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##
## twostage.R
##
## Two-stage Monte Carlo tests and envelopes
##
## $Revision: 1.18 $ $Date: 2022/04/06 07:49:20 $
##
bits.test <- function(X, ..., exponent=2, nsim=19,
alternative=c("two.sided", "less", "greater"),
leaveout=1, interpolate=FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE) {
twostage.test(X, ..., exponent=exponent,
nsim=nsim, nsimsub=nsim, reuse=FALSE,
alternative=match.arg(alternative),
leaveout=leaveout, interpolate=interpolate,
savefuns=savefuns, savepatterns=savepatterns,
verbose=verbose,
testblurb="Balanced Independent Two-stage Test")
}
dg.test <- function(X, ..., exponent=2, nsim=19, nsimsub=nsim-1,
alternative=c("two.sided", "less", "greater"),
reuse=TRUE, leaveout=1, interpolate=FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE) {
check.1.integer(nsim)
stopifnot(nsim >= 2)
if(!missing(nsimsub) && (nsimsub < 1 || !relatively.prime(nsim, nsimsub)))
stop("nsim and nsimsub must be relatively prime")
twostage.test(X, ..., exponent=exponent,
nsim=nsim, nsimsub=nsimsub, reuse=reuse,
alternative=match.arg(alternative),
leaveout=leaveout, interpolate=interpolate,
savefuns=savefuns, savepatterns=savepatterns,
verbose=verbose,
testblurb="Dao-Genton adjusted goodness-of-fit test")
}
twostage.test <- function(X, ..., exponent=2, nsim=19, nsimsub=nsim,
alternative=c("two.sided", "less", "greater"),
reuse=FALSE, leaveout=1, interpolate=FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE, badXfatal=TRUE,
testblurb="Two-stage Monte Carlo test") {
Xname <- short.deparse(substitute(X))
alternative <- match.arg(alternative)
env.here <- sys.frame(sys.nframe())
Xismodel <- is.ppm(X) || is.kppm(X) || is.lppm(X) || is.slrm(X)
check.1.integer(nsim)
check.1.integer(nsimsub)
stopifnot(nsim >= 2)
stopifnot(nsimsub >= 2)
## first-stage p-value
if(verbose) cat("Applying first-stage test to original data... ")
tX <- envelopeTest(X, ...,
nsim=if(reuse) nsim else nsimsub,
alternative=alternative,
leaveout=leaveout,
interpolate=interpolate,
exponent=exponent,
savefuns=savefuns,
savepatterns=savepatterns || reuse,
verbose=FALSE, badXfatal=badXfatal,
envir.simul=env.here)
pX <- tX$p.value
## check special case
afortiori <- !interpolate && !reuse && (nsimsub < nsim) &&
(pX == (1/(nsim+1)) || pX == 1)
if(afortiori) {
## result is determined
padj <- pX
pY <- NULL
} else {
## result is not yet determined
if(!reuse) {
if(verbose) cat("Repeating first-stage test... ")
tXX <- envelopeTest(X, ...,
nsim=nsim, alternative=alternative,
leaveout=leaveout,
interpolate=interpolate,
exponent=exponent,
savefuns=savefuns, savepatterns=TRUE,
verbose=FALSE, badXfatal=badXfatal,
envir.simul=env.here)
## extract simulated patterns
Ylist <- attr(attr(tXX, "envelope"), "simpatterns")
} else {
Ylist <- attr(attr(tX, "envelope"), "simpatterns")
}
if(verbose) cat("Done.\n")
## apply same test to each simulated pattern
if(verbose) cat(paste("Running second-stage tests on",
nsim, "simulated patterns... "))
pY <- numeric(nsim)
for(i in 1:nsim) {
if(verbose) progressreport(i, nsim)
Yi <- Ylist[[i]]
## if X is a model, fit it to Yi. Otherwise the implicit model is CSR.
if(Xismodel) Yi <- update(X, Yi)
tYi <- envelopeTest(Yi, ...,
nsim=nsimsub, alternative=alternative,
leaveout=leaveout,
interpolate=interpolate,
exponent=exponent, savepatterns=TRUE,
verbose=FALSE, badXfatal=FALSE,
envir.simul=env.here)
pY[i] <- tYi$p.value
}
pY <- sort(pY)
## compute adjusted p-value
padj <- (1 + sum(pY <= pX))/(1+nsim)
}
# pack up
method <- tX$method
method <- c(testblurb,
paste("based on", method[1L]),
paste("First stage:", method[2L]),
method[-(1:2)],
if(afortiori) {
paren(paste("Second stage was omitted: p0 =", pX,
"implies p-value =", padj))
} else if(reuse) {
paste("Second stage: nested, ", nsimsub,
"simulations for each first-stage simulation")
} else {
paste("Second stage:", nsim, "*", nsimsub,
"nested simulations independent of first stage")
}
)
names(pX) <- "p0"
result <- structure(list(statistic = pX,
p.value = padj,
method = method,
data.name = Xname),
class="htest")
attr(result, "rinterval") <- attr(tX, "rinterval")
attr(result, "pX") <- pX
attr(result, "pY") <- pY
if(savefuns || savepatterns)
result <- hasenvelope(result, attr(tX, "envelope"))
return(result)
}
dg.envelope <- function(X, ..., nsim=19,
nsimsub=nsim-1,
nrank=1,
alternative=c("two.sided", "less", "greater"),
leaveout=1,
interpolate = FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE) {
twostage.envelope(X, ...,
nsim=nsim, nsimsub=nsimsub, reuse=TRUE, nrank=nrank,
alternative=match.arg(alternative),
