Spatial context is known to influence the behavioral sensitivity (*d*′) and the decision criterion (*c*) when detecting low-contrast targets. Of interest here is the effect on the decision criterion. Polat and Sagi (2007) demonstrated that, for a Gabor target positioned between two similar co-aligned high-contrast flankers, the observers’ reports of seeing the target (Hit and False Alarm) decreased with increasing target–flanker distance. This effect was more pronounced when the distance was randomized within testing blocks compared to when it was fixed. According to signal detection theory (SDT), the latter result suggests that the decision criterion is adjusted to a specific distance-dependent combination of signal (*S*) and noise (*N*) when the *S* and *N* statistics are fixed, but not when they vary across trials. However, SDT cannot differentiate between changes in the decision bias (the criterion shift) and changes introduced by variations in *S* and *N* (the signal and noise shift). To circumvent this limitation of SDT, we analyzed the reaction time (RT) data within the framework of the drift diffusion model (DDM). We performed an RT analysis of the target–flanker interactions using data from Polat and Sagi (2007) and Zomet et al. (2008; 2016). The analysis revealed a stronger dependence on flankers for faster RTs and a weaker dependence for slower RTs. The results can be explained by DDM, where an evidence accumulation process depends on the flankers via a change in the rate of the evidence (signal and noise shift) and on observers’ prior knowledge via a change in the starting point (criterion shift), leading to RT-independent and RT-dependent effects, respectively. The RT-independent distance-dependent response bias is attributed to the observers’ inability to learn multiple internal distributions required to accommodate the distance-dependent effects of the flankers on both the signal and noise.

*d*′); however, 2AFC provides no insights into the perceived quality of targets, which is expected to be affected by filling-in processes (Anstis, 2010). Polat and Sagi (2007), employing the Yes/No method, found, in addition to detection facilitation, a distance-dependent detection bias; observers’ tendency to report “target present” increased at short target–flanker distances regardless of the presence of the target (Hit) or absence (False Alarm [FA]). This suggests that the gap between flankers is filled in with task-relevant information, supporting the “filling-in” hypothesis. Both the increased target sensitivity and the observed detection bias are thought to be caused by lateral interactions in the visual cortex, activated by the flankers. Report biases are also affected by decision strategies, possibly related here to statistical priors derived from the known characteristics of natural images (Geisler, Perry, Super, & Gallogly, 2001). To better understand the contributions of lateral interactions and decision strategies to the detection bias, we present a reaction time (RT) analysis of the experimental results collected in the previous Yes/No experiments (Polat & Sagi, 2007; Zomet, Amiaz, Grunhaus, & Polat, 2008; Zomet, Polat, & Levi, 2016). The data were modeled using signal detection theory (SDT) (Green & Swets, 1966) and the drift-diffusion model (DDM) (Ratcliff & McKoon, 2008; Ratcliff, Smith, Brown, & McKoon, 2016; Shadlen & Kiani, 2013). In the subsequent sections, we elucidate the unified SDT–DDM framework employed to model the data.

*p*(

_{S}*x*), may overlap with the internal noise distribution representing no target, termed Noise, or

*p*(

_{N}*x*), thus leading to detection errors (Figure 1). Consequently, Yes responses can be correct (Hit, where

*P*= the area under the green shaded curve in Figure 1A) or incorrect (FA, where

_{Hit}*P*= the area under the red-shaded curve in Figure 1A). SDT provides tools to compute a decision criterion from the

_{FA}*P*and

_{Hit}*P*values, which is the normalized internal response level above which the observer produces a Yes decision (denoted by the blue vertical line in Figure 1A). This criterion is assumed to be observer dependent, and it can shift according to task demands and the stimulus properties available to the observer. However, when observing a specific change in the Hit and FA rates, such as the increased rates seen in our experiments, SDT cannot distinguish between two potential causes: (1) a shift in the decision criterion toward lower response levels (Figure 1B), or (2) an elevation in activity levels at the target location, shifting both the signal and noise distributions to higher response levels (Figure 1C). In the realm of SDT, the first cause (a criterion shift) is believed to depend on the observers’ decision strategies, which are flexible and aim to optimize the task outcome, including the error rates, costs, and values, making the task outcome inherently subjective. On the other hand, the second cause is deemed sensory driven, or objective, and is tied to the stimulus (such as flankers), influencing the response of the system. Regarding the experimental paradigm studied here, one might anticipate an increase in Yes responses in the presence of flankers due to (1) the observers’ expectation for the gap between flankers to be filled in, or (2) the increased sensory activity at the target location (as in Figure 1C), prompted by the input from the flankers. Both causes might reflect adaptation of the visual system to the statistics of edge co-occurrence in natural images (Geisler et al., 2001).

