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Statistical analyses 2. Baseline and LBJ vs. VGS, with thresholds set to po 0. Effect of control condition on language and spatial hemi- FWE. The statistical threshold is set to p o 0.
LBJ vs. Baseline The second TPJ Baseline or ercular part VGS on which the further analyses will be performed. We R inferior frontal gyrus tri- 46 26 0 angular part R superior frontal gyrus 24 14 50 Relationships between spatial attention, language production Hemispheric LIs.
Asymmetry maps for language and spatial tasks for participants. The overlap of both contrasts is shown in green. B Asymmetry maps for spatial attention: LBJ vs. Baseline in red on axial slices and LBJ vs. VGS in blue , and the overlap of the two maps is in purple.
Here again, post- there was an effect of sex on the degree of asymmetry in spatial hoc analyses Holm-Bonferroni corrected p-values were per- attention. Post-hoc analyses Holm-Bonferroni corrected p-values were performed on the interaction to evaluate 2. LIs As strong left-handers are known to gather together the most 2. Regional LIs.
We investigated whether there was a re- atypical language dominant subjects, we investigated whether the lationship between spatial attention and language production relationship between language and spatial functions could be due within ROIs.
In the duction Mazoyer et al. These strong aty- parietal lobe, rightward asymmetries were restricted to the pos- pical individuals were removed of the analysis and the above- terior parietal cortex, in the precuneus and along the parieto-oc- mentioned ANCOVA model was performed again at the hemi- cipital sulcus.
Leftward asymmetry was observed in the supple- spheric and regional levels. These regions were not part of the motor ROI used to 3. Results parse out irrelevant activity arising from hand-related responses during LBJ task. Baseline contrast, except within ventral areas 3. Language including the occipito-temporal region, the posterior part of the On average, participants took 5. The average number of words per generated sentence was HLI values Table 1.
Effect of control condition on language and spatial hemispheric p o0. Post-hoc t-tests indicated that for language, 3. Asymmetrical brain patterns of language and spatial tasks contrasting a sentence production to a high-level control condition PRODLIST maximized the degree of leftward asymmetry as com- 3. Language production pared to baseline. Baseline showed large leftward asymmetries in the frontal vs.
Rightward asymmetry was LBJ vs. Relationships between spatial attention, language production gular and supramarginal gyri.
Note that restricted rightward LIs, MPS and spatial bias asymmetries were located in the caudate nucleus, the anterior 3. Spatial attention and the distribution of the residuals followed the Gaussian law As shown in Fig. As illustrated in Fig. The larger the lateral middle occipital gyrus MOG.
Rightward asymmetry was HLI for spatial attention was lateralized to one hemisphere i. As before, this interaction revealed that only the sLH group Fig. Scatterplot of the relationship between hemispheric lateralization indices during line bisection judgment LBJ-HLI and behavioral spatial response bias. Here again, only the sLH group showed a of spatial attention during line bisection. Finally, no effect of spatial response bias F language processing Mazoyer et al. Effect of strong atypical language right dominant subjects on gions in landmark tasks Badzakova-Trajkov et al.
These 3. Using Prod-HLIo as a cut-off point, 10 rightward asymmetries interested regions belonging to the dorsal individuals 9 sLH and 1 MH were found to be strongly right-la- frontoparietal network controlling for spatial attention, and the teralized for language production. Over these 10 subjects, the ventral attentional system involved in stimulus-driven reorienting mean LBJ-HLI was positive 9. Fink et al. In particular, the study of Rorden et al. Although cortex and MOG, and within the inferior frontal cortex.
Within the ventral network, important asymmetries were 3. Bush et al. In average, the subjects more frequently erroneously judged b.
This response bias can be related to the behavioral pseu- 4. Pseudoneglect has been between language and spatial attention lateralization see Fig. A negative correlation has been previously observed Bowers and Heilman, Here, we show that the degree of between inferior frontal region for language and parietal region for cerebral lateralization during LBJ is correlated with the degree of landmark task in a sample of left-handers including left- and pseudoneglect. Previous studies have found the association be- right-dominant language subjects Cai et al.
