|
nif:isString
|
-
Ten observers (6 male, 4 female) participated in this study. Their average age was 22.1 (s.d. = 1.4) years. Eight had normal vision and two had corrected-to-normal vision. All gave informed written consent. The project was given ethics approval (number AOD 02–09) by the Chief of Air Operations Division, Defence Science and Technology Organisation, in accordance with the National Statement on Ethical Conduct in Human Research [11].
Observers performed a change detection task for symbol shape while viewing displays modelled on military tactical displays in each of which eight symbols from the Hostile, Ambiguous, Friendly, Unknown (HAFU) symbol set [12] were presented (Fig 1). Observers were naive with respect to the semantic content of these symbols. Each symbol subtended approximately 0.6° in height and width and had a white line of length 1.3° emanating from its centre in a random direction. The location of each symbol was selected at random with the constraint that symbols did not overlap. Both symbol shape and symbol colour were selected at random with replacement from a set of three (open triangle, open rectangle, open semi-circle and blue, red, yellow, respectively). On each trial, an initial display was presented for 3 seconds and followed by a uniform grey mask of 0.25-second duration. A second display was then presented until the observer responded with his/her detection, confidence and identification decisions (see below). The second display was identical to the first except that on a proportion of trials (either .25 or .75) the shape of one randomly selected symbol had been changed to another in the set. Displays were presented on a 24" LCD monitor (Hewlett Packard 2465) at a viewing distance of approximately 60 cm.
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0149217.g001 Time course of a trial.There were eight randomly placed symbols. Each symbol was of one of three shapes and one of three colours, and had a random line orientation. On a proportion (.25 or .75) of trials, the shape of one symbol changed between the first and second displays. Observers made a yes/no change detection response and then rated their confidence in that response using five confidence bins ranging from guess (.5 correct) to certain (1.0 correct). Following the confidence rating, observers indicated with a mouse the symbol that they believed was most likely to have changed.
Data were collected in 12 blocks of 40 trials. The two conditions of change probability (.25 and .75) were presented in separate blocks. The order of presentation of these conditions was counterbalanced within and across observers. Observers were naive with respect to the probabilities of change. The observers' task was to indicate with a mouse whether or not one of the symbols had changed shape between presentations of the first and second displays. Observers then indicated their levels of confidence in their change detection decisions on a scale that was divided into 5 segments ranging from guess to certain. These confidence ratings were used to generate 9-point receiver operating characteristics (ROCs, following [13]). Observers were then asked to indicate with the mouse the item they believed was most likely to have changed. This change identification decision was made for all trials, including those where observers indicated they thought a change had not occurred. No feedback was given in regard to the accuracy of detection or identification responses.
This model is based on HTT and incorporates a limited number of noiseless memory representations. According to this model, when the number of items (N) exceeds the capacity of memory (k), only a proportion (k/N) of items is represented in memory. A change is correctly detected (i.e., a hit occurs) if, and only if, either of the following two mutually exclusive events occurs: (i) the changed item is held in memory or (ii) the changed item is not held in memory but the observer guesses that there was a change. An observer guesses that there was a change when a changed item is not held in memory at his/her false-alarm rate. The hit rate (H) is therefore given by H=kN+(1−kN)F where F is the false-alarm rate. Where a hit occurs, the changed item is correctly identified when it is held in memory. When it is not held in memory, its identity is guessed at from the set of items not held in memory. The correct identification rate for hits (HID) is therefore given by HID=1H[kN+(1−kN)FN−k] Where a change is missed, the identity of the changed item is guessed at from the set of items not held in memory. The correct identification rate for misses (MID) is therefore given by MID=1N−k Memory capacity is a free parameter. The HTT model generates linear ROCs which pass through the point 1,1 and have a y-intercept of k/N.
Noiseless slots with lapses of attention (HTTa): This model is a variant of HTT that allows for lapses of attention [5]. For this model, the observer is attentive on a proportion of trials (a) and inattentive on all others. Attended trials are processed according to standard HTT but on unattended trials no information is stored in memory, changes are detected at the false alarm rate for unattended trials, and identity is guessed at from the set of all items (Fig 2).