_{FA}*LLR*) value. This value assesses the odds ratio for one stimulus being present versus the other, and it accumulates over time intervals until a decision is triggered. This occurs when the accumulated value reaches one of two thresholds (bounds)—for example, +

*a*or –

*a*for positive or negative decisions, respectively. The starting point of the accumulator (

*sp*) can be selected to incorporate expectations, prior information (e.g., in the present context, the statistics of natural images), and the subjective value of the decision, such as payoff and reward. The rate of evidence accumulation, termed the “drift rate,” increases with the target sensitivity, resulting in faster attainment of the decision bounds. When the internal response offers no evidence of the target presence or absence, such as when

*p*(

_{S}*x*) =

*p*(

_{N}*x*), the drift rate (

*v*) is zero. Positive and negative drift rates correspond to target-present and target-absent trials, respectively. Thus, within the SDT framework, we assume that

*LLR*(

*x*) = log[

*p*(

_{S}*x*)/

*p*)] is integrated over time, where

_{N}(x*p*(

_{S}*x*) and

*p*(

_{N}*x*) (as illustrated in Figure 1) represent the momentary distributions of the sensory evidence (

*x*) in the signal (

*S*) and noise (

*N*) trials. More formally, for a time-varying response

*x*(

*t*) and an accumulated value

*L*, we have

*L*(

*t*) =

*L*(

*t – 1*)

*+ LLR*[

*x*(

*t*)], for all

*t*> 0, with

*L*(

*0*) =

*sp*. The mean drift rate (

*v*) in the

*S*and

*N*trials (

*v*and

_{S}*v*, respectively) is assumed to be proportional to the expected value of

_{N}*LLR*[

*x*(

*t*)] over the corresponding

*S*and

*N*trials. A decision is reached when

*L*(

*t*) ≥

*a*(a positive decision) or when

*L*(

*t*)

*≤*–

*a*(a negative decision). Importantly, note that the effect of

*L*(

*0*) on

*L*(

*t*) is expected to diminish with time as

*L*(

*t*) accumulates evidence and noise (Dekel & Sagi, 2020b).

*x*(

*t*) value so that

*LLR*[

*x*(

*t*)] can be accumulated. This necessity is often deemed challenging, if not unattainable, particularly in typical psychophysical experiments characterized by a limited number of trials. An alternative approach, employed by DDM, directly integrates the sensory evidence (Ratcliff & McKoon, 2008; Shadlen & Kiani, 2013). Gold and Shadlen (2001) proposed the difference between the momentary response and the criterion level as an alternative to the likelihood ratio computation, although the method of criterion setting is left open. The approach presented here explicitly assumes, as described below, that, in uncertain environments where observers encounter diverse stimuli with varying internal distributions, they fail to accurately estimate these distributions. Consequently, they base their decision on a mixed distribution, applying a single decision criterion to all stimuli (Gorea, Caetta, & Sagi, 2005; Gorea & Sagi, 2000).

*S*and

*N*distributions, when there are varying target–flanker distances between trials (Mix condition) (Figure 2). The findings of Gorea and Sagi (2000) suggest that observers are unable to learn the individual distributions, as required for optimal performance. Instead, they merge all

*S*and

*N*distributions (related to the different distances) into single

*S*and

*N*distributions, estimated to represent the average of the individual distributions. For the decision-making process, observers employ only one criterion that is optimized for these single

*S*and

*N*distributions. Consequently, it is predicted that only one accumulator is used in the mixed condition, with the estimated evidence for or against target presence being blind to the originating, distance-dependent distribution. Therefore, we expect zero evidence (i.e., the criterion) to correspond to the presence/absence of targets regardless of the specific flanker configurations. In essence, this is determined globally by amalgamating the diverse distributions related to the various target–flanker distances (as depicted in Figure 3).

