Inter-trial effects in visual pop-out search: Factorial comparison of Bayesian updating models
In everyday life , we are continuously engaged in selecting visual information to achieve our action goals , as the amount of information we receive at any time exceeds the available processing capacity ., The mechanisms mediating attentional selection enable us to act efficiently by prioritizing task-relevant , and deprioritizing irrelevant , information ., Of importance for the question at issue in the present study , the settings that ensure effective action in particular task episodes are , by default , buffered by the attentional control system and carried over to subsequent task episodes , facilitating performance if the settings are still applicable and , respectively , impairing performance if they no longer apply owing to changes in the task situation ( in which case the settings need to be adapted accordingly ) ., In fact , in visual search tasks , such automatic carry-over effects may account for more of the variance in the response times ( RTs ) than deliberate , top-down task set 1 ., A prime piece of evidence in this context is visual search for so-called singleton targets , that is , targets defined by being unique relative to the background of non-target ( or distractor ) items , whether they differ from the background by one unique feature ( simple feature singletons ) or a unique conjunction of features ( conjunction singletons ) : singleton search is expedited ( or slowed ) when critical properties of the stimuli repeat ( or change ) across trials ., Such inter-trial effects have been found for repetitions/switches of , for example , the target-defining color 2 , 3 , size 4 , position 5 , and , more generally , the target-defining feature dimension 6 , 7 ., The latter has been referred to as the dimension repetition/switch effect , that is: responding to a target repeated from the same dimension ( e . g . , color ) is expedited even when the precise target feature is different across trials ( e . g . , changing from blue on one trial to red on the next ) , whereas a target switch from one dimension to another ( e . g . , from orientation to color ) causes a reaction time cost ( ‘dimension repetition effect’ , DRE ) 8–10 ., While inter-trial effects have been extensively studied , the precise nature of the processes that are being affected remains unclear ., Much of the recent work has been concerned with the issue of the processing stage, ( s ) at which inter-trial effects arise ( for a review , see 11 ) ., Müller and colleagues proposed that inter-trial effects , in particular the dimension repetition effect , reflect facilitation of search processes prior to focal-attentional selection ( at a pre-attentive stage of saliency computation ) 10 ., However , using a non-search paradigm with a single item presented at a fixed ( central ) screen location , Mortier et al . 12 obtained a similar pattern of inter-trial effects–leading them to conclude that the DRE arises at the post-selective stage of response selection ., Rangelov and colleagues 13 demonstrated that DRE effects can originate from distinct mechanisms in search tasks making different task demands ( singleton feature detection and feature discrimination ) : pre-attentive weighting of the dimension-specific feature contrast signals and post-selective stimulus processing–leading them to argue in favor of a multiple weighting systems hypothesis ., Based on the priming of pop-out search paradigm , a similar conclusion 11 has also been proposed , namely , inter-trial effects arise from both attentional selection and post-selective retrieval of memory traces from previous trials 4 , 14 , favoring a dual-stage account 15 ., It is important to note that those studies adopted very different paradigms and tasks to examine the origins of inter-trial effects , and their analyses are near-exclusively based on differences in mean RTs ., Although such analyses are perfectly valid , much information about trial-by-trial changes is lost ., Recent studies have shown that the RT distribution imposes important constraints on theories of visual search 16 , 17 ., RT distributions in many different task domains have been successfully modeled as resulting from a process of evidence accumulation 18 , 19 ., One influential evidence accumulation model is the drift-diffusion model ( DDM ) 20–22 ., In the DDM , observers sequentially accumulate multiple pieces of evidence , each in the form of a log likelihood ratio of two alternative decision outcomes ( e . g . , target present vs . absent ) , and make a response when the decision information reaches a threshold ( see Fig 1 ) ., The decision process is governed by three distinct components: a tendency to drift towards either boundary ( drift rate ) , the separation between the decision boundaries ( boundary separation ) , and a starting point ., These components can be estimated for any given experimental condition and observer by fitting the model to the RT distribution obtained for that condition and observer ., Estimating these components makes it possible to address a question that is related to , yet separate from the issue