The study of tween cerebral lateralization and spatial bias. For example, Badzakova-Trajkov et al. Interestingly, a close inspection of the scatterplot of the was associated with increased right hemispheric engagement of Fig. Finally, Thiebaut de Schotten et al. To assess this effect, we reanalyzed their dataset gi- demonstrated, with diffusion tensor imaging DTI , a correlation ven in supporting information.
Applying our MPS categorization to between the rightward asymmetry of the volume of the second their sample of participants, 35 individuals were then cate- branch of the superior longitudinal fasciculus SLFII connecting gorized as sLH, 64 as MH and 56 as sRH.
We regressed the right- parietal and frontal regions and the pseudoneglect during the line parietal lobe LI by the left-frontal lobe LI, in function of MPS, and bisection Thiebaut de Schotten et al. As shown by Cai et al. According to 4. Complementary but not associated in right- and mixed-handers the causal hypothesis, two strong predictions can be put forward. First, an individual with atypical right language dominance should The present study including left-handers and right- simultaneously manifest left spatial dominance.
In other words, handers provided compelling evidence that the association be- the sole atypical pattern of HS consists in a mirror-reversed pat- tween language and spatial lateralization is only found in a group tern. It was indeed the case in Cai’s study , since all atypi- of left-handers characterized by a strong manual preference. Ex- cally right-lateralized language left-handers subjects in frontal ROI cept for this group of sLH, language and spatial asymmetries were were atypically left-lateralized in parietal ROI during landmark not associated in the other subjects, including right-handers and task, while all except one typically left-lateralized for language subjects with a weak manual preference subjects out of were typically right-lateralized for spatial function.
Second, the subjects, see Fig. First of all, these results help to re- correlation between both lateralized functions should be due to concile discrepant results found in the literature concerning the mirror-reversed subjects. Interestingly, the observation of RH co-lateralization of et al. The absence of correlation between language and language and spatial functions in healthy participants raises the spatial lateralization is consistent with previous fTCD studies question of the hemispheric crowding hypothesis Teuber, , showing no association, including only right-handers Lust et al.
Thus, associated lateralization of language and spatial of the complementary cerebral organization Bryden, The functioning in the right hemisphere affects non-verbal abilities. In potential sources of the left asymmetry for language processing healthy subjects, previous studies showed discrepant results.
While it is accepted that the teralized pattern left for language and right for spatial performed left-hemisphere bias for language processing is a multifactorial better than people showing bilateral representation for one or trait determined by several genetic and non-genetic factors, it is either function or both functions lateralized to the same hemi- still unclear which genes and environmental factors determine sphere only when carrying out a dual-task.
Scatterplots of the relationship between frontal lateralization indices during line bisection judgment and sentence production plotted for the whole sample and each manual preference strength group. The Prod-Frontal LI o cut-off point symbolized by a dashed line is given to indicate atypical rightward language lateralized subjects.
However, the correlation that Further investigations are now needed to compare individual we observed in sLH does not imply causality. In addition, spatial lateralization does not give any information about the ex- our results suggest that, the proportion of atypical HS patterns istence of a causal relationship between language and spatial varied depending on the ROI in which laterality index were cor- functions.
The corpus callosum CC is the major support for related. One characteristic By contrast, when the correlation was performed within the of CC connectivity at the macroscopic level is its spatial organiza- frontal ROI, we found subjects exhibiting a RH co-lateralization tion, as it connects cortical regions in mirroring homotopic areas Fig.
The transition of the division between hemispheres of complementary functions. Here, we to the hemispheric patterns of cerebral organization. By contrast, in the majority of the popula- are removed. Interestingly, the fact that this interaction was still tion, this mechanism may have been active across development to present between LBJ-Occipital and SENT-Frontal but not within the set up a stable complementary pattern of functions and does not frontal lobe, suggest that the contribution of each region to the need to be at play anymore.
To further explore this hypothesis, the pattern of HS needs to be further explored. The causal perspective suggests causal mechanisms manual preference strength. Scatterplots of the relationship between occipital lateralization indices during line bisection judgment and frontal LIs during sentence production plotted for the whole sample and each manual preference strength group.