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0149217.g002 HTTa model.Decision tree for the HTTa model for trials on which a change occurred. The total false—alarm rate (F) reflects the false—alarm rates on attended trials (f1) and unattended trials (f2), which are both assumed to be proportional to the number of items about which no information is held in memory. It is given by F=af1+(1−a)f2=af1+(1−a)f1NN−k A hit occurs on an attended change trial if, and only if, either of the following two mutually exclusive events occurs: (i) the changed item is held in memory or (ii) the changed item is not held in memory but the observer guesses that there was a change (which he/she does at rate f1). A hit occurs on an unattended change trial if the observer guesses that there was a change (which he/she does at rate f2). The hit rate is therefore given by H=a[kN+(1−kN)f1]+(1−a)f2 Where a hit occurs, the changed item is correctly identified when it is held in memory (which is the case only on attended trials). When it is not held in memory, its identity is guessed at from the set of items not held in memory (which in the case of unattended trials is the set of all items). The correct identification rate for hits is therefore given by HID=1H[a(kN+(1−kN)f1N−k)+(1−a)f2N] Where a change is missed, the identity of the changed item is guessed from the set of items not held in memory. The correct identification rate for misses is therefore given by MID=11−H[a(1−kN)(1−f1)N−k+(1−a)(1−f2)N] Memory capacity and attention rate are free parameters. The HTTa model generates linear ROCs which are not constrained to pass through the point 1,1, and have a y-intercept of ak/N.
This model is a variant of HTT in which memory representations are limited in both number and precision [10]. For this model, memory representations may be less precise than required to support accurate task performance. In the context of this study, an insufficiently precise representation would be one that results in the incorrect retrieval of a symbol's shape (e.g., the retrieval of a triangle or a rectangle when a semi-circular symbol was displayed). Obviously, a very imprecise representation would be required for that to occur, but this model was included as it is an implementation of a contemporary theory of VSTM [10]. A change to an item represented in memory is correctly detected if, and only if, any of the following four mutually exclusive events occurs: (i) the before-change shape of the changed item is correctly retrieved from memory, (ii) the before-change shape of the changed item is incorrectly retrieved from memory and the retrieved shape differs from the after-change shape of that item, (iii) the before-change shape of the changed item is incorrectly retrieved from memory as the shape that matches the after-change shape of that item but the shape of at least one of the non-changed items is incorrectly retrieved from memory, or (iv) the observer guesses that there was a change when he/she does not perceive a change to any of the items represented in memory (i.e., when the retrieved shapes of all items represented in memory match the shapes of the corresponding items in the second display). The probability that a change to an item represented in memory is correctly detected is therefore r+(d−2)(1−r)d−1+1−rd−1(1−rk−1)+1−rd−1rk−1t where r is the probability that the shape of an item represented in memory is correctly retrieved, d is the size of the set of possible item shapes, and t is the rate at which the observer reports change when he/she does not perceive a change to any of the items represented in memory. A change to an item not represented in memory is correctly detected if, and only if, either of the following two mutually exclusive events occurs: (i) the shape of at least one of the items represented in memory is incorrectly retrieved or (ii) the observer guesses that there was a change when he/she does not perceive a change to any of the items represented in memory. The probability that a change to an item not represented in memory is correctly detected is therefore (1−rk)+rkt The hit rate is therefore given by H=kN(r+(d−2)(1−r)d−1+1−rd−1(1−rk−1)+1−rd−1rk−1t)+N−kN(1−rk+rkt) Where a change is perceived, the identity of the changed item is guessed at from the set of items perceived to have changed. Only if a changed item is included in this set, therefore, can its identity be correctly guessed. When it is included in this set, the probability of its identity being correctly guessed depends on the size of this set (s). The probability that a changed item is included in the set of items perceived to have changed and that its identity is correctly guessed is ∑s=1k(kNr(1−r)s−1rk−s(k−1)!(s−1)!(k−s)! 1s+kN (d−2)(1−r)d−1(1−r)s−1rk−s(k−1)!(s−1)!(k−s)! 1s) =d−2+r(d−1)N∑s=1k(1−r)s−1rk−sk!s!