## Abstract

Inhibitory control such as active selective response inhibition is currently a major topic in cognitive neuroscience. Here we analyze the shape of behavioral RT and accuracy distributions in a visual masked priming paradigm. We employ discrete time hazard functions of response occurrence and conditional accuracy functions to study what causes the negative compatibility effect (NCE)—faster responses and less errors in inconsistent than in consistent prime target conditions—during the time course of a trial. Experiment 1 compares different mask types to find out whether response-relevant mask features are necessary for the NCE. After ruling out this explanation, Experiment 2 manipulates prime mask and mask target intervals to find out whether the NCE is time-locked to the prime or to the mask. We find that (a) response conflicts in inconsistent prime target conditions are locked to target onset, (b) positive priming effects are locked to prime onset whereas the NCE is locked to mask onset, (c) active response inhibition is selective for the primed response, and (d) the type of mask has only modulating effects. We conclude that the NCE is neither caused by automatic self-inhibition of the primed response due to backward masking nor by updating response-relevant features of the mask, but by active mask-triggered selective inhibition of the primed response. We discuss our results in light of a recent computational model of the role of the BG in response gating and executive control.

## INTRODUCTION

The nature of inhibitory control processes including response inhibition is currently a major topic in cognitive neuroscience (Banich & Depue, 2015; Stuphorn, 2015; Watanabe & Funahashi, 2015; Middlebrooks & Schall, 2014; Houghton & Tipper, 1996). Response inhibition can be triggered automatically in a bottom–up, stimulus-driven fashion (as in lateral inhibition between two stimulus-triggered candidate responses) or actively in a top–down, task-driven fashion (as in cognitive control). Physiological evidence from choice RT tasks indicates that response inhibition can be active (vs. automatic) as well as selective (vs. nonselective or global; Burle, Vidal, Tandonnet, & Hasbroucq, 2004). However, it is often possible to come up with an explanation without active selective response inhibition to explain mean performance patterns. For example, in task conditions involving competing responses, slowing in mean RT may be explained by lateral inhibition between response channels (which is considered automatic and nonselective because it is reciprocal), without considering the possibility of the additional presence of active and selective (as well as active and nonselective) response inhibition. For this reason, many mathematical two-choice RT process models such as Poisson accumulator models (Schubert, Palazova, & Hutt, 2013; Mattler & Palmer, 2012; Vorberg, Mattler, Heinecke, Schmidt, & Schwarzbach, 2003) may neglect the role of active inhibition in interference paradigms (Schroll & Hamker, 2013; Wiecki & Frank, 2013; Aron, 2011).

### The Masked (Response) Priming Paradigm

The visual masked priming paradigm (e.g., Marcel, 1983; for reviews, see Ansorge, Kunde, & Kiefer, 2014; Holender, 1986; Eriksen, 1960) is used to study how an irrelevant and invisible prime stimulus interferes with responding to a subsequently presented target. Typically, correct responses are faster, and error rates are lower when the prime contains features that are similar to the target than when prime and target features are dissimilar.

A special case of masked priming is the response priming paradigm (Vorberg et al., 2003; Klotz & Neumann, 1999; Klotz & Wolff, 1995) where the invisible prime is either mapped to the same response as the target (consistent trials) or to the opposite response (inconsistent trials). Even in the absence of awareness of the critical prime features, the prime is often able to influence motor responses and even nonmotor operations such as cognitive control (Palmer & Mattler, 2013; van Gaal, Lamme, & Ridderinkhof, 2010; Kunde, Kiesel, & Hoffmann, 2003; Mattler, 2003). Because of the fixed mapping of stimulus features to responses, a single prime feature is assumed sufficient to elicit the associated response directly, without conscious mediation (Neumann, 1990).

It has been suggested that, in response priming, prime and target elicit sequential feedforward sweeps (VanRullen & Koch, 2003; Lamme & Roelfsema, 2000) that activate the associated responses in strict sequence (Schmidt, Haberkamp, Veltkamp, et al., 2011). This leads to response conflict when the prime is inconsistent with the target. Indeed, sequential response activation by primes and targets can be observed in lateralized readiness potentials (Vath & Schmidt, 2007; Eimer & Schlaghecken, 1998; Leuthold & Kopp, 1998) and in the time courses of pointing movements and response forces (Schmidt, Weber, & Schmidt, 2014; Schmidt & Schmidt, 2009; Schmidt, 2002). The notion of sequential triggering of prime- and target-related responses explains many interesting properties of response priming. For instance, priming effects increase with prime target SOA, and error responses are typically fast and occur selectively in inconsistent trials at long SOAs, which would be expected if longer SOAs leave the prime more time to direct the response into the correct or incorrect direction. Moreover, it has repeatedly been shown that the first motor responses are exclusively controlled by the prime and not influenced at all by the actual target (e.g., Schmidt et al., 2014; Schmidt & Schmidt, 2009, 2010; Schmidt, Niehaus, & Nagel, 2006).

### The Negative Compatibility Effect

Positive response priming effects are typically observed for prime target SOAs up to about 100 msec (positive compatibility effect, PCE). For longer SOAs, the masked priming effect has often been found to reverse, resulting in a negative index with better mean performance in the inconsistent condition: the negative compatibility effect (NCE; Lingnau & Vorberg, 2005; Eimer, 1999; Eimer & Schlaghecken, 1998). Eimer and Schlaghecken (1998) employed double arrows (≪ or ≫) as primes and targets. A 17-msec prime was immediately followed by a 100-msec mask constructed from the superposition of left- and right-pointing double arrows. The mask was immediately followed by a target that was either consistent with the prime (pointing in the same direction, thus requiring the same response) or inconsistent (requiring the opposite response). To their surprise, the authors found that mean error rates were higher, and mean correct RT longer, when primes and targets were consistent than when they were inconsistent—a reversal of the expected PCE. They traced the effect in the lateralized readiness potential, observing a sequence of three response activations: an initial activation of the prime-related response, followed by a transient activation of the opposite (antiprime) response, and finally an activation of the target-triggered correct response. It is generally accepted that it is the emergence of antiprime activation that reverses the priming effect (Seiss, Klippel, Hope, Boy, & Sumner, 2014).

At least three different hypotheses have been developed to explain the emergence of antiprime activation in this particular paradigm (for reviews, see Jaśkowski & Verleger, 2007; Sumner, 2007). First, according to the self-inhibition account, the initial motor activation elicited by the prime is automatically and selectively inhibited due to self-inhibitory circuits at the motor level when (a) the perceptual evidence for the prime is immediately removed by the mask and (b) the delay between the prime and target is long enough for this inhibition to become effective (Eimer & Schlaghecken, 1998, 2002, 2003). Importantly, the inhibition itself is supposed to be triggered by the prime, not the mask, but it only occurs when the mask sufficiently reduces the visibility of the prime. Assuming lateral inhibition between response channels, the selective inhibition of the primed response is then supposed to lead to the temporary activation (disinhibition) of the opposite or antiprime response.

Second, according to the object-updating account, the NCE emerges when the mask contains features that call for the response opposite to the prime—a so-called relevant mask. The NCE thus simply reflects positive priming of the antiprime response by the corresponding features in the mask, instead of selective response inhibition (Lleras & Enns, 2004, 2006). Critically, the NCE is thus not expected to occur when an irrelevant mask is used that does not contain response-relevant features. This explanation applies in the case of Eimer and Schlaghecken's (1998) original stimuli, because their mask was a replica of the prime arrow with an additional antiprime arrow superimposed. Under this account, a response-relevant mask is a necessary condition of the NCE.

Third, according to the mask-triggered inhibition account, the role of the mask is to stop response accumulation by the prime by actively inhibiting the premature prime-triggered response (Jaśkowski, 2007, 2008, 2009; Jaśkowski, Białuńska, Tomanek, & Verleger, 2008; Jaśkowski & Przekoracka-Krawczyk, 2005). This active and selective response inhibition (sometimes called an “emergency break”) requires a strong mask signal, but not necessarily strong masking of the prime. Under the mask-triggered inhibition account, it is still expected that relevant masks are more effective than irrelevant masks in triggering inhibition and activating the antiprime response because of their response-relevant features. But in contrast to the self-inhibition account, inhibition is predicted to be time-locked to the mask, not the prime.