Conclusion Psychol. Bryden, M. Patterns of cerebral organization. Brain Lang. Trends Cognit. What can atypical language hemispheric specia- lization tell us about cognitive functions? Complementary hemispheric spe- ture investigations on inter-hemispheric organization using a cialization for language production and visuospatial attention.
USA 4 , — Probabilistic explore the mechanisms that control cerebral lateralization. Fur- topography of human corpus callosum using cytoarchitectural parcellation and thermore, the variability of the patterns of HS raises the question high angular resolution diffusion imaging tractography. Brain Mapp. Brain activity during landmark and line cognitive performance. Cook, N. Homotopic callosal inhibition. Brain and Lang. References Corballis, M. The evolution and genetics of cerebral asymmetry.
B, Biol. Badzakova-Trajkov, G. Magical ideation, crea- Corbetta, M. Control of goal-directed and stimulus-driven tivity, handedness, and cerebral asymmetries: a combined behavioural and attention in the brain. Neuropsychologia 49, — Dorst, J. Func- Badzakova-Trajkov, G. Cerebral tional transcranial doppler sonography and a spatial orientation paradigm asymmetries: complementary and independent processes.
Plos One 5 3 , identify the non-dominant hemisphere. Brain Cogn. Benwell, C. A rightward shift in the vi- Duecker, F. Hemispheric differences in the voluntary suospatial attention vector with healthy aging. Aging Neurosci. Pseudoneglect: effects of hemispace on a tactile Neuropsychologia 18 4—5 , — Dym, R. Is functional MR imaging as- Brooks, J. Representational pseudoneglect: a re- sessment of hemispheric language dominance as good as the wada test?
Meta view. Fan, J. Choosing sides: the left and right of the normal brain. Petit, L. Strong rightward lateralization of the dorsal attentional network in left- Freund, H. Line bisection judgments implicate right parietal cortex and handers with right sighting-eye: an evolutionary advantage. Neurology 54 6 , — Fink, G. The neural basis of vertical and Petit, L. Functional asymmetries revealed in visually guided saccades: NeuroImage 14 1 , S59—S Association between language and graphy.
Blood Flow. NeuroImage 59 2 , Phasic alerting of neglect Nature , healthy humans. Neurology 57 6 , — Gazzaniga, M. Cerebral specialization and interhemispheric communica- Rorden, C.
Disturbed line bisection is tion: does the corpus callosum enable the human condition? Brain: J. Brain Res. Revisiting Rosch, R. Lateralised visual attention is un- human hemispheric specialization with neuroimaging. In addition, the modeling results provided evidence of a zero-information, absence-of-memory state that required guessing. The data were not sufficiently strong to sharply distinguish whether the losses in memory strength across the retention interval were continuous in nature or all-or-none.
The authors argue that the construct of memory strength as distinct from memory variability is an important component of the nature of forgetting from visual working memory. In this research we examined the issue of how visual working memories VWMs are lost over time.
The predominant view in the field is that perceptual memories become progressively less precise with increases in the retention interval, with distinct visual objects becoming gradually less discriminable from one another e. Classic work has examined alternative psychophysical functions on their ability to describe the relation between perceptual discriminability and the retention interval for a review and critical analysis, see, e.
Models based on diffusion processes have been developed to provide mechanistic explanations for these gradual losses in precision and discriminability e. Modern work in visual working memory has also examined the ability of precision-based models to explain declines in perceptual discriminability that arise with increases in the retention interval e. In this paradigm, observers view a set of study objects, such as colors in different locations that vary in their hue.
Following a variable retention interval, a single location is probed, and the observer is required to reproduce the color that existed at that location by clicking on the appropriate portion of a color-wheel response device. According to precision-loss theories, the perceptual memory of the studied color follows a bell-shaped probability distribution that becomes more variable with the passage of time. Such models have yielded excellent quantitative accounts of performance in the color-reproduction task.
The central thesis that we advance in the present work is that beyond changes in visual-memory precision or variability, there are decreases in memory strength as the retention interval increases. We formally distinguish between precision and strength in the context of our subsequent model-fitting analyses.