*LLR*(

*x*)

*>*0; No, otherwise (

*x*is the internal response; see the black curve in Figure 3B). In a blocked condition (where the distance is fixed), observers can possibly estimate the specific distance-dependent distribution and derive an unbiased likelihood ratio value for each distance (illustrated by the colored curves in Figure 3B). The anticipated decision criteria for the example outlined in Figure 3A are depicted in Figure 3C.

*p*(

_{S}*x*) and

*p*(

_{N}*x*) distributions, akin to Figure 1C); and (2) biases corresponding to observers’ prior knowledge of the stimuli and the task at hand (resulting in a shifted criterion, similar to Figure 1B).

*S*and

*N*distributions. In the context of SDT, sensitivity is described by

*d*′, which is computed in a way that is assumed to be criterion independent (Figures 2C and 3D).

- P1. The criterion dependence on distance (Figure 2B) is expected to be larger at faster RTs compared with slower RTs (the effects of starting point). At slower RTs, we expect the criterion to depend on the distance when trials of different distances are mixed (the effect of mixing distributions), but not when the distances are blocked.
- P2. The criterion dependence on distance is expected to be larger at faster RTs due to biases introduced by the starting point of the accumulator,
*sp*=*L*(0). These biases are reduced with increasing RT due to the accumulation of internal noise (P1). However, high levels of external noise (Zomet et al., 2016), introduced at*t*= 0, are expected to dominate the internal noise and reduce the effect of the accumulation starting point. Thus, we predict RT to have a reduced effect on the dependence of the criterion on distance. - P3. The dependence of the criterion on distance is expected to decrease with the decreasing slope of the log-likelihood function presented in Figure 3B. It becomes evident that the slope decreases when the
*S*and*N*distribution width (σ) is increased. For the specific model presented, assuming normal distributions, the slope is proportional to (‹*S*› – ‹*N*›)/σ^{2}. Thus, in the presence of increasing noise (increasing σ values), when the*S*and*N*means are kept constant, the dependence of the criterion on distance is expected to decrease and to vanish at slower RTs. When the*S*and*N*difference is increased with σ, the dependence of the criterion on distance is expected to be preserved at higher noise levels. These predictions are tested by analyzing the results from experiments where external noise is added to the target (Zomet et al., 2016). - P4. The dependence of the criterion on distance is expected to be larger at faster RTs; thus, it will be reduced in slower observers (as discussed above, according to DDM, the starting-point–dependent bias decreases with RT) (Dekel & Sagi, 2020a). Here we analyzed data from a group of observers diagnosed for depression (Zomet et al., 2008), showing slower RTs. We expect the faster RTs of this group to have a reduced dependence of criterion on distance.

^{−2}(Figure 2) (Polat & Sagi, 2007). Stimuli were presented on a Philips multiscan 107P color monitor (Philips, Amsterdam, the Netherlands) using a PC system. The effective size of the monitor screen was 24 × 32 cm, which at the used viewing distance of 150 cm subtends a visual angle of 9.2° × 12.2°. Observers viewed the stimuli binocularly in a dark cubicle, where the only ambient light came from the display screen.

*p*= 0.097) regarding the mean contrast threshold. The mean contrast threshold of the control group was 5.12, and that of the patient group was 6. In each session, 20 trials for each target–flanker separation were presented, with a total of 120 trials per session.

*Diagnostic and Statistical Manual of Mental Disorders*, fourth edition (DSM-IV). All patients were found to be currently depressed during our testing period and were being treated with antidepressants and benzodiazepine medications (for more details, see Zomet et al., 2008).

*d*′) and the internal criterion (

*c*) (Green & Swets, 1966):

*P*is the probability that an observer correctly reported that the target is present in target-present trials,

_{Hit}*P*is the probability that the observer incorrectly reported that the target is present in target-absent trials, and

_{F}_{A}*z*is the inverse cumulative normal distribution function. To avoid saturation, the

*P*and

_{Hit}*P*probabilities were clipped to the range \([ {\frac{1}{{2n}},\frac{{2n - 1}}{{2n}}} ]\), where

_{FA}*n*is the number of trials in the measurement.