of the critical processing stage, ( s ) and that has received relatively less attention: do the faster RTs after stimulus repetition reflect more efficient stimulus processing , for example: expedited guidance of attention to more informative parts of the stimulus , or rather a bias towards giving a particular one of the two alternative responses or , respectively , a tendency to require less evidence before issuing either response ., The first possibility , more efficient processing , would predict an increase in the drift rate , that is , a higher speed of evidence accumulation ., A bias towards one response or a tendency to require less evidence would , on the other hand , predict a decreased distance between the starting point and the decision boundary associated with that response ., In the case of bias , this would involve a shift of the starting point towards that boundary , while a tendency to require less evidence would be reflected in a decrease of the boundary separation ., While response bias is more likely associated with changes at the post-selective ( rather than pre-attentive ) processing stage , the independence of the response selection and the attentional selection stage has been challenged 23 ., For simple motor latencies and simple-detection and pop-out search tasks 24 , there is another parsimonious yet powerful model , namely the LATER ( Linear Approach to Threshold with Ergodic Rate ) model 25 , 26 ., Unlike the drift-diffusion model , which assumes that evidence strength varies across the accumulative process , the LATER model assumes that evidence is accumulated at a constant rate during any individual perceptual decision , but that this rate varies randomly across trials following a normal distribution ( see Fig 1 ) ., Such a pattern has been observed , for instance , in the rate of build-up of neural activity in the motor cortex of monkeys performing a saccade-to-target task 27 ., Similar to the DDM , the LATER model has three important parameters: the ergodic rate, ( r ) , the boundary separation ( θ ) , and a starting point ( S0 ) ., However , the boundary separation and starting point are not independent , since the output of the model is completely determined by the rate and the separation between the starting point and the boundary; thus , in effect , the LATER model has only two parameters ., The evidence accumulation process can be interpreted in terms of Bayesian probability theory 26 , 28 ., On this interpretation , the linear approach to threshold with ergodic rate represents the build-up of the posterior probability that results from adding up the log likelihood ratio ( i . e . , evidence ) of a certain choice being the correct one and the initial bias that derives from the prior probability of two choices ., The prior probability should affect the starting point S0 of the evidence accumulation process: S0 should be the closer to the boundary the higher the prior probability of the outcome that boundary represents ., The drift rate , by contrast , should be influenced by any factor that facilitates or impedes efficient accumulation of task-relevant sensory evidence , such as spatial attentional selection ., The present study was designed to clarify the nature of the inter-trial effects for manipulations of target presence and the target-defining dimension as well as inter-trial dimension repetitions and switches ., If inter-trial effects reflect a decision bias , this should be reflected in changes of the decision boundary and/or the starting point ., By contrast , if inter-trial effects reflect changes in processing efficiency , which might result from allocating more attentional resources ( or weight ) to the processing of the repeated feature/dimension 6 , the accumulation rate r should be changed ., Note that neither the DDM nor the LATER model provides any indication of how the initial starting point might change across trials ., Given that the inter-trial effects are indicative of the underlying trial-by-trial dynamics , we aimed to further analyze trial-wise changes of the prior and the accumulation rate , and examine how a new prior is learned when the stimulus statistics change , as reflected in changes of the starting point to decision boundary separation during the learning process ., To address these inter-trial dynamics , we adopted the Dynamic Belief Model ( DBM ) 29 ., The DBM has been successfully used to explain why performance on many tasks is better when a stimulus matches local patterns in the stimulus history even in a randomized design where it is not actually possible to use stimulus history for ( better-than-chance ) prediction ., Inter-trial effects arise naturally in the DBM ., This is because the DBM assumes a prior belief about non-stationarity , that is: participants are updating their beliefs about the current stimulus statistics while assuming that these can change at any time ., The assumption of non-stationarity leads to something similar to exponential discounting of previous evidence , that is , the weight assigned to previous evidence decreases exponentially with the time ( or number of updating events ) since it was acquired ., Consequently , current beliefs about what is most likely to happen on an upcoming trial will always be significantly influenced by what occurred on the previous trial , resulting in inter-trial effects ., Thus , here we combine a belief-updating model closely based on the DBM , for modelling the learning of the prior , with the DDM and , respectively , the LATER model for predicting RTs ., A very similar model has previously been proposed to explain results in saccade-to-target experiments 30 ., We also consider the possibility that the evidence accumulation rate as well as the starting point may change from trial to trial ., To distinguish between different possible ways in which stimulus history could have an influence via updating of the starting point and/or the rate , we performed three visual search experiments , using both a detection and a discrimination task and manipulating the probability of target presence , as well as the target-defining dimension ., Based on the RT data , we then performed a factorial model comparison ( cf . 31 ) , where both the response history and the history of the target dimension can affect either the starting point or the rate ., The results show that the model that best explains both the effects of our probability manipulation and the inter-trial effects is the one in which the starting point is updated based on response history and the rate is updated based on the history of the target dimension ., The singleton search was quite easy , with participants making few errors overall: mean error rates were 1 . 5% , 2 . 5% , and 3 . 3% in Experiments 1 , 2 , and 3 respectively ( Fig 2 ) ., Despite the low average error rates , error rates differed significantly between blocks in both Experiments 1 and 2 F ( 1 . 34 , 14 . 78 ) =11 . 50 , p<0 . 01 , ηp2=0 . 51 , BF=8372 , and F ( 2 , 22 ) =12 . 20 , p<0 . 001 , ηp2=0 . 53 , BF=3729 , respectively: as indicated by post-hoc comparisons ( S1 Text ) , error rates were higher in the low-frequency blocks compared to the medium- and high-frequency blocks , without a significant difference between the latter ., In addition , in Experiment 1 , error rates were overall higher for target-present than for target-absent trials , that is , there were more misses than false alarms , F ( 1 , 11 ) =11 . 43 , p<0 . 01 , ηp2=0 . 51 , BF=75 ., In contrast , there was no difference in error rates between color and orientation targets in Experiment 2 , F ( 1 , 11 ) = 0 . 70 , p = 0 . 42 , BF = 0 . 33 ., In Experiment 3 , there was no manipulation of target ( or dimension ) frequency , but like in Experiment 1 , error rates were higher on target-present than on target-absent trials , t ( 11 ) = 4 . 25 , p < 0 . 01 , BF = 30 . 7; and similar to Experiment 2 , there was no significant difference in error rates between color and orientation targets , t ( 11 ) = 1 . 51 , p = 0 . 16 , BF = 0 . 71 ., Given the low error rates , we analyzed only RTs from trials with a correct response , though excluding outliers , defined as trials on which the inverse RT ( i . e . , 1/RT ) was more than three standard deviations from the mean for any individual participant ., Fig 3 presents the pattern of mean RTs for all three experiments ., In both Experiments 1 and 2 , the main effect of frequency was significant F ( 2 , 22 ) =10 . 25 , p<0 . 001 , ηp2=0 . 48 , BF=73 , and , respectively , F ( 1 . 27 , 13 . 96 ) =29 . 83 , p<0 . 01 , ηp2=0 . 73 , BF=8 . 7*108 ., Post-hoc comparisons ( see S2 Text ) confirmed RTs to be faster in high-frequency compared to low-frequency blocks , indicative of participants adapting to the stimulus statistics in a way such as to permit faster responses to the most frequent type of trial within a given block ., In addition , in Experiment 1 , RTs were faster for target-present than for target-absent trials F ( 1 , 11 ) =5 . 94 , p<0 . 05 , ηp2=0 . 35 , BF=51 , consistent with the visual search literature ., In contrast , there was no difference between color- and orientation-defined target trials in Experiment 2 , and no interaction between target condition and frequency in either Experiment 1 or 2 ( S2 Text ) –suggesting that the effect of frequency is independent of the target stimuli ., Comparing the error rates depicted in Fig 2 and the mean RTs in Fig 3 , error rates tended to be lower for those frequency conditions for which RTs were faster ., While this rules out simple speed-accuracy trade-offs , it indicates that participants were adapting to the statistics of the stimuli in a way that permitted faster and more accurate responding to the most frequent type of trial within a given block , at the cost of slower and less accurate responding on the less frequent trial type ., A possible explanation of these effects is a shift of the starting point of a drift-diffusion model towards the boundary associated with the response associated with the most frequent type of trial; as will be seen below ( in the modeling section ) , the shapes of the RT distributions were consistent with this interpretation ., Without a manipulation of frequency , Experiment 3 yielded a standard outcome: all three types of trial yielded similar mean RTs , F ( 2 , 22 ) = 2 . 15 , p = 0 . 