### Event History Analysis

To evaluate these accounts, we take a longitudinal approach by applying event history analysis (EHA). EHA is the standard distributional method for analyzing time-to-event data; it is also known as survival, hazard, duration, failure time, or transition analysis (Allison, 2010; Panis & Wagemans, 2009; Singer & Willett, 2003; Miller, 1981). We assume that for each time point since target onset (in each trial from each participant) there is a risk for the event (here: a response) to occur. The function relating this instantaneous likelihood or hazard of response occurrence to time is known as the continuous time hazard function (Luce, 1986).

Here we apply discrete time (descriptive and inferential) methods (Panis & Hermens, 2014; Allison, 1982, 2010; Chechile, 2003; Singer & Willett, 1991, 2003; Willett & Singer, 1993, 1995). We divide the first 600 msec after target onset into 15 bins of 40 msec indexed by *t* = 1–15 and estimate the discrete time hazard function of response occurrence: *h*(*t*) = *P*(*T* = *t*|*T* ≥ *t*), where *T* ≥ *t* denotes the event that the response does not occur before the start of bin *t*. This conditional probability function gives for each bin *t* the conditional probability of response occurrence sometime during bin *t*, given that the response has not yet occurred in any previous bin (*t* − 1*, t* − 2*,* …*,* 1). The survivor function, *S*(*t*), gives the probability that the response has not occurred yet by the time bin *t* is completed. It is the joint probability that the response has not occurred in any of the bins prior to *t*: *S*(*t*) = *P*(*T* > *t*) = [1 − *h*(*t*)] ⋅ [1 − *h*(*t* − 1)] ⋅ [1 − *h*(*t* − 2)] ⋅ … ⋅ [1 − *h*(1)]. Finally, *P*(*t*) = *P*(*T* = *t*) = *h*(*t*) ⋅ *S*(*t* − 1) gives the unconditional probability that the response occurs in bin *t*. Plotting *P*(*t*) over *t* gives the subprobability mass function of response occurrence. Whenever there are night-censored observations the *P*(*t*) estimates will not sum to 1 (Chechile, 2006).

We cannot simply estimate the hazard functions for error and correct response occurrence separately, because those two events cannot be assumed to be independent (Praamstra & Seiss, 2005; Burle et al., 2004; Eriksen, Coles, Morris, & O'Hara, 1985). Therefore, we take the so-called conditional processes approach by extending the *h*(*t*) analysis of response occurrence by an analysis of conditional accuracy (Allison, 2010, pp. 227–229). First, we estimate *h*(*t*) of response occurrence regardless of response accuracy to study whether and when responses occur. For each bin *t*, the sample-based estimate of *h*(*t*) is obtained by dividing the total number of observed responses in bin *t* by the risk set for bin *t*. The risk set equals the total number of trials that are response-free in all bins earlier than *t* and are thus still eligible to experience the response at the start of bin *t* (see Table 1). Note that right-censored observations—trials for which we only know that RT > 600 msec—do contribute to the risk set in each bin.^{1}

Time Bin ID
. | Time Bin Index t
. | No. of Censored
. | No. of Events
. | Risk Set
. | h(t)
. | 1 − h(t)
. | S(t)
. | P(t)
. | No. of Correct
. | No. of Error
. | ca(t)
. |
---|---|---|---|---|---|---|---|---|---|---|---|

(0,40] | 1 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(40,80] | 2 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(80,120] | 3 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(120,160] | 4 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(160,200] | 5 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(200,240] | 6 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(240,280] | 7 | 0 | 7 | 220 | .032 | .968 | .968 | .032 | 2 | 5 | 0.29 |

(280,320] | 8 | 0 | 13 | 213 | .061 | .939 | .909 | .059 | 10 | 3 | 0.77 |

(320,360] | 9 | 0 | 26 | 200 | .130 | .870 | .791 | .118 | 24 | 2 | 0.92 |

(360,400] | 10 | 0 | 40 | 174 | .230 | .770 | .609 | .182 | 40 | 0 | 1.00 |

(400,440] | 11 | 0 | 48 | 134 | .358 | .642 | .391 | .218 | 47 | 1 | 0.98 |

(440,480] | 12 | 0 | 37 | 86 | .430 | .570 | .223 | .168 | 37 | 0 | 1.00 |

(480,520] | 13 | 0 | 32 | 49 | .653 | .347 | .077 | .145 | 32 | 0 | 1.00 |

(520,560] | 14 | 0 | 9 | 17 | .529 | .471 | .036 | .041 | 9 | 0 | 1.00 |

(560,600] | 15 | 4 | 4 | 8 | .500 | .500 | .018 | .018 | 4 | 0 | 1.00 |

Time Bin ID
. | Time Bin Index t
. | No. of Censored
. | No. of Events
. | Risk Set
. | h(t)
. | 1 − h(t)
. | S(t)
. | P(t)
. | No. of Correct
. | No. of Error
. | ca(t)
. |
---|---|---|---|---|---|---|---|---|---|---|---|

(0,40] | 1 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(40,80] | 2 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(80,120] | 3 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(120,160] | 4 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(160,200] | 5 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(200,240] | 6 | 0 | 0 | 220 | 0 | 1 | 1 | 0 | 0 | 0 | NA |

(240,280] | 7 | 0 | 7 | 220 | .032 | .968 | .968 | .032 | 2 | 5 | 0.29 |

(280,320] | 8 | 0 | 13 | 213 | .061 | .939 | .909 | .059 | 10 | 3 | 0.77 |

(320,360] | 9 | 0 | 26 | 200 | .130 | .870 | .791 | .118 | 24 | 2 | 0.92 |

(360,400] | 10 | 0 | 40 | 174 | .230 | .770 | .609 | .182 | 40 | 0 | 1.00 |

(400,440] | 11 | 0 | 48 | 134 | .358 | .642 | .391 | .218 | 47 | 1 | 0.98 |

(440,480] | 12 | 0 | 37 | 86 | .430 | .570 | .223 | .168 | 37 | 0 | 1.00 |

(480,520] | 13 | 0 | 32 | 49 | .653 | .347 | .077 | .145 | 32 | 0 | 1.00 |

(520,560] | 14 | 0 | 9 | 17 | .529 | .471 | .036 | .041 | 9 | 0 | 1.00 |

(560,600] | 15 | 4 | 4 | 8 | .500 | .500 | .018 | .018 | 4 | 0 | 1.00 |

ID = identity; No. of Events = number of observed responses in bin *t*; hazard function *h*(*t*) = *P*(*T* = *t*|*T* ≥ *t*); survivor function *S*(*t*) = *P*(*T* > *t*); subprobability function *P*(*t*) = *P*(*T* = *t*); conditional accuracy function *ca*(*t*) = *P*(*correct*|*T* = *t*); NA = undefined. Four trials were right-censored at 600 msec (i.e., 600 < RT ≤ 800 msec or no response occurred during the entire 800-msec response collection period).

Second, once we know probabilistically whether and when responses occur, we estimate the conditional accuracy function of observed responses: *ca*(*t*) = *P*(*response correct*|*T* = *t*), which provides the conditional probability that an observed response is correct given that it occurs sometime during bin *t*. *Ca*(*t*) is obtained by dividing the number of correct responses observed during bin *t* by the total number of observed responses in bin *t*, as shown in Table 1. By using *h*(*t*) functions in combination with conditional accuracy functions, one can provide an unbiased, time-varying, and probabilistic description of the latency and accuracy of responses.^{2}

### Current Study

We investigate the role of response inhibition in the within-trial temporal dynamics of PCE and NCE in the masked priming paradigm. Two goals motivate our study. In Experiment 1, we compare different masks and use EHA to look for sudden decreases in the hazard of response occurrence as indicators of inhibitory processes. In Experiment 2, we manipulate the SOAs and investigate whether and when the PCE and NCE emerge in the hazard and conditional accuracy functions. We focus on individual performance patterns to evaluate similarities across participants and fit statistical models to the aggregated participant data (hazard models and conditional accuracy models). We find that the hazard functions display sudden decreases that indicate response inhibition, that the temporal dynamics of the NCE is very similar for relevant and irrelevant masks, that the onset of the NCE in conditional accuracy is time-locked to mask but not prime onset, and that the inhibitory cause of the NCE can be dissociated temporally from automatic lateral inhibition during response competition.