*d*′) (Equation 1) and the decision criterion (

*c*) (Equation 2) from SDT (Green & Swets, 1966).

*D*

_{tf}) and RT. We tested for significant contributions of these two factors and their interactions with the measured criterion (

*c*) (Equation 2), assuming:

*D*

_{tf}(six or four levels; see Table 1, Target–flanker distance) and

*RT*

_{bin}(four bins, 0:3, fast to slow) defined as a continuous effect, and the observers as random effects (slopes and intercepts). Our main interest is in α

_{2}, which measures the change in

*c*resulting from increasing

*D*

_{tf}, and α

_{3}, which measures the RT-dependent addition to α

_{1}, so that the

*D*

_{tf}slope equals α

_{2}+ α

_{3}×

*RT*

_{bin}. This simple model accounted for much of the variance in the data; the adjusted

*R*

^{2}value was between 0.5 and 0.8; the lower values were obtained in the external-noise experiments and in the experiments with patients.

*c*[

*D*

_{tf}] slope), the consequence of the different decision requirements presumably imposed by the mixing of different target–flanker distances in the Mix condition. Indeed, testing the dataset analyzed here with the linear mixed-effects model for the effect of the experimental condition (Mix:

*E*= 1; Fix:

*E*= 0), assuming

*c*(

*D*

_{tf}) slope, where α

_{3}= 0.035,

*t*(260) = 2.97,

*p*= 0.003; the slope more than doubled in the Mix condition (α

_{2}+ α

_{3}= 0.061 vs. α

_{2}= 0.026). The

*c*(

*D*

_{tf}) slope in the Fix condition (α

_{2}= 0.026) did not reach statistical significance (

*p*= 0.09). The intercept showed no statistical difference between conditions (α

_{1}= −0.19,

*p*= .09).

*c*(D

_{tf}) slope on RT. First, we considered the experimental data of the Mix condition from Polat and Sagi (2007). In this experiment, trials having different target–flanker distances were mixed within a block (Figure 2A). Our RT analysis, presented in Figure 4A, clearly shows that the criterion (

*c*) had lower values for slower RTs, especially at larger target–flanker distances (

*D*

_{tf}), implying that the criterion slope as a function of distance is reduced with increasing RT. This claim is strongly supported by the linear mixed-effects model described in Equation 1, showing that the interaction between the RT bin index and distance (α

_{3}= −0.02) was significant,

*t*(140) = −3.67,

*p*< 0.001. The

*c*(

*D*

_{tf}) slope of the fastest RT bin (α

_{2}= 0.09) was significant,

*t*(140) = 4.68,

*p*< 0.001; whereas, the slope at the slowest RT bin (α

_{2}+ 3 × α

_{3}= 0.03) approached statistical significance,

*t*(140) = 1.97,

*p*= 0.05, suggesting criterion modulation at slow RTs.

*d*′) by the flankers, as seen in Figure 2C for the available data. (Note that a much stronger modulation of sensitivity by the flankers is found when the detection task is replaced by a 2AFC discrimination task; see Polat & Sagi, 1993; Polat & Sagi, 2007.) The expected sensitivity modulation with distance is non-monotonic, showing a maximal effect at 3λ. Applying the RT analysis here revealed a gradual reduction of

*d*′ at slower RTs, with values decreasing from ∼1.5 at fast RTs to ∼1 at slow RTs,

*t*(142) = −4.01,

*p*< 0.001, for modulation of

*d*′ by RT when ignoring the target–flanker distance (Figure 4C). There was no significant interaction between RT and the target–flanker distance,

*t*(140) = −0.72,

*p*= 0.5. Importantly, the criterion and sensitivity exhibited different modulations by RT, as the criterion was modulated to a much greater extent than sensitivity, and its modulation dynamics differed (Figure 4A vs. Figure 4C).

_{3}= −0.01) was significant,

*t*(116) = −2.86,

*p*= 0.005. The

*c*(

*D*

_{tf}) slope of the fastest RT bin (α

_{2}= 0.04) was significant,

*t*(116) = 3.07,

*p*= 0.003), whereas the slope with the slowest RT bin (α

_{1}+ 3 × α

_{3}= 0.01) was not statistically different from zero,

*t*(116) = 0.64,

*p*= 0.52, suggesting, as predicted, no criterion modulation at slow RTs when the target–flanker distances are blocked.