14 , BF = 0 . 71 ., This is different from Experiment 1 , in which target-absent RTs were significantly slower than target-present RTs ., This difference was likely obtained because the target-defining dimension was kept constant within short mini-blocks in Experiment 1 , but varied randomly across trials in Experiment 3 , yielding a dimension switch cost and therefore slower average RTs on target-present trials ( see modeling section for further confirmation of this interpretation ) ., Given our focus on inter-trial dynamic changes in RTs , we compared trials on which the target condition was switched to trials on which it was repeated from the previous trial ., Fig 4 illustrates the inter-trial effects for all three experiments ., RTs were significantly faster on target-repeat than on target-switch trials , in all experiments: Experiment 1 F ( 1 , 11 ) =6 . 13 , p<0 . 05 , ηp2=0 . 36 , BF=0 . 81 , Experiment 2 F ( 1 , 11 ) =71 . 29 , p<0 . 001 , ηp2=0 . 87 , BF=2 . 6*107 , and Experiment 3 F ( 1 , 11 ) =32 . 68 , p<0 . 001 , ηp2=0 . 75 , BF=625 ., Note that for Experiment 1 , despite the significant target-repeat/switch effect , the ‘inclusion’ BF ( see Methods ) suggests that this factor is negligible compared to other factors; a further post-hoc comparison of repeat versus switch trials has a BF of 5 . 88 , compatible with the ANOVA test ., The target repetition effect in all three experiments is consistent with trial-wise updating of an internal model ( see the modeling section ) ., The target repetition/switch effect was larger for target-absent responses ( i . e . , comparing repetition of target absence to a switch from target presence to absence ) than for target-present responses in Experiment 3 ( interaction inter-trial condition x target condition , F ( 1 , 11 ) =14 . 80 , p<0 . 01 , ηp2=0 . 57 , BF=18 ) , while there was no such a difference in Experiment 1 , F ( 1 , 11 ) = 2 . 55 , p = 0 . 14 , BF = 0 . 43 , and also no interaction between target dimension and inter-trial condition in Experiment 2 , F ( 1 , 11 ) = 0 . 014 , p = 0 . 91 , BF = 0 . 76 ., These findings suggest that , while the target repetition/switch effect as such is stable across experiments , its magnitude may fluctuate depending on the experimental condition ., The interaction between target condition and inter-trial condition seen in Experiment 3 , but not in Experiment 1 , is likely attributable to the fact that color and orientation targets were randomly interleaved in Experiment 3 , so that target-present repetitions include trials on which the target dimension did either repeat or change–whereas the target dimension was invariably repeated on consecutive target-present trials in Experiment 1 ., The effects of repeating/switching the target dimension are considered further below ., Note that in all experiments , we mapped two alternative target conditions to two fixed alternative responses ., The repetition and switch effects described above may be partly due to response repetitions and switches ., To further examine dimension repetition/switch effects when both dimensions were mapped to the same response , we extracted those target-present trials from Experiment 3 on which a target was also present on the immediately preceding trial ., Fig 5 depicts the mean RTs for the dimension-repeat versus -switch trials ., RTs were faster when the target dimension repeated compared to when it switched , F ( 1 , 11 ) =25 . 06 , p<0 . 001 , ηp2=0 . 70 , BF=1905 , where this effect was of a similar magnitude for color- and orientation-defined targets interaction target dimension x dimension repetition , F ( 1 , 11 ) = 0 . 44 , p = 0 . 84 , BF = 0 . 33 ., There was also no overall RT difference between the two types of target main effect of target dimension , F ( 1 , 11 ) = 0 . 16 , p = 0 . 69 , BF = 0 . 34 , indicating that the color and orientation targets were equally salient ., This pattern of dimension repetition/switch effects is in line with the dimension-weighting account 8 ., Of note , there was little evidence of a dimension repetition benefit from two trials back , that is , from trial n-2 to trial n: the effect was very small ( 3 ms ) and not statistically significant t ( 23 ) = 0 . 81 , p = 0 . 43 , BF = 0 . 38 ., In addition to inter-trial effects from repetition versus switching of the target dimension , there may also be effects of repeating/switching the individual target-defining features ., To examine for such effects , we extracted those trials on which a target was present and the target dimension stayed the same as on the preceding trial , and examined them for ( intra-dimension ) target feature repetition/switch effects ., See Fig 6 for the resulting mean RTs ., In Experiments 1 and 3 , there was no significant main effect of feature repetition/switch Exp . 1: F ( 1 , 11 ) = 0 . 30 , p = 0 . 593 , BF = 0 . 30 , Exp . 3: F ( 1 , 11 ) = 3 . 77 , p = 0 . 078 , BF = 0 . 76 , nor was there an interaction with target dimension Exp . 1: F ( 1 , 11 ) = 2 . 122 , p = 0 . 17 , BF = 0 . 44 , Exp . 3: F ( 1 , 11 ) = 0 . 007 , p = 0 . 93 , BF = 0 . 