## EXPERIMENT 1: THE EFFECTS OF MASK TYPE ON WITHIN-TRIAL DYNAMICS OF COMPATIBILITY EFFECTS

In Experiment 1, we examine the temporal dynamics of the PCE and NCE using event history and conditional accuracy analyses. When looking at mean performance measures, we expect a PCE when the mask is absent and an NCE when a mask is present. When looking at distributional measures, response-relevant and -irrelevant masks should trigger the same, stimulus-independent inhibition process and thus lead to the same NCE according to the self-inhibition account. According to the object-updating account, an NCE should occur only for relevant but not for irrelevant masks because only the response-relevant mask features can activate the antiprime response. According to the mask-triggered inhibition account, any mask should be able to trigger an NCE, but a relevant mask might trigger a stronger NCE than an irrelevant one because of its additional response-relevant features.

### Methods

#### Participants

Six volunteers (one man, all right-handed) participated. Mean age was 26.5 years (range = 23–32 years). All had normal or corrected-to-normal vision. Our approach is to make precise measurements on each single participant to demonstrate homogeneity of effects on an individual basis, rather than to emphasize the total number of participants (Schmidt, Haberkamp, & Schmidt, 2011).

#### Materials

Targets were double arrowheads pointing left or right (Figure 1A). Primes could be either blank (no prime, NP) or double arrows with direction consistent (CON) or inconsistent (INCON) with that of the target. Masks could be either blank (no mask, NM), response-relevant (REL, with arrow primes in both directions superimposed), response-irrelevant (IRREL, a symmetrical figure consisting of horizontal and vertical line elements), or random lines (LIN, 32 randomly oriented lines, generated anew for each trial; Figure 1A). The arrow stimuli and relevant mask subtended an area of approximately 1.2° × 1.2° in visual angle. The irrelevant and random line masks subtended an area of approximately 1.5° × 1.5° and 1.7° × 1.7°, respectively. All stimuli were presented in black on a white background in the center of a 40-cm 75-Hz CRT screen.

#### Design

The factors Prime Type (NP, CON, INCON) and Mask Type (NM, REL, IRREL, LIN) were crossed orthogonally, resulting in 12 trial types (NP-NM, CON-NM, …, INCON-LIN).

#### Procedure

Each trial started with a fixation cross for 536 msec (40 frames) followed by a blank for 402 msec (30 frames; Figure 1A). The prime stimulus (i.e., a double arrow or blank) was presented for 13 msec (1 frame), followed by a 1-frame blank. Then the mask stimulus (i.e., REL, IRREL, LIN, or a blank) was presented for 94 msec (7 frames) followed by a blank for 67 msec (5 frames). Finally, the target was presented for 94 msec and replaced with a blank. Prime target SOA was fixed at 187 msec.

The participant's task was to categorize the target as pointing left or right as quickly and as accurately as possible by pressing one of two keyboard buttons (“F” for left, “J” for right). The response collection period started at target onset and lasted 800 msec. If no response was detected before the end of this period, the message “Too slow” was presented; if an error response was detected, the message “Error” was presented (all in German).

There was one practice block and 70 experimental blocks with 22 trials per block. Every seventh experimental block exclusively contained target-only trials (i.e., condition NP-NM; 10 blocks in total). We presented the target-only trials in separate blocks because we noticed during pretesting that there was a tendency to withhold responding in target-only trials when all 12 trial types were intermixed randomly (see General Discussion). The remaining 60 experimental blocks each contained two trials for each of the remaining 11 conditions (one with target pointing right, one with target pointing left). Order of presentation was randomized within each block.

#### Analysis of Mean Error Rate and Mean Correct RT

Mean error rate was calculated for each condition and participant based on the trials with observed responses between 250 and 600 msec (4.2% of the data excluded). The mean correct RT was calculated after ignoring trials with an error, trials without a response, and trials with a correct response that had a latency below 250 msec or above 600 msec (10.1% of the data excluded). Repeated-measures ANOVAs are reported with Greenhouse–Geisser corrections when necessary. All significant effects are reported.

#### Event History Analysis

For each participant, we first calculated the sample-based descriptive estimates of *h*(*t*), *S*(*t*), *P*(*t*), and *ca*(*t*) for each condition. Next, discrete time hazard models and conditional accuracy models were implemented as generalized linear mixed-effects regression models in *R* (R Core Team, 2014; function *glmer* of package *lme4*). We used a logit link for the *ca*(*t*) models and a complementary log–log (cloglog) link for the *h*(*t*) models (Allison, 2010).^{3} Next to dummy-coding the levels of our experimental factors (prime type and mask type), we also included TRIAL number as a predictor in the hazard models (centered on value 1000 and then divided by 1000) to model across-trial learning effects in the speed of responses. For both models, the predictor variable TIME was the time bin index *t* centered on value 8, or 320 msec. We denote time bins by the endpoint of the interval they span, so that Bin 8 = Bin 320 = (280,320]. The intercept and the linear and quadratic effects of TIME were treated as random effects. For both analyses, we started with a full model encompassing all possible fixed effects-of-interest and used an automatic backward selection procedure to select a final model. Specifically, during each iteration, the effect with the largest *p* value that was not part of any higher-order effect was deleted, and the model refitted. This continued until each of the remaining effects that was not part of any higher-order effect had a *p* < .05 (see highlighted *p* values in Tables S1–S4). The NP-REL condition (no prime, relevant mask) was chosen as a baseline condition to facilitate comparisons of relevant versus irrelevant masks. Thus, with all effects set to zero, the *h*(*t*) model's intercept refers to the estimated cloglog[*h*(*t*)] for Bin 320 in trial 1000 of the NP-REL condition.

To estimate the parameters of the *h*(*t*) model, we must create a data set where each row corresponds to a time bin of a trial of a participant. Specifically, each time bin that was at risk for event occurrence in a trial was scored on the dependent variable EVENT (1 = *response occurred*; 0 = *no response*), the covariate TIME (centered on Bin 320), and the dummy-coded predictor variables including TRIAL. Because most responses occurred before 600 msec after target onset, all trials with observed RTs > 600 msec and all trials without a response during the observation period were treated as right-censored observations; they provide the information that the response did not occur during the first 600 msec or 15 bins (i.e., each of these trials contributes 15 rows, and each row has a value 0 for EVENT). In addition, we deleted the first two bins because all observed RTs were larger than 80 msec. The resulting *h*(*t*) data set contained 75,180 rows.

For the *ca*(*t*) model, we used the usual data set where each row corresponds to a trial of a participant (1540 × 6 = 9240 trials). Each trial without a response and each trial with a response latency below 160 msec or above 480 msec was deleted (10.37% of the data). This latency range was chosen to avoid problems of linear separability during model fitting. Each remaining trial (a single row in the data set) was scored on the dependent variable ACCURACY (1 = *correct*; 0 = *error*), the covariate TIME (centered on Bin 320), and the dummy-coded independent variables. The *ca*(*t*) data set contained 8282 rows.

### Results

#### Mean Error Rate and Mean Correct RT

As expected, priming effects are positive in the no-mask condition (PCE, with faster responses and lower error rates in consistent than in inconsistent trials) and negative in the three masked conditions (NCE). Accordingly, a two-way repeated-measures ANOVA on mean correct RT shows a significant interaction between Prime Type and Mask Type, *F*(1.414, 7.071) = 25.051, *p* = .001, η_{p}^{2} = .834 (Figure 2A). There is also a significant main effect of Mask Type, *F*(1.524, 7.622) = 4.927, *p* = .049, η_{p}^{2} = .496. Planned dependent samples *t* tests (two-tailed, uncorrected) show that the difference between consistent and inconsistent conditions was significant for all mask types; NM (*t*(5) = 5.807, *p* = .002), REL (*t*(5) = −4.08, *p* = .010), IRREL (*t*(5) = −4.158, *p* = .009), and LIN (*t*(5) = −2.598, *p* = .048). RTs in the no-prime conditions were intermediate between those with consistent and inconsistent primes.

A one-way repeated-measures ANOVA on the priming effects in mean correct RT (consistent minus inconsistent) shows a significant effect of Mask Type, *F*(3, 15) = 27.841, *p* < .001, η_{p}^{2} = .848. Planned dependent samples *t* tests (two-tailed, uncorrected) showed that the priming effect for the mask-absent condition was significantly different from that for REL (*t*(5) = 5.39, *p* = .003), IRREL (*t*(5) = 5.861, *p* = .002), and LIN (*t*(5) = 5.316, *p* = .003), with no significant differences between the three mask-present conditions.