*c*(

*D*

_{tf})

*d*′ value when the noise level increased (Main,

*n*= 12 observers) (Figure 5B). The other, an unpublished pilot of that study, in which the target contrast was increased with noise to maintain a roughly fixed

*d*′ (Pilot,

*n*= 7) (Figure 5C); this pilot is particularly convenient for performing the RT analyses because of the large number of trials per observer) (Table 1).

*c*(

*D*

_{tf}) slope. Specifically, the

*c*(

*D*

_{tf}) slope was reduced with RT; for Pilot,

*t*(164) = −4.66,

*p*< 0.001, and for Main,

*t*(188) = −3.01,

*p*= 0.003. In addition, the criterion slope at the slowest RT was positive; for Pilot,

*t*(164) = 4.62,

*p*< 0.001, and for Main,

*t*(188) = −3.88,

*p*< 0.001, as predicted for the Mix condition (the estimated slopes are presented in Figure 8).

*c*(

*D*

_{tf}) slope in the presence of noise. As shown in Figure 5 and Figure 8, introducing noise reduces the interaction of the criterion and the RT. This is seen in Figure 8, manifested by more similar

*c*(

*D*

_{tf}) slopes for the fast and slow RT bins in the presence of noise. There is one exception, when the noise level was 75% of the noise threshold in the pilot experiment,

*t*(164) = −3.39,

*p*< 0.001; otherwise, as predicted, none of the interactions reached statistical significance (

*p =*0.1–0.9). This effect was not due to a reduction in sensitivity (

*d*′), as shown in Figure 5C, where the target contrast was increased with the added noise, so that the sensitivity was fixed.

*c*(

*D*

_{tf}) slope

*c*(

*D*

_{tf}) slopes at the slowest RT show that it is significant in the Pilot experiment, in which the target contrast was increased with noise,

*t*(164) = −3.01,

*p*= 0.003, but not in the Main experiments in which the target contrast was not scaled with noise,

*t*(172) = 0.51,

*p*= 0.5.

*t*(764) = −2.41,

*p*= 0.02; Patients:

*t*(644) = −0.52,

*p*= 0.6. The sensitivity (

*d*′) was reduced with RT—Controls:

*t*(764) = −2.22,

*p*= 0.03; Patients:

*t*(644) = −3.06,

*p*= 0.002—independent of the target–flanker distance—Controls:

*t*(764) = 0.19,

*p*= 0.85; Patients:

*t*(644) = −1.46,

*p*= 0.14.

*x*-axis of Figure 6B). This is much slower than the ∼650 ms measured for observers in similar experimental conditions (Figures 4A and 5, no noise). Overall, the differences between experiments can possibly be explained by RT. In addition, we considered differences between observers in the control group of Zomet et al. (2008), where wide inter-individual differences in RT were measured (see the

*x*-axis of Figure 6B). We correlated individual RTs with the individual size of the criterion modulation by RT (for 15λ distance); we found a significant correlation (adjusted

*R*= 0.54,

*p*< 0.001) (Figure 6B). To summarize, the difference between the experiment by Zomet et al. (2008) and the other experiments appears to be well explained by slower RTs. In addition, the difference in RT between experiments and observers can possibly be attributed to age and/or practice effects (Table 1).

*sp*in

*DDM*), but not if it was caused by changes in the internal distributions associated with the different stimuli (affecting the drift rate in

*DDM*). Our results, summarized in Figures 7 and 8, support the latter.

*c*(

*D*

_{tf}) functions for the four RT bins (1 being the fastest). In the slowest RT bin the differences between experiments and conditions are largely abolished (but note the flat Fix curve), as clearly seen when comparing all curves in bin 4 (slow RTs). In the fastest RTs (bin 1; see Figure 7), the curves corresponding to the different conditions present a much larger variability.