In brief, and as we expand upon below, whereas precision influences the extent to which distinct objects are similar to one another, strength is a construct pertaining to the memory representation of a single object. We pursue this thesis involving the joint roles of precision and strength in VWM forgetting by examining performance in a change-detection paradigm rather than the continuous-recall task e.
In the present change-detection paradigm, a single location from the visual display was probed with a color, and the observer was required to judge whether the color at that location changed or stayed the same. As we explain below, the change-detection paradigm allowed us to test for key aspects of the nature of VWM forgetting, about which the continuous-recall paradigm does not provide information.
We had three main motivations for testing the change-detection version of the task. The primary motivation was that we sought to gain evidence of more detailed forms of memory loss than is currently hypothesized in extant precision-based accounts of VWM. As noted earlier, the dominant approach to modeling precision loss in VWM is in terms of increased variance of an underlying perceptual memory distribution. Thus, in a color-recall task, the locations to which the observer points on the color wheel will become increasingly variable.
In our view, however, the hypothesis that the value of the remembered color simply becomes more variable with the passage of time is only part of what may constitute visual memory loss. A conceptually distinct idea is that the strength of the memory trace of the to-be-remembered object may also decrease with the passage of time.
Ultimately, we will flesh out these constructs in terms of distinct formal parameters of mathematical models of VWM change detection. We start, however, by trying to provide intuitions of the psychological meaning of the terms. Suppose that an observer studies the color green.
Following a retention interval, the memory for the color may wander from the true value, such that the remembered value is now closer to aqua. Although the remembered value of the object has undergone change, something more seems to be involved in fully characterizing the nature of the memory loss. Subjectively, besides changing value, the original memory seems also to have faded away. Stated another way, the retained memory seems to have less intensity than immediately after the original study experience.
The memory-strength construct that we incorporate in our modeling is aimed at formalizing this intuition. Indeed, numerous memory models outside the domain of VWM have distinct formal constructs related to similarity discriminability between pairs of objects and strength a factor pertaining to individual objects.
For example, in spreading-activation models of memory e. Items that are more closely related are connected by stronger links. In addition, however, the individual-item nodes may have different baseline strengths determined by factors such as the frequency or recency with which those individual items have been experienced. The extent to which an individual-item node is activated is determined jointly by its baseline strength in memory and the spreading activation it receives from its connecting links.
Likewise, formal exemplar models of perceptual identification and categorization and short-term and long-term memory have long distinguished between the similarity between distinct exemplars and the memory-strength or stimulus bias associated with those individual exemplars e.
Upon presentation of a test probe, the extent to which any exemplar is activated is a joint function of its similarity to the test probe and its underlying memory strength.
For example, in recent work, Nosofsky et al. In these tasks, the observer is presented with a short list of study items, followed by a test probe, and the observer judges whether the test probe occurred in the study list. Nosofsky et al. The results were well modeled by assuming that, independent of the test probe that was presented, the strength of the individual study items on the list decreased as their lag of presentation increased.
By analogy, in a VWM change-detection task, it seems reasonable to hypothesize that the probability that the observer judges a test probe to be the same as a remembered object may be influenced by two factors: a the similarity between the test probe value and the remembered value, which will be influenced by the amount of memory variability that has taken place, and b the strength of the remembered value.
In a continuous-recall color-reproduction task, one is attempting to probe only the estimated value of the remembered object: the strength of that remembered value is not being assessed. As will be seen, in the present study, by testing instead how change-detection judgments vary with the retention interval, we sought to test for a joint role of variability and strength in VWM.
In cases of sudden death, the observer is forced to guess regarding the identity of a presented study item. The sudden-death hypothesis can be viewed as providing an extreme form of the loss-of-memory-strength hypothesis: at some moment in time, there is a complete absence of memory for the study item i.
The evidence for sudden death, however, has been obtained using the continuous-recall paradigm. A potential limitation is that the properties of the continuous-recall paradigm itself may interfere with the information stored in VWM. For example, in the typical version of the paradigm, the response is produced by indicating a location along a continuous-valued response device.
