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

In bozenne/lavaSearch2: Tools for Model Specification in the Latent Variable Framework

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)

bozenne/lavaSearch2 documentation built on Feb. 13, 2024, 10:18 p.m.