*sp*) of the accumulation process, which leads to increased bias in faster decisions if put closer to one of the bounds (Figure 9, second row) (Dekel & Sagi, 2020b); and (2) the rates at which evidence is accumulated for target-present and target-absent trials (Figure 9, first row). As shown in Figure 9, this simple idea can explain the criterion measurements quite well. We provide here some information as to how this model works by describing the predictions of four simple model variations and analyzing the effect of the drift rate and the starting point on the results. The analysis is sufficiently general for its predictions to be independent of the specific assumptions made regarding the drift rate (see the Introduction). For simplicity, the drift rate is considered here as an abstract variable monotonically related to the log-likelihood ratio (Gold & Shadlen, 2001).

*v*) depends on the target stimulus (

*v*= +1 for target present,

_{+}*v*= −1 for target absent), and the starting point (

_{–}*sp*) is fixed at 0.5 (unbiased). This model predicts no bias (

*c*= 0) at all RTs, with fixed

*d*′, independent of distance. This model fails to explain the data.

*v*and

_{+}*v*is increased, thus showing larger

_{–}*d*′ values at these distances. Both

*v*and

_{+}*v*

_{–}are positive at short distances (supporting the positive responses), thus showing a negative criterion (

*c*< 0) at these distances, RT independent. This model can explain the distance dependence, but not the RT dependence of the measured criterion.

*sp*). The effect of this bias (

*sp*< 0.5) is short term, resulting in higher criteria (

*c*) in trials with fast RTs; slow RTs show criteria equal to those produced by Model 2. The RT effect on

*c*is distance independent. This model predicts an RT effect but cannot explain the dependence of the criterion slope on RT (Figure 8).

*sp*allowed to change with distance, resulting in distance-dependent RT effects, the RT-dependent slope of the

*c*(

*distance*) curve. This model captures the main features of the experimental results. Overall, the DDM framework considered here can qualitatively account for the most salient RT effects, but a precise modeling, requiring several more parameters and assumptions, remains somewhat speculative. In the Appendix (Figure A2) we present a detailed fit of Model 4 to the behavioral data, using the fast-dm software with the Kolmogorov–Smirnov (KS) setting (Voss & Voss, 2007).

*d*′

*d*′). As seen in Figure A2, the fitted drift rates for both target-present and target-absent gradually decrease with longer target–flanker distances, as predicted by the theory illustrated in Figure 1. The differential sensitivity, which is the difference in the fitted drift rates between the target-present and target-absent trials, was mostly fixed, showing a small decrease at longer target–flanker distances. This is consistent with the slightly improved

*d*′ value in the presence of proximal flankers. We noted that the fitted drift rate in the target-absent trials was usually negative. A negative drift indicates that the evidence supports the negative (target-absence) response. That is, the reduced sensory response in the target-absent trials is mapped into

*negative values*(see the Discussion). This finding is reasonable in the sense that what is accumulated is target-presence evidence, with “zero” values corresponding to no evidence for or against target presence (see the Introduction).

*d*′, Equation 1) and the decision criterion (

*c*, Equation 2). Although the bias-independent sensitivity measure (

*d*′) is the standard measure used to quantify the perceptual effects, our interest here lies in the effects on the decision criterion (bias), shown in Figure 2. SDT, with limited access to internal distributions (Gorea & Sagi, 2000), provides an observer-independent account of the biases found, as illustrated in Figure 3 (see the Introduction). Here, for the first time, to the best of our knowledge, an RT analysis of the lateral masking effect was performed, attempting to isolate the subjective (observer dependent) and objective (observer independent) factors underlying the observed biases in perception.

*LLR*function (P3, Figure 3).

*d*′ approaching zero), caused by the external noise level approaching the threshold, as indicated by the results presented in Figure A4.

*v*

_{+}+

*v*

_{–}). For an unbiased observer, this sum is expected to be zero. Figure 10A presents the drift rate asymmetry in the fitting results (Figure A2) for both the Mix and the Fix conditions of Polat and Sagi (2007), showing a marked difference between conditions. In contradistinction, biases due to shifts in the starting point (

*sp*) are very similar in the Mix and the Fix conditions (Figure 10B). Accordingly, we attribute the differences in results between the Mix and the Fix conditions to objective factors affecting decisions—that is, to differences in the internal responses rather than to subjective factors such as priors (see the Introduction). We can conclude that the biases in the Mix condition can be explained by the distance-dependent excitatory effects of the flankers, operating in both target-present and target-absent trials, underlying the perceived filling-in effect.

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