ZEST: ZEST

Description

An implementation of the Bayesian test procedures of King-Smith et al. and Watson and Pelli. Note that we use the term pdf throughout as in the original paper, even though they are discrete probability functions in this implementation.

Usage

ZEST(
  domain = 0:40,
  prior = rep(1/length(domain), length(domain)),
  likelihood = sapply(domain, function(tt) 0.03 + (1 - 0.03 - 0.03) * (1 -
    stats::pnorm(domain, tt, 1))),
  stopType = "S",
  stopValue = 1.5,
  minStimulus = utils::head(domain, 1),
  maxStimulus = utils::tail(domain, 1),
  maxSeenLimit = 2,
  minNotSeenLimit = 2,
  maxPresentations = 100,
  minInterStimInterval = NA,
  maxInterStimInterval = NA,
  verbose = 0,
  makeStim,
  stimChoice = "mean",
  ...
)
ZEST.start(
  domain = 0:40,
  prior = rep(1/length(domain), length(domain)),
  likelihood = sapply(domain, function(tt) 0.03 + (1 - 0.03 - 0.03) * (1 -
    stats::pnorm(domain, tt, 1))),
  stopType = "S",
  stopValue = 1.5,
  minStimulus = utils::head(domain, 1),
  maxStimulus = utils::tail(domain, 1),
  maxSeenLimit = 2,
  minNotSeenLimit = 2,
  maxPresentations = 100,
  makeStim,
  stimChoice = "mean",
  ...
)
ZEST.step(state, nextStim = NULL, fixedStimValue = NA, fixedResponse = NA)
ZEST.stop(state)
ZEST.final(state)

Value

Single location

ZEST returns a list containing

npres Total number of presentations used.
respSeq Response sequence stored as a matrix: row 1 is dB values of stimuli, row 2 is 1/0 for seen/not-seen, row 3 is fixated 1/0 (always 1 if checkFixationOK not present in stim objects returned from makeStim).
pdfs If verbose is bigger than 0, then this is a list of the pdfs used for each presentation, otherwise NULL.
final The mean/median/mode of the final pdf, depending on stimChoice, which is the determined threshold.
opiResp A list of responses received from each successful call to opiPresent within ZEST.

Multilple locations

ZEST.start returns a list that can be passed to ZEST.step, ZEST.stop, and ZEST.final. It represents the state of a ZEST at a single location at a point in time and contains the following.

name ZEST.
pdf Current pdf: vector of probabilities the same length as domain.
numPresentations The number of times ZEST.step has been called on this state.
stimuli A vector containing the stimuli used at each call of ZEST.step.
responses A vector containing the responses received at each call of ZEST.step.
responseTimes A vector containing the response times received at each call of ZEST.step.
fixated A vector containing TRUE/FALSE if fixation was OK according to checkFixationOK for each call of ZEST.step (defaults to TRUE if checkFixationOK not present).
opiResp A list of responses received from each call to opiPresent within ZEST.step.
A copy of all of the parameters supplied to ZEST.start: domain, likelihood, stopType, stopValue, minStimulus, maxStimulus, maxSeenLimit, minNotSeenLimit, maxPresentations, makeStim, stimChoice, currSeenLimit, currNotSeenLimit, and opiParams.

ZEST.step returns a list containing * state The new state after presenting a stimuli and getting a response. * resp The return from the opiPresent call that was made.

ZEST.stop returns TRUE if the ZEST has reached its stopping criteria, and FALSE otherwise.

ZEST.final returns an estimate of threshold based on state. If state$stimChoice is mean then the mean is returned. If state$stimChoice is mode then the mode is returned. If state$stimChoice is median then the median is returned.

A list containing * state The new state after presenting a stimuli and getting a response. * resp The return from the opiPresent call that was made.

Arguments

domain: Vector of values over which pdf is kept.
prior: Starting probability distribution over domain. Same length as domain.
likelihood: Matrix where likelihood[s,t] is likelihood of seeing s given t is the true threshold. That is, Pr(s|t) where s and t are indexes into domain.
stopType: N, for number of presentations; S, for standard deviation of the pdf; and H, for the entropy of the pdf.
stopValue: Value for number of presentations (stopType=N), standard deviation (stopType=S) or Entropy (stopType=H).
minStimulus: The smallest stimuli that will be presented. Could be different from domain[1].
maxStimulus: The largest stimuli that will be presented. Could be different from tail(domain,1).
maxSeenLimit: Will terminate if maxStimulus value is seen this many times.
minNotSeenLimit: Will terminate if minStimulus value is not seen this many times.
maxPresentations: Maximum number of presentations regardless of stopType.
minInterStimInterval: If both minInterStimInterval and maxInterStimInterval are not NA, then between each stimuli there is a random wait period drawn uniformly between minInterStimInterval and maxInterStimInterval.
maxInterStimInterval: minInterStimInterval.
verbose: verbose=0 does nothing, verbose=1 stores pdfs for returning, and verbose=2 stores pdfs and also prints each presentation.
makeStim: A function that takes a dB value and numPresentations and returns an OPI datatype ready for passing to opiPresent. See examples.
stimChoice: A true ZEST procedure uses the "mean" of the current pdf as the stimulus, but "median" and "mode" (as used in a QUEST procedure) are provided for your enjoyment.
...: Extra parameters to pass to the opiPresent function
state: Current state of the ZEST returned by ZEST.start and ZEST.step.
nextStim: A valid object for opiPresent to use as its nextStim.
fixedStimValue: A number in state$domain that, is !is.na, will be used as the stimulus value overriding state$minStimulus, state$maxStimulus and state$stimChoice.
fixedResponse: Ignored if !is.na otherwise used as the response to the stim shown.