Similarly, a two-way repeated-measures ANOVA on mean error rate shows a significant main effect of Prime Type, *F*(2, 10) = 6.037, *p* = .015, η_{p}^{2} = .547, and a significant interaction between Prime Type and Mask Type, *F*(1.406, 7.028) = 5.865, *p* = .035, η_{p}^{2} = .54 (Figure 2B). Planned *t* tests show that the difference between consistent and inconsistent conditions was marginally significant for NM (*t*(5) = 2.458, *p* = .057), significant for REL (*t*(5) = −3.497, *p* = .017) and IRREL (*t*(5) = −3.027, *p* = .029) and not significant for LIN (*t*(5) = −2.017, *p* = .1).

A one-way repeated-measures ANOVA on the priming effects in mean error rate (consistent minus inconsistent) shows a significant effect of Mask Type, *F*(1.283, 6.417) = 6.89, *p* = .032, η_{p}^{2} = .579. Planned dependent samples *t* tests (two-tailed, uncorrected) showed that the priming effect for the mask-absent condition was different from that for REL (*t*(5) = 2.725, *p* = .042), IRREL (*t*(5) = 3.029, *p* = .029), and LIN (*t*(5) = 2.481, *p* = .056), with no significant differences between the three mask-present conditions.

#### Event History Analysis: Descriptive Statistics

The 48 sample-based functions for a single participant are shown in Figure 3. To grasp the correct interpretation of the functions, the key is to shift along with the passage of time starting at target onset and interpret the (vertical differences between the) estimates for each successive bin. Let us first focus on the NP-NM (or target-only) condition (black lines, first column in Figure 3; Table 1).

The first responses occur in Bin 280 or (240,280] (*n* = 7), and there are 220 trials that are response-free before 240 msec (the risk set for Bin 280), so the sample estimate of *h*(280) = 7/220 = .032. In other words, once the waiting time has reached 240 msec, then there is an estimated hazard of .032 that the response is about to occur in the impending bin (240,280]. The probability that the response has not yet occurred by the end of Bin 280 equals *S*(280) = .968 (=1 − .032), and the unconditional probability of response occurrence equals *P*(280) = .032. If it does occur during Bin 280, then there is an estimated conditional probability of *ca*(280) = 2/7 = .29 that it will be correct.

In Bin 320 or (280,320], 13 responses occur and there are only 213 trials left that are response-free before 280 msec, so *h*(320) = 13/213 = .061. So, once the waiting time has reached 280 msec, the estimated probability that the response will occur sometime in Bin 320 or (280,320] is .061. The probability that the response has still not occurred by the end of Bin 320 equals *S*(320) = .909 (= [1 − .032][1 − .061]), and the unconditional probability of response occurrence in Bin 320 equals *P*(320) = 13/220 = .059. If the response does occur during Bin 320, then there is a conditional probability of *ca*(320) = 10/13 = .77 that it will be correct. Continuing these calculations for the other bins, we see that *h*(*t*) increases steadily and reaches its peak in Bin 520, that *S*(*t*) decreases monotonically over time towards zero, and that *P*(*t*) peaks in Bin 440, with 48 responses in (400,440]. The conditional accuracy equals 1 for Bin 480 and onward, so every response that occurs later than 440 msec after target onset was a correct response for target-only trials. Note that the high hazard of .653 in bin (480,520] is experienced only by those 49 of 220 trials that are still response-free until at least 480 msec after target onset.

When an unmasked prime is added (green and red lines, Column 1 of Figure 3), *h*(*t*) and *P*(*t*) start to increase—and *S*(*t*) starts to decrease—earlier, that is, around Bin 200. Furthermore, if a response occurs during Bins 200–360, it is always correct when the prime is consistent (CON-NM; green lines), but always incorrect when the prime is inconsistent (INCON-NM; red lines). Those early responses in both unmasked prime conditions are thus triggered by the prime's identity only.

Interestingly, after the *h*(*t*) functions in conditions CON-NM and INCON-NM increase together until Bin 280, response hazard keeps increasing for a while in consistent trials but declines and even reaches zero in Bin 400 in inconsistent trials. This temporary decline in *h*(*t*) for an unmasked inconsistent prime may represent response competition due to the target, which is becoming overtly available in Bin 280 (see NP-NM) and activates the opposite (correct) response. After Bin 400, *h*(*t*) starts to increase again in the inconsistent condition, and if a response occurs at least 400 msec after target onset, it is always correct. Thus, the response conflict has now been resolved in favor of the target, and these late responses are triggered entirely by the target's identity. Note that *h*(*t*) in the consistent condition is always higher than in the inconsistent condition from Bin 280 onward, which would not be apparent by looking only at *P*(*t*). Conversely, most responses for NP-NM, CON-NM, and INCON-NM occur in Bin 440, 320, and 280, respectively, which is not apparent by looking only at *h*(*t*). Finally, the estimated median RT is defined as percentile *S*(*t*)_{.50} and is lowest for CON-NM, intermediate for NP-NM, and highest for INCON-NM.

When a relevant mask is followed by the target in the absence of primes (NP-REL; black lines in Column 2 of Figure 3), the first responses appear in Bin 320 (compared with Bin 280 when no mask is presented). Compared with the target-only condition, *h*(*t*) starts to increase a bit later and *S*(*t*) starts to decrease later. Thus, the mask seems to interfere with target processing and to delay the occurrence of the first responses (e.g., by forward-masking the visual target signal).

More importantly, when a prime is presented before the relevant mask, earlier responses occur compared with NP-REL, similar to the no-mask conditions. Specifically, *h*(*t*) and *P*(*t*) are a bit higher in Bin 320 for CON-REL and INCON-REL compared with NP-REL, so their *S*(*t*) functions start to decrease a bit earlier. Furthermore, if a response occurs in Bin 320, it is always correct in INCON-REL and always incorrect in CON-REL. This striking pattern is opposite to the PCE in the no-mask condition and indicates an NCE in *ca*(320). This NCE also appears in the hazard functions, but *later* than in the conditional accuracies. Although *h*(*t*) keeps increasing after Bin 360 for an inconsistent prime (INCON-REL), there is a temporary dip in the *h*(*t*) function (or a delay in its rise) for a consistent prime (CON-REL). Following this dip, *h*(*t*) sharply increases, at a similar rate as in INCON-NM, and all responses emitted after 480 msec are correct, indicating that a response conflict has been solved in favor of the target. The NCE in *h*(*t*) emerges first in Bin 360 and thus must represent the consequence and not the cause of the NCE in *ca*(320). Finally, in this participant, the overall time course with relevant masks is similar to that with irrelevant or random line masks.

In Figures S1–S5 we present the sample distributional data for the other five participants. Their time-varying behavior is qualitatively similar to that in Figure 3 except for the following. First, when a mask is present, some participants also show a few very early responses (before Bin 240). These seem to be triggered by the prime's identity as they occur around the same time when the first responses appear in the primed no-mask conditions. Second, for many participants the NCE in *h*(*t*) and *ca*(*t*) is smaller for random line masks compared with relevant or irrelevant masks.

Figure 4A shows how priming effects (differences between consistent and inconsistent conditions) in conditional accuracy functions develop over time within and across individual participants. In these state transition plots, we see that all participants tend to show perfect performance for responses emitted after about 400 msec. Furthermore, all participants show a PCE sometime between 80 and 400 msec after target onset in the mask-absent condition. In the conditions with relevant and irrelevant masks, all participants show an NCE sometime between 200 and 400 msec after target onset. With a random line mask, participants tend to show an NCE of a shorter duration sometime between 240 and 400 msec.

#### EHA: Inferential Statistics

To test whether the main and interaction effects including TIME, Prime Type, and Mask Type are significant across participants, we fitted discrete time hazard models and conditional accuracy models to the aggregated data (generalized linear mixed-effects models). The predicted cloglog[*h*(*t*)] and logit[*ca*(*t*)] functions from both selected models are shown in Figure 5, as well as the predicted *h*(*t*) and *ca*(*t*) functions, which are obtained by applying the inverses of the cloglog and logit link functions, respectively. Specifically, an increase in cloglogs by an additive constant *a* corresponds to a multiplicative increase in hazards (or hazard ratio, HR) by a factor of exp(*a*). Parameter estimates and test statistics are shown in Tables S1 and S2. During model selection, TIME was centered on Bin 320 (*t* = 8). For the hazard models, TRIAL was centered on value 1000, so that any numerical values of main and interaction effects not explicitly involving TIME or TRIAL refer to Bin 320 of trial number 1000. To explicitly model the temporally localized dip in the sample *h*(*t*) functions for condition INCON-NM, we added a predictor INH (for “inhibition”) to the hazard model, which took on value 1 for Bins 320 and 360, and 0 otherwise and included the three interaction effects involving INH, INCON, and NM (see Table S1). Thus, the interaction INCON:NM:INH is included to model a specific drop in response hazard around Bins 320 and 360 in INCON-NM. After initial model selection, we refitted both selected models three times with TIME centered on Bins 240 (*t* = 6), 400 (*t* = 10), and 480 (*t* = 12) to see explicitly what values the parameter estimates take on in these bins and whether they represent a significant effect or not.

