the variance-covariance of the joint distribution of the test statistics.

quantile.previous

[numeric] significance quantile used at the previous step.

distribution

[character] distribution of the test statistics. Can be "pmvnorm" (normal distribution) or "pvmt" (Student's t distribution)

df

[integer > 0] the degree of freedom of the joint Student's t distribution. Only used when distribution="pvmt".

n

[integer > 0] number of points for the numerical integration

correct

[logical] if true, correct the level to account for previous testings.

...

arguments passed to intDensTri.

Details

The number of tests at the current step (i.e. after selection) is assumed to be one less than the number of tests at the previous step (i.e. before selection).

Arguments mu and Sigma must contain the moments for the vector of test statistics before and after selection (in that order).

Value

[numeric] the type 1 error.

Author(s)

Brice Ozenne

Examples

library(mvtnorm)
n <- 350

#### only 2 tests
Sigma <- rbind(c(1,0,0),c(0,1,1),c(0,1,1))
z2 <- qmvnorm(0.95, mean = rep(0,2), sigma = Sigma[1:2,1:2], tail = "both.tails")$quantile

## no selection since strong effect
mu <- c(10,0,0)
calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = TRUE)

## strong selection
## Not run: 
mu <- c(0,0,0)
levelC <- calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma)
print(levelC) # more liberal than without selection
calcType1postSelection(levelC, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = FALSE)

## End(Not run)

#### 3 tests
Sigma <- diag(1,5,5)
Sigma[4,2] <- 1
Sigma[2,4] <- 1
Sigma[5,3] <- 1
Sigma[3,5] <- 1

z2 <- qmvnorm(0.95, mean = mu[1:3], sigma = Sigma[1:3,1:3], tails = "both.tails")$quantile

## no selection since strong effect
## Not run: 
mu <- c(10,0,0,0,0)
calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = TRUE)

## strong selection
mu <- c(0,0,0,0,0)
levelC <- calcType1postSelection(0.95, quantile.previous = z2,
                        mu = mu, Sigma = Sigma, distribution = "gaussian")
calcType1postSelection(levelC, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = FALSE)

## End(Not run)