calcDistMax {lavaSearch2}

Adjust the p.values Using the Quantiles of the Max Statistic

Description

Adjust the p.values using the quantiles of the max statistic.

Usage

calcDistMaxIntegral(
  statistic,
  iid,
  df,
  iid.previous = NULL,
  quantile.previous = NULL,
  quantile.compute = lava.options()$search.calc.quantile.int,
  alpha,
  cpus = 1,
  cl = NULL,
  trace
)

calcDistMaxBootstrap(
  statistic,
  iid,
  iid.previous = NULL,
  quantile.previous = NULL,
  method,
  alpha,
  cpus = 1,
  cl = NULL,
  n.sim,
  trace,
  n.repmax = 100
)

Arguments

statistic

[numeric vector] the observed Wald statistic. Each statistic correspond to a null hypothesis (i.e. a coefficient) that one wish to test.

iid

[matrix] zero-mean iid decomposition of the coefficient used to compute the statistic.

df

[numeric] the degree of freedom defining the multivariate Student's t distribution. If NULL the multivariate Gaussian distribution will be used instead.

iid.previous

[matrix, EXPERIMENTAL] zero-mean iid decomposition of previously tested coefficient.

quantile.previous

[numeric, EXPERIMENTAL] rejection quantiles of the previously tested hypotheses. If not NULL the values should correspond the variable in to the first column(s) of the argument iid.previous.

quantile.compute

[logical] should the rejection quantile be computed?

alpha

[numeric 0-1] the significance cutoff for the p-values. When the p-value is below, the corresponding link will be retained.

cpus

[integer >0] the number of processors to use. If greater than 1, the computation of the p-value relative to each test is performed in parallel.

cl

[cluster] a parallel socket cluster generated by parallel::makeCluster that has been registered using registerDoParallel.

trace

[logical] should the execution of the function be traced?

method

[character] the method used to compute the p-values.

n.sim

[integer >0] the number of bootstrap simulations used to compute each p-values. Disregarded when the p-values are computed using numerical integration.

n.repmax

[integer >0] the maximum number of rejection for each bootstrap sample before switching to a new bootstrap sample. Only relevant when conditioning on a previous test. Disregarded when the p-values are computed using numerical integration.

Value

A list containing

• p.adjust: the adjusted p-values.

• z: the rejection threshold.

• Sigma: the correlation matrix between the test statistic.

• correctedLevel: the alpha level corrected for conditioning on previous tests.

Examples

library(mvtnorm)

set.seed(10)
n <- 100
p <- 4
link <- letters[1:p]
n.sim <- 1e3 # number of bootstrap simulations 

#### test - not conditional ####
X.iid <- rmvnorm(n, mean = rep(0,p), sigma = diag(1,p))
colnames(X.iid) <- link
statistic <- setNames(1:p,link)


r1 <- calcDistMaxIntegral(statistic = statistic, iid = X.iid, 
            trace = FALSE, alpha = 0.05, df = 1e6) 

r3 <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            method = "residual",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

r4 <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            method = "wild",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

rbind(integration = c(r1$p.adjust, quantile = r1$z),
      bootResidual = c(r3$p.adjust, quantile = r3$z),
      bootWild    = c(r4$p.adjust, quantile = r4$z))

#### test - conditional ####
## Not run: 
Z.iid <- rmvnorm(n, mean = rep(0,p+1), sigma = diag(1,p+1))
seqQuantile <- qmvnorm(p = 0.95, delta = rep(0,p+1), sigma = diag(1,p+1), 
                    tail = "both.tails")$quantile

r1c <- calcDistMaxIntegral(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, 
            trace = FALSE, alpha = 0.05, df = NULL)

r3c <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, method = "residual",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

r4c <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, method = "wild",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

rbind(integration = c(r1c$p.adjust, quantile = r1c$z),
      bootResidual = c(r3c$p.adjust, quantile = r3c$z),
      bootWild    = c(r4c$p.adjust, quantile = r4c$z))

## End(Not run)