##### Discrete time hazard model

In this and later sections, we start with a fairly complete interpretation of the model parameters in the reference condition (no prime and relevant mask, NP-REL), and then we will switch to a more panoramic description of the significant changes that occur when adding primes or changing mask type.

###### No prime and relevant mask

The first five parameter estimates in Table S1 model the shape of the cloglog[*h*(*t*)] function for the reference condition, trial 1000 of NP-REL (Figure 5, Row 1, Column 2, black line). Because TIME and TRIAL are centered, the intercept of our regression model refers to the model estimate at Bin 320 of trial 1000. Because INH is coded as 1 in Bins 320 and 360 and zero otherwise, the predicted cloglog[*h*(320)] value is the sum of the estimates of intercept and INH, −2.943 − .101 = −3.044, when the effects CON, INCON, NM, IRREL, LIN, TIME, and TRIAL are set to zero. Converting back from cloglogs to hazards, *h*(320) = .047 (=1 − exp[−exp(−3.044)]; Figure 5, Row 2, Column 2, Bin 320). Parameters 2–4 show a significant linear and quadratic effect of TIME on this intercept estimate, such that the predicted response hazard increases over time: *h*(240) = 0.0015, *h*(320) = .047, *h*(400) = 0.38, and *h*(480) = 0.68, respectively. This reflects the intuition that the more waiting time passes in a trial, the greater the likelihood that a response is emitted in the next time instant given that it has not occurred yet.

###### Primes and relevant mask

Now we add a consistent prime to the reference condition NP-REL. Parameters 6–9 show a significant main effect of a consistent prime (CON) in Bin 320 (Parameter 6, PE = .268, *p* = .022), and CON interacts with TIME, changing from positive to negative over time. Compared with the cloglog[*h*(*t*)] estimates in the reference condition (Figure 5, Row 1, Column 2, black), adding a consistent prime increases the estimated cloglog[*h*(*t*)] by 1.774 units in Bin 240, which corresponds to an increase in response hazard by a factor of 5.9 (*HR*(240) = exp[1.774] = 5.9) compared with the corresponding condition without a prime. Similarly, *HR*(320) = 1.3, *HR*(400) = 0.7, and *HR*(480) = 0.74, indicating that the consistent prime increases the hazard of an early response and lowers the hazard of a later response (Figure 5, Row 2, Column 2, green).

What happens if we add an inconsistent instead of a consistent prime? Parameters 10–13 show a significant main effect of an inconsistent prime (INCON) in Bin 320 (Parameter 10, PE= .563, *p* < .001) and interactions with TIME. Additionally, there is an interaction between INCON and INH (Parameter 14), revealing a very slight increase in response hazards during Bins 320 and 360 for inconsistent primes. In summary, adding an inconsistent prime to the reference condition NP-REL increases the hazard of an early response by a factor of *HR*(240) = 4.7, just like the addition of a consistent prime does. However, whereas the effect of a consistent prime reverses over time, the inconsistent prime's early positive effect simply vanishes over time: *HR*(320) = 2.12, *HR*(400) = 1.16, and *HR*(480) = 1.04 (Figure 5, Row 2, Column 2). This demonstrates an NCE emerging in *h*(*t*) around 280–320 msec after target onset.

###### No mask

In the following, we will switch to a more qualitative description of the effects. Note that from here on, all additional regression parameters have to be interpreted relative to the reference condition: for instance, there will be an additional main effect of Mask Absence (a dummy variable coded 0 when any mask is present and 1 when no mask is presented). This variable may form interactions with all the variables described so far for the relevant mask condition (CON, INCON, INH, TIME, TIME^{2}, and TIME^{3}).

Parameters 15–18 in Table S1 show a significant main effect of Mask Absence (NM) (Parameter 15, PE = 1.174, *p* < .001) and significant interactions with TIME. Compared with the reference condition (NP-REL), removing the mask increases the hazard of response occurrence in Bins 240–400 (Figure 5, Row 2, Columns 1 vs. 2, black lines).

Now we add the interaction effects between NM and consistent (CON) versus inconsistent primes (INCON) and compare their additional effects with the effects of CON and INCON in the relevant-mask condition to examine what removal of the mask does to the NCE. In line with the effects in mean RT, removal of the relevant mask turns the priming effect from slightly negative to strongly positive (Figure 5, Column 1, Row 2). This switch in the sign of the priming effect is marked by a significant interaction of the independent variables CON and NM that varies over TIME (Parameters 20–21) and by a significant interaction between INCON and NM that varies over TIME (Parameters 22–24). The former reflects an upward shift of the hazard function in consistent trials when the mask is removed. The latter reflects a decrease in the response hazards in inconsistent trials from Bin 320 onwards, next to an early increase in Bin 240. This leads to a reversal in the ordering of the hazard functions: In opposition to the relevant mask condition, the hazard function for consistent trials is now above that for inconsistent trials from Bin 280 onwards (Figure 5, Row 2, Column 1). As expected, the interaction INCON:NM:INH is significantly negative (Parameter 25), reflecting the marked dip in *h*(*t*) during Bins 320 and 360 of the unmasked inconsistent prime condition.

###### Irrelevant mask

Compared with the large differences between the relevant mask and no-mask conditions, the differences between relevant and irrelevant masks are minimal. Parameters 26–29 mainly show a significant positive main effect of IRREL that tends to change over time, reflecting slightly elevated hazards of responding compared with NP-REL: *HR*(240) = 1.09, *HR*(320) = 1.72, *HR*(400) = 1.43, and *HR*(480) = 1.05 (Figure 5, Rows 1 and 2, Columns 3 vs. 2; black lines). Parameters 30–37 show the interaction effects of IRREL with the variables for consistent primes (CON), inconsistent primes (INCON), and TIME. None of them is statistically significant, in line with the overall impression that compatibility effects are similar to the relevant-mask condition. (We only left them in the model to make the comparison between the masks explicit).

###### Random line mask

Parameters 38–41 show that LIN interacts with TIME. Compared with NP-REL, LIN decreases the hazard of fast response occurrence and somewhat elevates the hazard of later responses: *HR*(240) = 0.26, *HR*(320) = 1.16, *HR*(400) = 1.23, and *HR*(480) = 0.9 (Figure 5, Rows 1 and 2, Columns 4 vs. 2, black lines). Parameters 42–49 show that LIN significantly neutralizes REL's negative effect of CON in Bin 480 and REL's positive effect of INCON in Bin 320. The NCE is thus smaller and reduced in duration relative to REL.

###### Trial number

The significant main effect of Trial Number in Bin 320 interacts with TIME (Parameters 50–53). Each additional trial increases the estimated response hazards by a factor of 1.000058 in Bin 240, 1.00029 in Bin 320, 1.00025 in Bin 400, and 1.00014 in Bin 480.

##### Conditional Accuracy Model

###### No prime and relevant mask

The first four parameters in Table S2 model the shape of the logit[*ca*(*t*)] function for the reference condition: NP-REL. The intercept of 0.843 is the predicted logit[*ca*(320)] value in the reference condition, so that *ca*(320) = exp(.843)/[1 + exp(.843)] = .70; see Figure 5, Row 3, Column 2, Bin 320). Parameters 2–4 show a significant linear, quadratic, and cubic effect of TIME on the intercept, *ca*(240) = .58, *ca*(320) = .70, *ca*(400) = .98, and *ca*(480) = .99, respectively (Figure 5, Row 3, Column 2, black line). We only plotted a *ca*(*t*) estimate in Figure 5 if the corresponding *h*(*t*) estimate is larger than a threshold value of 0.02, thus omitting accuracy estimates when responses are too unlikely.