38 ., In contrast , in Experiment 2 ( which required an explicit target dimension response ) , RTs were significantly faster when the target feature repeated compared to when it switched within the same dimension , F ( 1 , 11 ) =35 . 535 , p<0 . 001 , ηp2=0 . 764 , BF=13 , and this effect did not differ between the target-defining , color and orientation , dimensions , F ( 1 , 11 ) = 1 . 858 , p = 0 . 2 , BF = 0 . 57 ., Note though that , even in Experiment 2 , this feature repetition/switch effect was smaller than the effect of dimension repetition/switch ( 20 vs . 54 ms , t ( 11 ) = 5 . 20 , p<0 . 001 , BF = 122 ) ., In summary , the results revealed RTs to be expedited when target presence or absence or , respectively , the target-defining dimension ( on target-present trials ) was repeated on consecutive trials ., However , the origin of these inter-trial effects is unclear: The faster RTs for cross-trial repetitions could reflect either more efficient stimulus processing ( e . g . , as a result of greater ‘attentional ‘weight’ being assigned to a repeated target dimension ) or a response bias ( e . g . , an inclination to respond ‘target present’ based on less evidence on repeat trials ) , or both ., In the next section , we will address the origin ( s ) of the inter-trial effects by comparing a range of generative computational models and determining which parameters are likely involved in producing these effects ., Because feature-specific inter-trial effects , if reliable at all ( they were significant only in Exp . 2 , which required an explicit target dimension response ) , were smaller than the inter-trial effects related to either target presence/absence or the target-defining dimension ( e . g . , in Exp . 3 , a significant dimension-based inter-trial effect of 39 ms compares with a non-significant feature-based effect of 11 ms ) , we chose to ignore the feature-related effect in our modeling attempt ., With the full combination of the four factors , there were 144 ( 2 x 2 x 6 x 6 ) models altogether for comparison: non-decision time ( with/without ) , evidence accumulation models ( DDM vs . LATER ) , RDF-based updating ( 6 factor levels ) , and TDD-based updating ( 6 factor levels ) ., We fitted all models to individual-participant data across the three experiments , which , with 12 participants per experiment , yielded 5184 fitted models ( see S7 Text for RT distributions and model fits for the factor levels with no updating but with a non-decision time ) ., Several data sets could not be fitted with the full memory version of the starting point updating level ( i . e . , Level 2 ) of the dimension-based updating factor , due to the parameter updating to an extreme ., We therefore excluded this level from further comparison ., To obtain a better picture of the best model predictions , we plotted predicted versus observed RTs in Fig 11 ., Each point represents the average RT over all trials from one ratio condition , one trial condition , and one inter-trial condition in a single participant ., There are 144 points each for Experiments 1 and 2 ( 12 participants x 3 ratios x 2 trial conditions x 2 inter-trial conditions ) and 108 for Experiment 3 ( 12 participants x 3 trial conditions x 3 inter-trial conditions ) ., The predictions were made based on the best model for each experiment , in terms of the average AIC ( see Figs 8 , 9 and 10 ) ., The r2 value of the best linear fit is 0 . 85 for Experiment 1 , 0 . 86 for Experiment 2 , and 0 . 98 for Experiment 3 , and 0 . 89 for all the data combined ., Fig 12 presents examples of how the starting point ( S0 ) and rate were updated according to the best model ( in AIC terms ) for each experiment ., For all experiments , the best model used starting point updating based on the response-defining feature ( Fig 12A , 12C and 12E , left panels ) ., In Experiments 1 and 2 , the trial samples shown were taken from blocks with an unequal ratio; so , for the starting point , the updating results are biased towards the ( correct ) response on the most frequent type of trial ( Fig 12A and 12C ) ., In Experiment 3 , the ratio was equal; so , while the starting point exhibits a small bias on most trials ( Fig 12E ) , it is equally often biased towards either response ., Since , in a block with unequal ratio , the starting point becomes biased towards the most frequent response , the model predicts that the average starting point to boundary separation for each response will be smaller in blocks in which that response is more frequent ., This predicts that RTs to a stimulus requiring a particular response should become faster with increasing frequency of that stimulus in the block , which is what we observed in our behavioral data ., In addition , since , after each trial , the updating rule moves the starting point towards the boundary associated with the response on that trial , the separation between the starting point and the boundary will be smaller on trials on which the same response was required on the previous trial , compared to a response switch ., This predicts faster RTs when the same response is repeated , in line with the pattern in the behavioral data ., The forgetting mechanism used in the best models ensures that such inter-trial effects will