Details

This is an implementation of King-Smith et al.'s ZEST procedure and Watson and Pelli's QUEST procedure. All presentations are rounded to an element of the supplied domain.

Note this function will repeatedly call opiPresent for a stimulus until opiPresent returns NULL (ie no error occurred).

The checkFixationOK function is called (if present in stim made from makeStim) after each presentation, and if it returns FALSE, the pdf for that location is not changed (ie the presentation is ignored), but the stim, number of presentations etc is recorded in the state.

If more than one ZEST is to be interleaved (for example, testing multiple locations), then the ZEST.start, ZEST.step, ZEST.stop and ZEST.final calls can maintain the state of the ZEST after each presentation, and should be used. If only a single ZEST is required, then the simpler ZEST can be used, which is a wrapper for the four functions that maintain state. See examples below.

References

P.E. King-Smith, S.S. Grigsny, A.J. Vingrys, S.C. Benes, and A. Supowit. "Efficient and Unbiased Modifications of the QUEST Threshold Method: Theory, Simulations, Experimental Evaluation and Practical Implementation", Vision Research 34(7) 1994. Pages 885-912.

A.B. Watson and D.G. Pelli. "QUEST: A Bayesian adaptive psychophysical method", Perception and Psychophysics 33 1983. Pages 113-l20.

A. Turpin, P.H. Artes and A.M. McKendrick "The Open Perimetry Interface: An enabling tool for clinical visual psychophysics", Journal of Vision 12(11) 2012.

Examples

Run this code

chooseOpi("SimHenson")
if(!is.null(opiInitialize(type="C", cap=6)$err))
  stop("opiInitialize failed")

##############################################
# This section is for single location ZESTs
##############################################
# Stimulus is Size III white-on-white as in the HFA
makeStim <- function(db, n) {
  s <- list(x=9, y=9, level=dbTocd(db), size=0.43, color="white",
            duration=200, responseWindow=1500, checkFixationOK=NULL)
  class(s) <- "opiStaticStimulus"
  return(s)
}

repp <- function(...) sapply(1:50, function(i) ZEST(makeStim=makeStim, ...))
a <- repp(stopType="H", stopValue=  3, verbose=0, tt=30, fpr=0.03)
b <- repp(stopType="S", stopValue=1.5, verbose=0, tt=30, fpr=0.03)
c <- repp(stopType="S", stopValue=2.0, verbose=0, tt=30, fpr=0.03)
d <- repp(stopType="N", stopValue= 50, verbose=0, tt=30, fpr=0.03)
e <- repp(prior=dnorm(0:40,m=0,s=5), tt=30, fpr=0.03)
f <- repp(prior=dnorm(0:40,m=10,s=5), tt=30, fpr=0.03)
g <- repp(prior=dnorm(0:40,m=20,s=5), tt=30, fpr=0.03)
h <- repp(prior=dnorm(0:40,m=30,s=5), tt=30, fpr=0.03)

layout(matrix(1:2,1,2))
boxplot(lapply(list(a,b,c,d,e,f,g,h), function(x) unlist(x["final",])))
boxplot(lapply(list(a,b,c,d,e,f,g,h), function(x) unlist(x["npres",])))

##############################################
# This section is for multiple ZESTs
##############################################
makeStimHelper <- function(db,n, x, y) {  # returns a function of (db,n)
  ff <- function(db, n) db+n
  body(ff) <- substitute({
    s <- list(x=x, y=y, level=dbTocd(db), size=0.43, color="white",
              duration=200, responseWindow=1500, checkFixationOK=NULL)
    class(s) <- "opiStaticStimulus"
    return(s)
  }, list(x=x,y=y))
  return(ff)
}

# List of (x, y, true threshold) triples
locations <- list(c(9,9,30), c(-9,-9,32), c(9,-9,31), c(-9,9,33))

# Setup starting states for each location
states <- lapply(locations, function(loc) {
  ZEST.start(
    domain=-5:45,
    minStimulus=0,
    maxStimulus=40,
    makeStim=makeStimHelper(db,n,loc[1],loc[2]),
    stopType="S", stopValue= 1.5, tt=loc[3], fpr=0.03, fnr=0.01)})

# Loop through until all states are "stop"
while(!all(st <- unlist(lapply(states, ZEST.stop)))) {
  i <- which(!st)                         # choose a random,
  i <- i[runif(1, min=1, max=length(i))]  # unstopped state
  r <- ZEST.step(states[[i]])             # step it
  states[[i]] <- r$state                  # update the states
}

finals <- lapply(states, ZEST.final)    # get final estimates of threshold
for(i in 1:length(locations)) {
  #cat(sprintf("Location (%+2d,%+2d) ",locations[[i]][1], locations[[i]][2]))
  #cat(sprintf("has threshold %4.2f\n", finals[[i]]))
}

if (!is.null(opiClose()$err))
  warning("opiClose() failed")

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