leaveout=leaveout, interpolate=interpolate,
savefuns=savefuns, savepatterns=savepatterns,
verbose=verbose, testlabel="bits")
}
bits.envelope <- function(X, ..., nsim=19,
nrank=1,
alternative=c("two.sided", "less", "greater"),
leaveout=1,
interpolate = FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE) {
twostage.envelope(X, ...,
nsim=nsim, nsimsub=nsim, reuse=FALSE, nrank=nrank,
alternative=match.arg(alternative),
leaveout=leaveout, interpolate=interpolate,
savefuns=savefuns, savepatterns=savepatterns,
verbose=verbose, testlabel="bits")
}
twostage.envelope <- function(X, ..., nsim=19, nsimsub=nsim,
nrank=1,
alternative=c("two.sided", "less", "greater"),
reuse=FALSE,
leaveout=1,
interpolate = FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose=TRUE, badXfatal=TRUE,
testlabel="twostage") {
# Xname <- short.deparse(substitute(X))
alternative <- match.arg(alternative)
env.here <- sys.frame(sys.nframe())
Xismodel <- is.ppm(X) || is.kppm(X) || is.lppm(X) || is.slrm(X)
check.1.integer(nsim)
check.1.integer(nsimsub)
stopifnot(nsim >= 2)
stopifnot(nsimsub >= 1)
############## first stage ##################################
if(verbose) cat("Applying first-stage test to original data... ")
tX <- envelopeTest(X, ...,
alternative=alternative,
leaveout=leaveout,
interpolate = interpolate,
nsim=if(reuse) nsim else nsimsub,
nrank=nrank,
exponent=Inf, savepatterns=TRUE, savefuns=TRUE,
verbose=FALSE, badXfatal=badXfatal,
envir.simul=env.here)
if(verbose) cat("Done.\n")
envX <- attr(tX, "envelope")
if(!reuse) {
if(verbose) cat("Repeating first-stage test... ")
tXX <- envelopeTest(X, ...,
alternative=alternative,
leaveout=leaveout,
interpolate = interpolate,
nsim=nsim, nrank=nrank,
exponent=Inf, savepatterns=TRUE, savefuns=TRUE,
verbose=FALSE, badXfatal=badXfatal,
envir.simul=env.here)
## extract simulated patterns
Ylist <- attr(attr(tXX, "envelope"), "simpatterns")
} else {
Ylist <- attr(attr(tX, "envelope"), "simpatterns")
}
if(verbose) cat("Done.\n")
############## second stage #################################
## apply same test to each simulated pattern
if(verbose) cat(paste("Running tests on", nsim, "simulated patterns... "))
pvalY <- numeric(nsim)
for(i in 1:nsim) {
if(verbose) progressreport(i, nsim)
Yi <- Ylist[[i]]
# if X is a model, fit it to Yi. Otherwise the implicit model is CSR.
if(Xismodel) Yi <- update(X, Yi)
tYi <- envelopeTest(Yi, ...,
alternative=alternative,
leaveout=leaveout,
interpolate = interpolate, save.interpolant = FALSE,
nsim=nsimsub, nrank=nrank,
exponent=Inf, savepatterns=TRUE,
verbose=FALSE, badXfatal=FALSE,
envir.simul=env.here)
pvalY[i] <- tYi$p.value
}
## Find critical deviation
if(!interpolate) {
## find critical rank 'l'
rankY <- pvalY * (nsimsub + 1)
twostage.rank <- orderstats(rankY, k=nrank)
if(verbose) cat(paste0(testlabel, ".rank"), "=", twostage.rank, fill=TRUE)
## extract deviation values from top-level simulation
simdev <- attr(tX, "statistics")[["sim"]]
## find critical deviation
twostage.crit <- orderstats(simdev, decreasing=TRUE, k=twostage.rank)
if(verbose) cat(paste0(testlabel, ".crit"), "=", twostage.crit, fill=TRUE)
} else {
## compute estimated cdf of t
fhat <- attr(tX, "density")[c("x", "y")]
fhat$z <- with(fhat, cumsum(y)/sum(y)) # 'within' upsets package checker
## find critical (second stage) p-value
pcrit <- orderstats(pvalY, k=nrank)
## compute corresponding upper quantile of estimated density of t
twostage.crit <- with(fhat, { min(x[z >= 1 - pcrit]) })
}
## make fv object, for now
refname <- if("theo" %in% names(envX)) "theo" else "mmean"
fname <- attr(envX, "fname")
result <- (as.fv(envX))[, c(fvnames(envX, ".x"),
fvnames(envX, ".y"),
refname)]
refval <- envX[[refname]]
##
newdata <- data.frame(hi=refval + twostage.crit,
lo=refval - twostage.crit)
newlabl <- c(makefvlabel(NULL, NULL, fname, "hi"),
makefvlabel(NULL, NULL, fname, "lo"))
alpha <- nrank/(nsim+1)
alphatext <- paste0(100*alpha, "%%")
newdesc <- c(paste("upper", alphatext, "critical boundary for %s"),
paste("lower", alphatext, "critical boundary for %s"))
switch(alternative,
two.sided = { },
less = {
newdata$hi <- Inf
newlabl[1L] <- "infinity"
newdesc[1L] <- "infinite upper limit"
},
greater = {
newdata$lo <- -Inf
newlabl[2L] <- "infinity"
newdesc[2L] <- "infinite lower limit"
})
result <- bind.fv(result, newdata, newlabl, newdesc)
fvnames(result, ".") <- rev(fvnames(result, "."))
fvnames(result, ".s") <- c("lo", "hi")
if(savefuns || savepatterns)
result <- hasenvelope(result, envX)
return(result)
}
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