Note that presentation of the device itself in which all continuous values are simultaneously present may be highly interfering of the original memory, thereby leading to underestimates of the amount of information that was immediately available when memory was probed e.
Because the change-detection paradigm involves presentation of only a single-valued test probe in a given location, it might not lead to the same pronounced interference, so could perhaps provide a more sensitive test of a role of gradual and fine-grained visual-memory decay. In an effort to develop diagnostic tests between gradual-decay and sudden-death explanations, we manipulated in our design the magnitude of change on change trials.
First, the magnitude of change was either small or big. As explained in our Modeling Analyses section, the big-change trials were included because they could help to provide evidence of sudden-death and guessing processes. Second, on small-change trials, we manipulated the distance of the test probe from the to-be-remembered color 1, 2, or 3 distance units.
Our hope was that this latter manipulation might provide evidence of a gradual-decay process perhaps operating alongside sudden-death mechanisms. The intuition is illustrated in Fig. Following classic work Shepard, , our modeling presumes that similarity is an exponential decay function of psychological distance, with higher precision memory corresponding to a steeper slope of the exponential function.
If there is decay in precision with time, then the increase in confusion probabilities as one shifts from the high-precision to the low-precision curve is predicted to be nonuniform across distances 1 through 3. By contrast, if only sudden death operates, then the increase in confusion probabilities is predicted to be more nearly uniform. The third motivation for our study was to conduct preliminary tests of a potential variable-resources account of the manner in which VWM declines with the retention interval e.
Variable-resources models have been applied successfully to account for the well-known finding that VWM performance declines with increases in memory set size. Such models adopt the idea that memory representations are doubly stochastic: The hypothesis is that not only does the variability of the memory representations tend to increase as set size increases but, in addition, there is a great deal of variability across individual items in terms of how variable these memory representations are.
In an extreme case, for example, because minimal memory resources may be devoted to some particular item, an extremely dispersed memory representation may develop for that item.
If an observer were relying on this type of extremely dispersed representation to recall a color in the continuous-recall task, it would be akin to a random guessing process.
Indeed, van den Berg, Awh, and Ma found that such variable-resources models provided better detailed quantitative fits to continuous-recall data than did models that assumed mixtures of perceptual memory and guessing. Variable-resources models might be adapted to account for how VWM declines with the retention interval by positing that there is some probability that a highly dispersed memory representation develops for items at some point in time. Note that whereas the sudden-death hypothesis posits the absence of memory and so the need for a true guessing process , the variable-resources model instead posits the presence of a highly variable representation.
In our view, these hypotheses are conceptually and psychologically distinct. Furthermore, as will be seen, the hypotheses can be distinguished with use of the present VWM change-detection task.
To anticipate the results our study, we believe that we were successful in achieving some but not all of these goals. Specifically, we believe that our results provide clear evidence that change-detection judgments across the retention interval involve something more than only increased perceptual-memory variability or confusability.
Something akin to changes in individual-item memory strength or related item biases also appear to play a major role. Furthermore, we find evidence for the role of a zero-information state involving the absence of memory in the paradigm: The alternative hypothesis of extreme variability from variable-resources models does not appear to be a substitute for the absence-of-memory construct.
Despite these successes, our data proved to be ultimately insufficient to allow us to distinguish between gradual-decay and sudden-death models of short-term visual memory decay. We conducted a VWM change-detection task involving color stimuli. On each trial, three colors from a degree color wheel were briefly displayed in simultaneous fashion at distinct spatial locations on the computer screen. On the key trials of interest, all three study colors were highly discriminable from one another adjacent colors from the wheel were 82—98 degrees apart.
Following a variable retention interval 1, 2, 4, or 10 s , a single test-probe color was presented at one of the spatial locations on the screen. The test probe was either the same as the original color; 16, 32, or 48 degrees away small-change trials ; or roughly 90 or degrees away big-change trials.
Across blocks, change trials occurred with probability. Subjects were informed of the objective change probability at the start of each block and were encouraged to adjust their response biases in accordance with the operating change probability. For example, on blocks in which change probability was high. Two issues that arise in trying to discriminate between sudden-death and gradual-decay explanations of VWM loss involve spatial-position uncertainty and verbal-labeling strategies.