occur even after a long history of previous updates ., In Experiment 1 , the best model did not use any updating of the drift rate , but a different rate was used for each dimension and for target-absent trials ( Fig 12B ) ., In Experiment 2 the best model updated the rate based on the ‘Rate with decay’ rule described above ., The rate is increased when the target-defining dimension is repeated , and decreased when the dimension switches , across trials , and these changes can build up over repetitions/switches , though with some memory decay ( Fig 12D ) ., Since the target dimension was ( also ) the response-defining feature in Experiment 2 , the rate updating would contribute to the ‘response-based’ inter-trial effects ., In Experiment 3 , the best model involved the ‘Weighted rate’ rule ., Note that the rate tends to be below the baseline level ( dashed lines ) after switching from the other dimension , but grows larger when the same dimension is repeated ( Fig 12F ) ., This predicts faster RTs after a dimension repetition compared to a switch , which is what we observed in the behavioral data ., In three experiments , we varied the frequency distribution over the response-defining feature ( RDF ) of the stimulus in a visual pop-out search task , that is , target presence versus target absence ( Experiments 1 and 3 ) or , respectively , the dimension , color versus orientation , along which the target differed from the distractors ( Experiment 2 ) ., In both cases , RTs were overall faster to stimuli of that particular response-defining feature that occurred with higher frequency within a given trial block ., There were also systematic inter-trial ‘history’ effects: RTs were faster both when the response-defining feature and when the target-defining dimension repeated across trials , compared to when either of these changed ., Our results thus replicate previous findings of dimension repetition/switch effects 6 , 9 ., In contrast to studies on ‘priming of pop-out’ ( PoP ) 3 , 32–34 , we did not find significant feature-based repetition/switch effects ( consistent with 6 ) , except for Experiment 2 in which the target dimension was also the response-defining feature ., The dimension repetition/switch effects that we observed were also not as ‘long-term’ compared to PoP studies , where significant feature ‘priming’ effects emerged from as far as eight trials back from the current trial ., There are ( at least ) two differences between the present study and the PoP paradigms , which likely contributed to these differential effect patterns ., First , we employed dense search displays ( with a total of 39 items , maximizing local target-to-non-target feature contrast ) , whereas PoP studies typically use much sparser displays ( e . g . , in the ‘prototypical’ design of Maljkovic & Nakayama 3 , 32–34 , 3 widely spaced items: one target and two distractors ) ., Second , the features of our distractors remained constant , whereas in PoP studies the search-critical features of the target and the distractors are typically swapped randomly across trials ., There is evidence indicating that , in the latter displays , the target is actually not the first item attended on a significant proportion of trials ( according to 35 , on some 20% up to 70% ) , introducing an element of serial scanning especially on feature swap trials on which there is a tendency for attention ( and the eye ) to be deployed to a distractor that happens to have the same ( color ) feature as the target on the previous trial ( for eye movement evidence , see , e . g . , 36 , 37 ) ., Given this happens frequently , feature checking would become necessary to ensure that it is the ( odd-one-out ) target item that is attended and responded to , rather than one of the distractors ., As a result , feature-specific effects would come to the fore , whereas these would play only a minor role when the target can be reliably found based on strong ( local ) feature contrast 38 ., For this reason , we opted to start our modeling work with designs that , at least in our hand , optimize pop-out ( see also 39 ) , focusing on simple target detection and ‘non-compound’ discrimination tasks in the first instance ., Another difference is that we used simple detection and ‘non-compound’ discrimination tasks in our experiments , while PoP experiments typically employ ‘compound’ tasks , in which the response-defining feature is independent of the target-defining feature ., We do not believe that the latter difference is critical , as reliable dimension repetition/change effects have also been observed with compound-search tasks ( e . g . , 40 ) , even though , in terms of the final RTs , these are weaker compared to simple response tasks because they are subject to complex interactions arising at a post-selective processing stage ( see below and 41 , 42 ) ., To better understand the basis of the effects we obtained , we analyzed the shape of the RT distributions , using the modified LATER model 26 and the DDM 21 , 22 ., Importantly , in addition to fitting these models to the RT distribution across trials , we systematically compared and contrasted different rules of how two key