(k−s)! =d−2+r(d−1)N 1−rk1−r Where no change is perceived, the identity of the changed item is guessed at from the set of items not held in memory. Only if a changed item is not held in memory, therefore, can its identity be correctly guessed. The probability that a changed item is not held in memory, no change is perceived but the observer guesses that there was a change, and the identity of the changed item is correctly guessed is N−kNrkt1N−k The correct identification rate for hits is therefore given by HID=1H(d−2+r(d−1)N1−rk1−r+rktN) Where a change is missed, the identity of the changed item is guessed at from the set of items not held in memory. Only if the changed item is not held in memory, therefore, can its identity be correctly guessed. The probability that a changed item is not held in memory, the change is missed, and the identity of the changed item is correctly guessed is N−kNrk(1−t)1N−k The correct identification rate for misses is therefore given by MID=11−H rk(1−t)N Memory capacity and the probability that the shape that an item represented in memory is correctly retrieved are free parameters. Where the precision of memory representation is always sufficient for the shape of an item to be correctly retrieved (i.e., r = 1), the model reduces to the standard HTT model. The HTTn model produces linear ROCs which pass through the point 1,1 and have a y-intercept equal to k(dr−1)rk−1(d−1)N−rk+1 Eight independent, noisy change detectors (i.e., one for each symbol on the display) were modelled with unequal-variance SDT. For this model, a change is detected when the activation of at least one change detector exceeds criterion. A false alarm is made when this occurs on a no-change trial. The item associated with the detector with the highest activation is identified as having changed. According to this model, no change is reported on a no-change trial (i.e., a correct rejection occurs) where the activity in none of the change detectors reaches criterion. The correct-rejection rate (CR) is therefore given by CR =[∅(c)]N Where ϕ is the standard normal cumulative distribution function and c is the criterion measured in standard deviations of the noise distribution from its the mean. A miss occurs where the activity in the stimulated change detector fails to reach criterion and the remaining change detectors correctly reject. The miss rate (M) is therefore given by M=∅(c−d′s)[∅(c)]N−1 where d' is detector sensitivity measured in standard deviations of the noise distribution, and s is the ratio of the standard deviations of the signal-plus-noise and noise distributions. The HID and MID rates for this model were estimated by Monte Carlo simulation of ten thousand trials for each combination of parameters evaluated during model parameter estimation. Detector sensitivity and the ratio of the standard deviations of the signal-plus-noise and the noise distributions are free parameters. This multidimensional SDT model generates asymmetric, nonlinear ROCs which are constrained to pass through the points 0,0 and 1,1. When expressed in z coordinates, the ROCs are linear if the variances of the noise and signal-plus-noise distributions are equal and nonlinear if they are not.
Each model process was programmed in Matlab (Mathworks) and fitted to data for each observer and condition of change probability. For each model, the free parameters discussed above define its ROC. Nine response biases are additional free parameters that define the points on the model’s ROC that correspond to the observed ROC hit and false-alarm pairs. Maximum likelihood estimates of model parameters were first obtained by minimising the summed deviance from the set of observed hit and false-alarm pairs using a simplex gradient descent algorithm [14]. As ROCs describe change detection performance, models based on these parameter estimates are best fits to the change detection data. We then examined whether the models could parsimoniously predict both change detection and change identification performance. Model parameters were re-estimated by minimising summed deviance from the observed identification rate for hits (HID) and for misses (MID) in addition to the set of observed hit and false-alarm pairs. For all models it was necessary to estimate the average response criterion when fitting identification data. This was done by including the observed false-alarm rate as a fixed parameter. Models were compared by calculating the Bayes Information Criterion (BIC; [15]) to allow for differences in model flexibility arising from differences in the number of free parameters. The model with the lowest BIC is that with the highest posterior probability given the observed data. If all models are assigned equal prior probability, the posterior probability of each model relative to the most likely model is given by the Bayes factor (BF). Model comparison was conducted for each individual observer.
|
![[This page as RDF]](http://data.gesis.org/somesci/static/rdf-icon.gif){kind=icon}