When the observer is tested regarding the identity of an object from a given spatial position, there may be some probability that the observer makes the judgment with respect to an item from the wrong position e. One approach to addressing this issue is to conduct paradigms in which the observer is presented with only a single object from a single spatial position on each trial.
Unfortunately, this alternative procedure makes it much more likely that observers will generate verbal labels for the to-be-remembered objects. Under such conditions, the memory becomes a complex amalgam of true VWM along with verbal codes, and specialized techniques are needed to tease the components apart Donkin et al. Following Zhang and Luck , in the present study observers were presented briefly and simultaneously with three visual objects in order to minimize verbal-labeling strategies.
In addition, they were given explicit instructions to avoid using verbal-labeling strategies and to silently repeat the word the if they found themselves using such strategies. Although we will not be able to rule out the possibility that positional uncertainty contributes to our forgetting data, we believe that our use of three highly discriminable to-be-remembered objects together with Far-probe test trials helps reduce the role of such uncertainty.
In addition, on trials with small changes, the test probe will tend to be similar to only the probed study object, making even clearer to the observer which of the to-be-remembered objects is the relevant one. The subjects were five members of the Indiana University community who were paid for their participation. Each subject participated for between 9 and 11 sessions, with each session lasting approximately 1.
The subjects all had normal or corrected-to-normal vision, and all reported having normal color vision. None of the subjects was aware of the issues under investigation in the research. The background color of the screen was white. The luminance and color calibration measurements were obtained using in-house software and a Photo Research PR SpecraScan radiometer. The maximum and minimum displayable luminances were Viewing distance was approximately 57 cm, and the visual angle of the individual squares was approximately.
On each trial, three colored squares were presented on the computer screen in random locations within the central rectangular region, subject to the constraint that the centers of each square were at least 60 pixels away. On each such trial, the middle-color square was selected at random from the color wheel; the left-color square was 82 to 98 degrees less than the middle square chosen randomly within this interval ; and the right-color square was 82 to 98 degrees greater than the middle square.
Left and right values less than 0 or greater than degrees were translated to appropriate values on the degree color wheel. We used these widely spaced colors on the key trials in order to minimize certain potential effects of positional uncertainty on the change-same judgments see below. On filler trials, which were presented with probability.
On each trial, a single randomly chosen location from the study array was probed with a test square presented at that location. There was a variable retention interval 1, 2, 4, or 10 s between the presentation of the study colors and the test probe.
The retention interval on each trial was chosen at random. Each session of the experiment was divided into nine blocks of 56 trials each. We manipulated objective change probability across blocks:.
Each change-probability condition occurred once every three blocks in a random order. All trials began with a ms fixation asterisk, followed by the presentation of the three study squares ms. The screen then went blank for the chosen retention interval minus a ms cue time. A ms asterisk cue then appeared at the location of the to-be-presented test probe, which was presented immediately after the cue. Following each block, subjects were informed of their overall percentage of correct responses.
Subjects were informed at the start of each block of the objective change probability operating during that block. They were instructed to adjust their response biases in accord with the objective change probability. Subjects were also instructed to rest their left and right index fingers on the F and J keys throughout each block and to press the appropriate key as soon as they made their same versus change judgment.
Such trials were likely cases involving motor-response errors or failures to attend to the task. Each of the individual subjects showed similar patterns of results. Therefore, although we conduct modeling analyses at the level of individual subjects, we present the data averaged across the subjects to illustrate the main trends. The data are shown at their most fine-grained level in Fig. The different symbol types show the observed data, whereas the different line types are the predictions from a full version of the formal model to be presented in the Modeling Analyses section.
To allow for easier observation of the main trends, Fig. Mean P Respond Change judgments plotted as a joint function of change probability cp , stimulus type Same, D1, D2, D3 and Far , and the retention interval 1, 2, 4 or 10 seconds.
Different symbol types represent the observed data and different lines types are the predictions from the full version of a formal model used to analyze the results. Symbols: observed data, line types: model predictions.