parameters of the LATER/DDM models–the starting point ( S0 ) or the rate ( r ) of the evidence accumulation process–might be dynamically adapted , or updated , based on trial history ., We assumed two aspects of the stimuli to be potentially relevant for updating the evidence accumulation parameters: the response-defining feature ( RDF ) and the target-defining dimension ( TDD; in Experiment 2 , RDF and TDD were identical ) ., Thus , in our full factorial model comparison , trial-by-trial updating was based on either the response-defining feature or the target dimension ( factor 1 ) , combined with updating of either the starting point or the rate of evidence accumulation ( factor 2 ) , with a number of different possible updating rules for each of these ( 6 factor levels each ) ., An additional factor ( factor 3 ) in our model comparison was the evidence accumulation model used to predict RT distributions: either the DDM or the LATER model ., Finally , to compare the DDM and LATER models on as equal terms as possible , we modified the original LATER model by adding a non-decision time component ., Thus , the fourth and final factor concerned w
Many previous studies on visual search have reported inter-trial effects , that is , observers respond faster when some target property , such as a defining feature or dimension , or the response associated with the target repeats versus changes across consecutive trial episodes ., However , what processes drive these inter-trial effects is still controversial ., Here , we investigated this question using a combination of Bayesian modeling of belief updating and evidence accumulation modeling in perceptual decision-making ., In three visual singleton ( ‘pop-out’ ) search experiments , we explored how the probability of the response-critical states of the search display ( e . g . , target presence/absence ) and the repetition/switch of the target-defining dimension ( color/ orientation ) affect reaction time distributions ., The results replicated the mean reaction time ( RT ) inter-trial and dimension repetition/switch effects that have been reported in previous studies ., Going beyond this , to uncover the underlying mechanisms , we used the Drift-Diffusion Model ( DDM ) and the Linear Approach to Threshold with Ergodic Rate ( LATER ) model to explain the RT distributions in terms of decision bias ( starting point ) and information processing speed ( evidence accumulation rate ) ., We further investigated how these different aspects of the decision-making process are affected by different properties of stimulus history , giving rise to dissociable inter-trial effects ., We approached this question by, ( i ) combining each perceptual decision making model ( DDM or LATER ) with different updating models , each specifying a plausible rule for updating of either the starting point or the rate , based on stimulus history , and, ( ii ) comparing every possible combination of trial-wise updating mechanism and perceptual decision model in a factorial model comparison ., Consistently across experiments , we found that the ( recent ) history of the response-critical property influences the initial decision bias , while repetition/switch of the target-defining dimension affects the accumulation rate , likely reflecting an implicit ‘top-down’ modulation process ., This provides strong evidence of a disassociation between response- and dimension-based inter-trial effects .
When a perceptual task is performed repeatedly , performance becomes faster and more accurate when there is little or no change of critical stimulus attributes across consecutive trials ., This phenomenon has been explored in previous studies on visual ‘pop-out’ search , showing that participants can find and respond to a unique target object among distractors faster when properties of the target are repeated across trials ., However , the processes that underlie these inter-trial effects are still not clearly understood ., Here , we approached this question by performing three visual search experiments and applying mathematical modeling to the data ., We combined models of perceptual decision making with Bayesian updating rules for the parameters of the decision making models , to capture the processing of visual information on each individual trial as well as possible mechanisms through which an influence can be carried forward from previous trials ., A systematic comparison of how well different combinations of models explain the data revealed the best model to assume that perceptual decisions are biased based on the response-critical stimulus property on recent trials , while repetition of the visual dimension in which the target differs from the distractors ( e . g . , color or orientation ) increases the speed of stimulus processing .
learning, decision making, reaction time, social sciences, neuroscience, learning and memory, cognitive neuroscience, cognitive psychology, mathematics, probability distribution, computer vision, cognition, memory, vision, computer and information sciences, target detection, probability theory, psychology, biology and life sciences, sensory perception, physical sciences, cognitive science