###### Primes and relevant mask

Parameters 5–6 in Table S2 show a significant main effect of adding a consistent prime, CON, in Bin 320 (Figure 5, Row 4, Column 2). Compared with the reference condition, adding a consistent prime decreases the estimated logit[*ca*(*t*)] in Bins 240–480—an NCE in conditional accuracy. As a measure of effect size, one can exponentiate the parameter estimate to obtain odds ratios (OR). Thus, the odds of a correct response in Bin 240 of CON-REL are estimated to be 0.12 (= exp[−2.148]) times those in Bin 240 of NM-REL, or *OR*(240) = 0.12. Similarly, *OR*(320) = 0.2, *OR*(400) = 0.32, and *OR*(480) = 0.62 (Figure 5, Row 3, Column 2, green vs. black).

Parameters 7–10 show a significant main effect of an inconsistent prime (INCON) in Bin 320, and interactions with TIME. Compared with the reference condition, adding an inconsistent prime massively *increases* response accuracies: *OR*(240) = 0.99, *OR*(320) = 6.2, *OR*(400) = 5.75, and *OR*(480) = 13.6 (Figure 5, Row 3, Column 2, red vs. black). Again, this indicates an NCE in conditional accuracies.

###### No mask

Conditional accuracy functions in the relevant-mask condition show an NCE that vanishes with time. This should turn into a PCE when the mask is removed. In the following, all additional regression effect parameters have to be interpreted relative to NP-REL.

Parameters 11–13 show a significant main effect of Mask Absence (NM) in Bin 320 (Figure 5, Row 4, Columns 1 vs. 2, black lines). Compared with the reference condition, removing the mask increases the odds of a correct response by a factor of 1.5 in Bin 240. Similarly, *OR*(320) = 2.4, *OR*(400) = 3.2, *OR*(480) = 6.8. Thus, compared with NP-REL, the removal of the mask leads to higher conditional accuracies, especially for midrange latencies.

In line with the effects in mean error rate, removal of the mask turns the priming effect in *ca*(*t*) from mildly negative to strongly positive (Figure 5, Row 3, Column 1). This switch in the sign of the priming effect is marked by a significant interaction between CON and NM that varies linearly over TIME (Parameters 14–15) and by a significant interaction between INCON and NM that varies linearly and quadratically over TIME (Parameters 16–18).

###### Irrelevant mask

Again, differences between the relevant and irrelevant mask conditions are relatively small. Parameters 19–21 show that presenting an irrelevant instead of a relevant mask significantly increases the odds of a late correct response, *OR*(400) = 3.3, *OR*(480) = 15.5. Overall, the model predicts similar time courses for irrelevant and relevant masks (Figure 5, Row 3, Columns 3 vs. 2).

###### Random line mask

Parameters 25–26 show a nonsignificant main effect of LIN in Bin 320 but a linear interaction with time: *OR*(240) = .13, *OR*(320) = .9, *OR*(400) = 5.3, and *OR*(480) = 31.0 (Figure 5, Row 4, Columns 4 vs. 2, black lines). Parameters 27–30 show that both interaction effects CON:LIN and INCON:LIN change linearly with TIME, from positive to negative. The model thus predicts a smaller and shorter NCE in conditional accuracies for the random line mask as compared with the relevant mask (Figure 5, Row 3, Columns 4 vs. 2).

### Discussion

The classical indices of priming effects (mean correct RT and mean error rate) show large positive priming effects when the mask is absent. Interestingly, any type of mask in our study reverses the positive priming effect (PCE) into a negative one (NCE), with faster and more accurate responses in inconsistent that in consistent trials. This finding is in line with the self-inhibition and the mask-triggered inhibition accounts, which both maintain that response inhibition can be elicited by different types of masks, not only those containing response-relevant features. However, our data are inconsistent with the object-updating account, which predicts that only a response-relevant mask should lead to an NCE. We thus conclude that the NCE cannot be explained on basis of response-relevant stimulus features only and that a selective response inhibition process is required. The major question for Experiment 2 thus becomes whether this inhibition process is triggered by the prime or the mask.

Event history analysis allows us to trace the within-trial time course of PCE and NCE. It shows that the summary indices of mean RT and mean error rate only give a very cursory account of the dynamics of underlying processes. For example, the positive priming effect in mean RT has a magnitude of about 90 msec (the only time estimate available when looking at mean performance). In contrast, an EHA can provide time estimates for both *h*(*t*) and *ca*(*t*). Hazard and conditional accuracy functions reflect different aspects of the ongoing, continuous decision process (Mulder & van Maanen, 2013), as indicated by the fact that the time courses of an effect they reveal typically differ in duration and location: The PCE in *h*(*t*) actually lasts at least 320 msec (eight bins) and the (earlier emerging) PCE in *ca*(*t*) lasts about 240 msec (six bins; Figure 4A). Similarly, the NCE in *h*(*t*) and *ca*(*t*) lasts at least 120 msec, compared with the 20- to 40-msec differences measured in mean RT. Differences in mean RT clearly underestimate the actual duration of the effect in *h*(*t*) and *ca*(*t*). Similarly, priming effects in mean error rates conceal that there are stretches of time where the response is controlled completely by the prime or target, leading to conditional accuracy functions that can move from 0% to 100% correct as the target takes over the response process from the inconsistent prime. Event history analysis thus reveals that analyzing only mean performance can give a misleading picture of the underlying processing dynamics.

In the no-mask condition, the response dynamics suggest that the response is at first controlled exclusively by the prime (Schmidt, Haberkamp, Veltkamp, et al., 2011; Schmidt et al., 2006), that a response conflict develops via automatic lateral inhibition as target information becomes available, and that the response conflict is finally resolved in favor of the target, which ultimately controls the response on its own (provided that a prime-triggered response has not occurred in the trial). When a mask is present, some early prime-triggered responses before Bin 240 can occur, but in general response occurrence is delayed. The early responses for consistent and inconsistent trials in Bin 280 only differ in their conditional accuracy, with more errors in the consistent condition than in the inconsistent one. This earlier emergence of the NCE in *ca*(*t*) than in *h*(*t*) implies that, by this time in the trial, selective inhibition has already taken place that was directed specifically against the primed response and so reversed the priming effect. In the hazard functions, the NCE becomes visible a bit later, around Bin 320, reflecting the consequence of (a) the resulting target-triggered response conflict in the consistent condition (which temporarily increases over time) or (b) the head start in correct response activation in the inconsistent condition (which decreases over time).

Two other observations are worth mentioning. First, the NCE in *h*(*t*) and *ca*(*t*) for the random line mask was smaller and more short-lived than for the relevant and irrelevant masks. It is possible that the changing line mask interfered with the feedforward signal from the prime more than both unchanging mask patterns did, curtailing its effective duration relatively more than the other masks. Also, the line mask decreased the hazard and conditional accuracy of early responses compared with the relevant mask. It is unknown at present whether the magnitude of the NCE depends on the strength of the initial prime signal; but if so, differences across mask types might be explained by different degrees of mask prime interference in the prime's feedforward signal (not to be confused with the degree of masking in visual awareness).

Second, notice how hazard increases at a similar rate in all conditions except for those with unmasked primes. The difference with the other 10 conditions is that participants are perceptually aware of two and not one task-relevant double arrowhead stimulus. In the General Discussion, we will revisit the distributional data of Experiment 1 and argue that active response inhibition is also present in both visible prime conditions.

## EXPERIMENT 2: IS RESPONSE INHIBITION TIME-LOCKED TO THE PRIME OR TO THE MASK?

After having rejected the object-updating account, we vary the prime mask (PM) and mask target (MT) SOAs to see whether the NCE is time-locked to prime or mask onset, thus allowing us to decide between the remaining accounts. According to the self-inhibition account, the prime triggers its own inhibition, which should accordingly be time-locked to prime onset, and inhibition should be triggered only when the prime is effectively masked. According to the mask-triggered inhibition account, inhibition is time-locked to mask onset, and because the mask only serves to signal the prematureness of the prime-induced response, efficient masking of the prime is not necessary. We employ the same materials as in Experiment 1, except that only the relevant mask is used and that instead of the no-prime condition we employ a neutral prime (NEU, a black ring).

### Methods

#### Participants

Six volunteers participated (two men, one left-handed). Mean age was 25.7 years (range = 23–29 years). All had normal or corrected-to-normal vision.

#### Materials

The same materials were employed as in Experiment 1, except that only the relevant mask was used and that instead of the no-prime condition we employed a neutral prime (a black ring subtending 1.2° × 1.2°).

