Nothing
bootstrap_ci_th <- function( TH, r, m, x, N, h0, alpha = 0.05,
X = (max(x)-min(x))*(0:999)/999+min(x),
link = c( "logit" ), guessing = 0, lapsing = 0,
K = 2, p = 1, ker = c( "dnorm" ), maxiter = 50,
tol = 1e-6 ) {
#
# Finds a bootstrap estimate of a confidence interval at a significance level alpha
# for the estimated threshold for the local polynomial estimate of the psychometric function
# with guessing and lapsing rates. The confidence interval is based on bootstrap percentiles.
#
# See Efron & Tibshirani's "An introduction to the bootstrap", 1993
#
# INPUT
#
# TH - required threshold level
# r - number of successes at points x
# m - number of trials at points x
# x - stimulus levels
# N - number of bootstrap replications; N should be at least 1000 for reliable results
# h0 - bandwidth
#
# OPTIONAL INPUT
#
# alpha - significance level of the confidence interval; default is 0.05
# X - set of values at which estimates of the psychometric function
# for the threshold estimation are to be obtained; if not given, 1000
# equally spaced points from minimum to maximum of x are used
# link - name of the link function; default is "logit"
# guessing - guessing rate; default is 0
# lapsing - lapsing rate; default is 0
# K - power parameter for Weibull and reverse Weibull link; default is 2
# p - degree of the polynomial; default is 1
# ker - kernel function for weights; default is "dnorm"
# maxiter - maximum number of iterations in Fisher scoring; default is 50
# tol - tolerance level at which to stop Fisher scoring; default is 1e-6
#
# OUTPUT
#
# Object with 2 components:
# ci - confidence interval based on bootstrap percentiles
# th0 - threshold estimate
####
# KZ 28-Mar-12
# included on.exit function which restores warning settings to their
# original state
####
# MAIN PROGRAM
# First 6 arguments are mandatory
if( missing("TH") || missing("r") || missing("m") || missing("x") ||
missing("N") || missing("h0") ) {
stop("Check input. First 6 arguments are mandatory");
}
# CHECK ROBUSTNESS OF INPUT PARAMETERS
if( !is.double(TH) || length( TH ) > 1 ) {
stop( "Threshold level must be scalar" );
}
checkdata<-list();
checkdata[[1]] <- x;
checkdata[[2]] <- r;
checkdata[[3]] <- m;
checkinput( "psychometricdata", checkdata );
rm( checkdata )
checkinput( "bootstrapreplications", N );
if( !is.vector( X ) ) {
stop("X (values where to estimate the PF) has to be a vector");
}
if( length( X ) < 2 ) {
stop("At least 2 values needed for vector X");
}
if( min(x) > min(X) || max(x) < max(X) ) {
stop("Supplied values of X are outside the range of stimulus levels x");
}
checkinput( "bandwidth", h0 );
if( length(alpha)>1 ){
stop('Significance level must be scalar');
}
if( alpha <= 0 || alpha > 0.5 ) {
stop('Significance level must be between 0 and 0.5');
}
checkinput( "linkfunction", link );
if( length( guessing ) > 1 ) {
stop( "Guessing rate must be scalar" );
}
if( length( lapsing ) > 1 ) {
stop( "Lapsing rate must be scalar" );
}
checkinput( "Guessingandlapsing", c( guessing, lapsing ) );
if( any( TH <= guessing )) {
stop( "Threshold level should be greater than guessing rate" );
}
if( any( TH >= 1-lapsing ) ) {
stop( "Threshold level should be smaller than 1 - lapsing rate" );
}
if (link == "weibull" || link == "revweibull"){
checkinput( "exponentk", K );
}
pn <- list()
pn[[1]] <- p
pn[[2]] <- x
checkinput( "degreepolynomial", pn );
checkinput( "kernel", ker );
checkinput( "maxiter", maxiter );
checkinput( "tolerance", tol );
if( N < 1000 ) {
warning( "number of bootstrap should be larger than 1000\n otherwise results might be unreliable" );
}
n <- length( x );
# INITIAL ESTIMATE
# initial estimates with bandiwdth h0
# KZ 28-03-2012 included on.exit routine so that the warning settings are
# restored when the function terminates even if interrupted by user
warn.current <- getOption("warn")
on.exit(options(warn = warn.current));
options(warn=-1)
f <- locglmfit( x, r, m, x, h0, FALSE, link, guessing, lapsing, K,
p, ker, maxiter, tol )$pfit;
# dense version for estimation of the threshold
F <- locglmfit( X, r, m, x, h0, FALSE, link, guessing, lapsing, K,
p, ker, maxiter, tol )$pfit;
# THRESHOLD ESTIMATE
ci <- NULL;
th0 <- threshold_slope( F, X, TH )$x_th;
# BOOTSTRAP SAMPLING
# re-sampling
samp <- matrix( 0, n, N );
samp <- matrix(rbinom(N*n,m,f),n,N)
# exclude "degenerate samples" if min(M)>1
if( min( m ) > 1 ) {
ok <- NULL;
for( i in 1:N ) {
ok[i] = length( unique( samp[,i] ) ) > 3;
}
while( any( ok == FALSE ) ) {
lis <- which( ok == 0 )
samp[,lis] <- matrix(rbinom(length(lis)*n,m,f),n,length(lis))
for( i in 1:length( lis ) ) {
ok[lis[i]] <- length( unique( samp[,lis[i]] ) ) > 3;
}
}
}
# INITIATE VARIABLE IN WHICH DATA ARE STORED
th_boot <- NULL;
# BOOTSTRAP ESTIMATES OF THE THRESHOLD
for( i in 1:N ) {
ftmp <- locglmfit( X, samp[,i], m, x, h0, FALSE, link, guessing,
lapsing, K, p, ker, maxiter, tol )$pfit;
th_boot[i] <- threshold_slope( ftmp, X, TH )$x_th;
}
ci[1] <- quantile( th_boot, probs = alpha / 2 );
ci[2] <- quantile( th_boot, probs = 1 - alpha / 2 );
value <- NULL
value$ci <- ci
value$th0 <- th0
return( value );
}
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