As can be seen in Fig. The results of greatest interest concern interactive effects of the retention interval and probe distance see Figs. Not surprisingly, for same stimuli, respond-change probabilities i. The increased false-alarm rate is predicted by essentially all models that assume that forms of forgetting increase with the retention interval.
Interestingly, however, respond-change probabilities for stimuli at probe-distance levels D1 and D2 i.
In other words, at these probe distances, accuracy improved with increases in the retention interval. Finally, at the largest probe distances D3 and Far , change probabilities either stayed the same or decreased across the retention interval. These patterns of results will prove challenging for VWM models based solely on the assumption that only perceptual confusability increases with the retention interval.
Intuitively, this result provides evidence of guessing behavior i. We provide documentation of this point in the Modeling Analyses section. In Fig. These same patterns were observed at all three levels of objective change probability. The most general models that we use for fitting the data and interpreting the results assume that the change judgments arise from a mixture of two processes: one based on perceptual memory and one based on guessing.
If the to-be-remembered object has been encoded and has not undergone sudden death, then the observer is presumed to use her perceptual memory to make the change-same judgment. Otherwise, the subject must rely on guessing. The probability that the studied object resides in perceptual memory pmem at time of test is assumed to depend solely on the retention time t.
Given that it resides in perceptual memory, the probability that use of that memory leads the observer to make a change judgment is denoted memc and depends jointly on probe-distance d , retention-time t , and objective-change-probability cp. We used two approaches to modeling the probability that use of perceptual memory leads to a change judgment memc.
In both approaches, following Shepard , we assumed that the similarity s between the probe and the to-be-remembered object was an exponential decay function of their psychological distance d ,. Distances d between test items and study items were computed with respect to these variable memory distributions and transformed to similarities s via Eq. For both approaches, the probability that use of perceptual memory led to a change judgment memc in Eq.
Presumably, if memory strength varies, then it gets weaker as retention time t increases. Forms of Eq. As described in our introduction, this memory-trace activation is a joint function of the strength of the trace M t and its similarity to the test probe s. If the activation is strong, then there is a good deal of evidence that the probe is old — thus, a reduced probability that the observer would make a change judgment. Note that as the distance d from the probe to the item increases, similarity s decreases Eq.
Thus, the model naturally predicts increasing change judgments with increases in the distance of the test probe from the to-be-remembered item. Next, consider the predicted effect of increased retention time.
Thus, there is increased similarity of distinct probes to the to-be-remembered item. Therefore, without any additional mechanisms operating, the perceptual-memory-based model is forced to predict that as retention time increases, there should be a reduction in change judgments for all probes that are distinct from the to-be-remembered item. Because change judgments instead often increase with the retention interval see Fig. Because activation of the item trace is a joint function of memory strength and similarity, item activation may therefore decrease with retention time, leading to the increased change judgments seen in the data.
As will be seen, instead of assuming continuous decreases in memory strength with time, another approach to predicting the increasing change judgments is to assume all-or-none changes in memory strength i. Recall that according to the second approach to modeling precision loss, the sampled distance d has increasing variability as the retention interval increases.
Whether this increasing variability would lead to increasing or decreasing values of similarity s in Eq. We will see, however, that without making allowance for some second factor beyond increases in memory variability, the pure variability-based version of the precision-loss model runs into the same problems as does the sensitivity-based version. Thus far in our discussion the focus has been on the gradual precision-loss component of the model.
Alternatively, memory loss may arise due to sudden death, modeled in Eq. In the case of sudden death, the observer is forced to guess whether or not a change has occurred. In the most general version of the model that we tested, the guess-change probability was given by the product of two guess-change factors, the first related to objective change probability and the second to the retention interval:.
Presumably, for example, as objective change-probability cp increases, the magnitude of the first guess-change factor will increase.
As currently described, the formal model has a surplus of available free parameters for fitting the data. The full version of the variability-based model has 21 free parameters: the 4 sensitivity parameters are replaced by a single sensitivity parameter and 4 perceptual-memory variability parameters.