#### Design

The factors Prime Type (NEU, CON, INCON) and SOA Combination (PM-SOA long and MT-SOA short: L-S, similarly S-L, S-S, and L-L) were crossed orthogonally, resulting in 12 trial types (NP-S-S, CON-S-S, …, INCON-L-L).

#### Procedure

Each trial started with a fixation cross for 536 msec (40 frames) followed by a blank for 402 msec (30 frames). This was followed by a sequence of a 27-msec prime, a 67-msec mask, and a 67-msec target with their respective SOAs (Figure 1B). PM-SOA was either 40 or 120 msec, MT-SOA was either 80 or 160 msec. Note that L-L and S-L as well as L-S and S-S share the same mask target SOA (160 and 80 msec, respectively) and that S-L and L-S share the same prime target SOA (200 msec).

The participant's task was the same as in Experiment 1, and there was the same feedback. The response collection period started at target onset and lasted 700 msec. There was one practice block and 60 experimental blocks with 24 trials per block. Each block contained two trials from each condition (one with target pointing to the right, one with target pointing to the left). Order of presentation was randomized.

#### Analysis of Mean Error Rate and Mean Correct RT

Mean error rate was calculated based on observed responses between 250 and 600 msec (3.0% of the data excluded). The mean correct RT was calculated after ignoring trials with an error, trials without a response, and trials with a correct response but a latency below 250 msec or above 600 msec (6.1% of the data excluded).

#### Event History Analysis

The reference condition was chosen to be the NEU-S-S condition. To fit the *h*(*t*) model, trials were right-censored at 600 msec after target onset, and the first two bins of each trial were deleted. The *h*(*t*) data set contained 71,084 rows. For the *ca*(*t*) model, each trial without a response and each trial with a response latency below 160 msec or above 480 msec was deleted (7.53% of the data). The *ca*(*t*) data set contained 7,989 rows.

### Results

#### Mean Error Rate and Mean Correct RT

As expected, priming effects are negative for all SOA combinations in mean correct RT as well as mean error rate. A two-way repeated-measures ANOVA on mean correct RT shows a significant main effect of Prime Type, *F*(2, 10) = 60.983, *p* < .001, η_{p}^{2} = .924, and a significant main effect of SOA Combination, *F*(3, 15) = 46.137, *p* < .001, η_{p}^{2} = .902 (Figure 2C). Planned dependent samples *t* tests (two-tailed, uncorrected) show that differences between consistent and inconsistent prime conditions were significant for each SOA combination, all *t*(5) ≤ −4.885, all *p*s ≤ .005. A one-way repeated-measures ANOVA on the priming effects in mean correct RT (consistent minus inconsistent) shows no significant effect of SOA Combination.

A two-way repeated-measures ANOVA on mean error rate shows only a significant main effect of Prime Type, *F*(2, 10) = 14.916, *p* < .001, η_{p}^{2} = .749 (Figure 2D). Differences between consistent and inconsistent prime conditions were significant for S-S, S-L, and L-L, all *t*(5) ≤ −3.806, all *p*s < .013, and marginally significant for L-S, *t*(5) = −2.514, *p* = .054. A one-way repeated-measures ANOVA on the priming effect in mean error rate (consistent minus inconsistent) shows no significant effect of SOA Combination.

#### EHA: Descriptive Statistics

The sample-based estimates for each participant are shown in Figures S6–S11 and the state transition plots are shown in Figure 4B. The latter clearly show how PCE and NCE are time-locked to primes and masks, respectively. In all SOA conditions, we see an NCE in *ca*(*t*). It lasts for two or three time bins (80–120 msec) and is time-locked to mask onset: It occurs about 80 msec earlier for long rather than short mask target SOAs, a delay corresponding exactly to the difference in mask onsets. Thus, in all conditions, the NCE appears a fixed 360 msec after mask onset.

When the prime is immediately followed by a mask (S-S and S-L), we only see this NCE. But when there is a 120-msec gap between prime and mask (L-L and L-S), a PCE unexpectedly precedes the NCE. This PCE lasts for about 120 msec and is time-locked to prime onset just as the NCE is time-locked to mask onset, shifted by the same 80 msec that separate prime onsets in the L-L and L-S conditions. It thus occurs a fixed 320 msec after prime onset, comparable to Experiment 1.

#### EHA: Inferential Statistics

The predicted cloglog[*h*(*t*)] and logit[*ca*(*t*)] functions from both selected models are shown in Figure 6, together with the predicted *h*(*t*) and *ca*(*t*) functions. The parameter estimates are shown in Tables S3 and S4. During model selection, TIME was centered on Bin 280, and TRIAL was centered on value 1000. To explicitly model the systematic temporary drop in response hazards for consistent primes in the S-L and L-L conditions (see Figures S6–S11), we added a predictor “INH8” to the hazard model, which took on value 1 for Bin 8 or (280,320] and 0 otherwise, as well as the relevant interactions (see Table S3).

##### Discrete time Hazard Model

###### Neutral prime, short–short condition

The first five parameter estimates in Table S3 model the shape of the cloglog[*h*(*t*)] function for the reference condition: trial 1000 of NEU-S-S. The estimated intercept of −5.488 is the predicted cloglog[*h*(280)], corresponding to *h*(280) = .004 (Figure 6, Row 2, Column 1, black). Parameters 2–4 show that response hazards increase over time: *h*(280) = 0.004, *h*(320) = .024, *h*(360) = 0.16, and *h*(440) = 0.7 (Figure 6, Row 2, Column 1, black line).

###### Response-relevant primes, short–short condition

Now we change the neutral prime into a consistent one (CON-S-S). Parameters 6–9 show no main effect of CON in Bin 280 but significant interactions with TIME in a linear and quadratic fashion. The interaction between CON and INH8 is not significant (Parameter 10). Compared with the reference condition, adding a consistent prime decreases the likelihood of response occurrence as expected under the NCE, *HR*(280) = 0.64, *HR*(320) = 0.46, *HR*(360) = 0.29, and *HR*(440) = 0.37 (Figure 6, Row 2, Column 1, green vs. black). Conversely, adding an inconsistent instead of a consistent prime (Parameters 11–14) increases the likelihood of response occurrence, especially for faster responses, *HR*(280) = 2.16, *HR*(320) = 1.71, *HR*(360) = 1.41, and *HR*(440) = 1.08 (Figure 6, Row 2, Column 1, red vs. black). These patterns show that the nature of the NCE in *h*(*t*) changes over time: It starts out as a higher hazard for inconsistent compared with neutral primes in Bin 280, and it turns into a lower hazard for consistent compared with neutral primes in later bins.

###### Short–long condition

Again, our analysis describes this data pattern relative to NEU-S-S by introducing a new dummy variable (S-L, coding for the difference between S-S and S-L) and its interactions with previous effects. Parameters 15–18 show a significant main effect of S-L in Bin 280 and significant interactions with TIME. The interaction between S-L and INH8 is also significant (Parameter 19). As a result and compared with the reference condition, changing the SOA combination from S-S to S-L increases the response hazards, especially for earlier bins: *HR*(280) = 6.0, *HR*(320) = 4.0, *HR*(360) = 1.9, and *HR*(440) = 1.1 (Figure 6, Row 2, Columns 2 vs. 1, black lines). Thus, compared with NEU-S-S, increasing the MT-SOA leads to earlier response occurrence.

Parameters 20–28 describe how the effects of CON and INCON change when changing from S-S to S-L. Parameters 20–24 show that the disadvantage in *h*(*t*) in CON versus NEU as observed for S-S (see Parameter 6 in Table S3) becomes even larger in Bin 320 (−0.445 = 0.666 − 1.111; see Parameters 20 and 24), but smaller in Bins 9 and 11 (+0.727 and +0.432; Figure 6, Row 2, Column 2). Parameters 25–28 show that the *h*(*t*) advantage for INCON versus NEU as observed for S-S (Parameter 11) is similar for S-L compared with S-S and thus decreases over time (just as in the mask-present conditions of Experiment 1).

###### Long–short condition

Again, we introduce a new parameter, L-S. Parameters 29–32 show that changing the SOA combination from S-S to L-S leads to earlier response occurrence (but less strong than with S-L; compare parameter lines 29 and 15). Parameters 33–40 show that the compatibility effects for L-S are in general similar to those for S-S, except that the *h*(*t*) advantage for inconsistent compared with neutral primes (parameter line 11) becomes even larger in Bin 280 (+0.577), but smaller in Bin 360 (−0.248; Figure 6, Row 2, Columns 3 vs. 1).