As explained below, potentially more parsimonious versions of the models arise by constraining some of the free parameters a priori. Tests of these constrained models can be used to provide evidence of whether changes in memory strength operate along with changes in memory variability in the change-detection task; and whether forgetting arises due to gradual loss of visual-memory precision or sudden death.
Specifically, we conducted computer searches for the free parameters that maximized the likelihood function. The latter term in each criterion is a penalty term for use of free parameters. The fits of all models to be described in this section are listed in Table 1.
We started by fitting the full version of the sensitivity-based model to the data to confirm that it provided a reasonable organizing framework. The predictions from the full model are illustrated along with the observed data in Figs.
As can be seen, the full model achieves precise quantitative fits of all averaged results. To evaluate the importance of different components of the model, we fitted restricted i. We start by describing cases in which the free parameters were critical to achieving good fits and then move to cases in which more parsimonious fits can be achieved. To provide some understanding of the reason for the resulting fit values, we plot predictions from the special-case models of respond-change probabilities as a function of probe distance and the retention interval see Fig.
Predictions from perfect-memory-probability model. Predictions from constant memory-strength and memory-probability model. Predictions from constant memory-precision model. Predictions from constant memory-probability model. To begin, we fitted a version of the model that assumed no sudden death at any retention times i.
Because there was no sudden death, there was no guessing behavior, so the g 1 and g 2 parameters are not used either. The reason for these poor fits is shown in Fig. Without allowing for an absence-of-memory state, the perceptual-memory component of the model needs to estimate extremely low values of sensitivity to try to account for those errors and still falls short in doing so.
These low sensitivity estimates then force the model to greatly under-predict the probability of correct change judgments for probes at distance levels D2 and D3. Thus, apparently, there was at least some proportion of trials in which subjects relied on pure guessing behavior in the absence of any perceptual memory for the study stimuli. Footnote 2. A second special-case model of interest that can be easily rejected is one that assumes no changes in any form of memory strength across the retention interval.
In addition, the memory-strength parameters from the continuous visual-memory component of the model the M t values in Eq. As reported in Table 1 , the AIC fits of this constant memory-strength model are dramatically worse than those of the full model for all five subjects, and the BIC fits are much worse for four of the five subjects.
The reason for the extremely poor fits is shown in Fig. Recall that the respond-change probabilities increased for same probes and for D1 and D2 probes as the retention interval increased. Without allowing for any changes in memory strength, the reduced-sensitivity model predicts decreases in respond-change probabilities, not increases. The present version of the model tries to compensate for this difficulty by assuming increasing guess-change probabilities across the retention interval the g 2 parameter in Eq.
However, this assumption then forces the model to incorrectly predict increasing respond-change probabilities for the D3 and Far probes, so the model yields very poor fits. To summarize, using the sensitivity-based approach to modeling precision loss, our interim conclusions are that a there is a role of a zero-stimulus-information state i.
However, we have yet to contrast sudden-death versus gradual-decay accounts of the results. For example, the losses in memory strength may be all-or-none reflecting sudden death or gradual the continuous M t parameters.
To address the sudden-death versus gradual-precision-loss hypotheses, we fitted additional special-case models to the data. Only the all-or-none memory parameters pmem and retention-based guessing parameters g 2 were allowed to vary across the retention interval. As shown in Table 1 , the AIC fits of this constant perceptual-confusability model were approximately the same as those of the full model and the BIC fits of the model were considerably better than those of the full model.
Thus, the data are consistent with the hypothesis that there were no continuous changes in precision or memory strength across the retention interval and that the results can be interpreted in terms of sudden death and guessing.
However, we also fitted a model to the data that assumed a constant probability of using memory a fixed value of pmem in Eq. Figure 6c and d reveal that both special-case models are capable of providing good accounts of how the change-detection judgments varied with stimulus distance and the retention interval.
It appears that the present data are not sufficiently strong to sharply discriminate between the sudden-death and gradual precision-loss views. The best-fitting parameters from these two parsimonious models, averaged across subjects, are reported in Table 2. The best-fitting parameter estimates are easily interpretable. Second, the criterion parameters k as well as the guessing factor g 1 increase systematically as objective change-probability increases.
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