###### Long–long condition

Parameters 41–44 show that, compared with NEU-S-S, the L-L condition shows earlier response occurrence and more so than L-S and S-L (compare parameter lines 41, 29, 15). The compatibility effects for L-L are very similar to those for S-L (Parameters 45–48; Figure 6, Row 2, Columns 4 vs. 2). Note that our model does not capture the few early responses around Bin 120 (see Figures S6–S11).

###### Trial number

Each additional trial increases the estimated response hazards by a factor of 1.00024 in Bin 280, 1.00036 in Bin 320, 1.00037 in Bin 360, and 1.0002 in Bin 440 (Parameters 49–52).

##### Conditional Accuracy Model

###### Short–short condition

The first three parameters in Table S4 model the shape of the logit[*ca*(*t*)] function for the reference condition, NEU-S-S (Figure 6, Row 4, Column 1, black line). The intercept corresponds to a predicted *ca*(280) = .78. Parameters 2–3 show that there is a significant linear effect of TIME on the intercept such that conditional accuracy increases over time; *ca*(280) = .78, *ca*(320) = .91, *ca*(360) = .97, and *ca*(440) = .99, respectively (Figure 6, Row 3, Column 1, black line).

Parameters 4–6 show that, compared with the reference condition, changing the neutral prime to a consistent one greatly decreases the accuracy of fast responses in particular, *OR*(280) = 0.14, *OR*(320) = 0.04, and *OR*(360) = 0.03 (Row 3, Column 1, green vs. black). Note that we only plotted a *ca*(*t*) estimate in Figure 6 if the corresponding response hazard was at least .002. Parameters 7–9 show that, compared with the reference condition, changing the neutral prime to an inconsistent one greatly increases response accuracy, resulting in *OR*(280) = 6.9, *OR*(320) = 4.3, *OR*(360) = 2.7. The model thus predicts an NCE in conditional accuracy for Bins 280–400 in the short–short condition (Figure 6, Row 3, Column 1).

###### Short–long condition

Although there is no significant effect of S-L in any bin (parameter line 10), the interaction between CON and S-L is significant in Bin 360 (PE = 1.307, *p* = .03) and Bin 440 (PE = 3.394, *p* = .002). The significant interaction between INCON and S-L does not change over time (Parameter 15, PE = 2.333, *p* = .04). The model thus predicts an NCE in conditional accuracy for Bins 200–360 in the short–long condition (Figure 6, Row 3, Column 2).

###### Long–short condition

The main effect of L-S is significant in Bin 360 (PE = −0.959, *p* = .02) and Bin 440 (PE = −1.619, *p* = .02), and the interaction effect between CON and L-S does not change over time (Parameter 19, PE = 1.582, *p* = .001). The interaction effect between INCON and L-S is significant in Bin 280 (PE = −2.66, *p* = .002) and Bin 360 (PE = 1.805, *p* = .02). The model thus predicts a PCE in conditional accuracies for Bins 200 and 240 and an NCE for Bins 320 and 360 (Figure 6, Row 3, Column 3; see also Figure 4B).

###### Long–long condition

The main effect of L-L is not significant in any bin (Parameters 23–24), and the interaction between CON and L-L is significant in Bin 320 (PE = 1.392, *p* = .01), Bin 360 (PE = 2.979, *p* < .001), and Bin 440 (PE = 6.154, *p* < .001). The model thus predicts an NCE in conditional accuracies for Bins 200–320 (Figure 6, Row 3, Column 4). Again, our model does not capture the unexpectedly early responses around Bin 120.

### Discussion

The classical indices of priming effects (mean RT and error rate) consistently show NCEs under all SOA combinations. NCE effects are invariably time-locked to the mask and start about 360 msec after mask onset, as predicted by mask-triggered inhibition. In contrast, the self-inhibition account would have predicted time-locking to the prime. Moreover, it predicts that the NCE should only occur when the prime is effectively masked (i.e., at short prime mask intervals), which is not observed here. Our findings thus reject the self-inhibition account.

In both conditions with long prime mask SOAs (L-S and L-L), EHA reveals a sequence of three motor states: first a PCE state where the primed response is activated, then an NCE state where the antiprime response is activated, and finally a target-controlled state that invariably leads to correct responses. The PCE state lasts about 120 msec and emerges around 320 msec after prime onset. This state is not observed for short prime mask SOAs (S-S and S-L), suggesting that an early mask abolishes the initial overt positive priming effect. The PCE state is followed by an NCE state, which is time-locked to the mask just like the PCE state is time-locked to the prime. The NCE state starts about 360 msec after mask onset, and its duration depends on the mask target interval: It lasts about 80 msec for short intervals (S-S and L-S) and about 120 msec for long intervals (S-L and L-L) and thus outlasts the prime mask interval, indicating that some impact of the prime persists after mask onset. The NCE thus seems to end when target-controlled (correct) responses start to emerge, which occurs sooner when the MT-SOA is longer. Note that a sequence of PCE and NCE states has also been observed in lateralized readiness potentials (Eimer & Schlaghecken, 1998). Moreover, Jaśkowski et al. (2008) have shown that lateralized readiness potentials in antiprime direction are time-locked to the mask. In summary, our findings thus suggest that the NCE is a case of active, selective inhibition of the prime-induced response (Jaśkowski & Przekoracka-Krawczyk, 2005).

## GENERAL DISCUSSION

### Evidence for an Active Selective Response Inhibition Process

Our results are compatible with the main tenet of mask-triggered inhibition, namely, that a stimulus signaling that the current response activation is premature can trigger selective response inhibition directed specifically against the activated response (Verleger, 2011). The same conclusion can be drawn from a study of primed pointing movements by Schmidt, Hauch, and Schmidt (2015). In that study, participants performed movements in different directions by pointing to the horizontal one of two target bars (basically, a 2AFC task; but see the article for details). Targets were preceded by primes (identical to the targets in consistent trials, spatially switched in inconsistent trials), so that consistent primes induced a movement in the same vectorial direction as the targets, whereas inconsistent primes induced a movement in the opposite direction. An NCE occurred only when a mask was presented early after the prime, and it depended on the time of response initiation (Ocampo & Finkbeiner, 2013). Although fast responses (Quartiles 1 and 2) started out in the direction of the prime, slower responses (Quartiles 3 and 4) started out in the precise opposite vectorial direction, even in consistent trials. Thus, when the prime and target pairs both afforded a response to, say, the lower left, responses first went to the upper right, in the opposite direction to both stimuli. This surprising movement in antiprime direction for slow responses, named thrust reversal, was much larger than suggested by the modest NCEs in RTs (i.e., arrival times at the correct target location). Thrust reversal started about 350 msec after mask onset, very similar to the 360 msec observed here. Importantly, even though different types of mask modulated the time course of the pointing movements, thrust reversal was indistinguishable between response-relevant and response-irrelevant masks. In addition, Schmidt et al. (2015) point out the role of global response inhibition for the NCE. Because prime target SOAs are long, participants are required to actively withhold their response until the target has appeared to avoid responding to the prime and incurring a high error rate. Indeed, during pretesting of Experiment 1, participants actively withheld their response to the target temporarily in target-only trials when these were intermixed with the other trial types, presumably because in many trials that start with a visible arrow, a second visible arrow can be expected (the target in both unmasked prime conditions).

Boy, Husain, and Sumner (2010) likewise conclude that response inhibition in the NCE is active (not merely due to automatic lateral inhibition) and selective (directed specifically against the primed response). They combine a masked priming paradigm with an Eriksen flanker task, concluding that the inhibitory mechanisms involved in masked priming and flanker paradigms are overlapping whereas the previous trial or Gratton effect does not interact with response inhibition. They suggest that the NCE is related to a poststimulus reactive control process that selectively inhibits a specific motor response and not to a proactive control process that modulates perceptual processing through attention.^{4}

Interestingly, Schlaghecken, Münchau, Bloem, Rothwell, and Eimer (2003) showed that slow-frequency repetitive TMS of motor and premotor cortex slows mean RT but does not affect masked priming effects, concluding that masked priming effects are generated at earlier stages of visuomotor processing, such as the BG. Similarly, D'Ostilio, Collette, Philips, and Garraux (2012) used fast event-related fMRI and a weighted parametric analysis to show that, over and above mere response conflict, the NCE is related to activity changes in a cortico-subcortical network, involving the cortical SMA and subcortical striatum, the input nucleus of the BG.

### The Role of the BG in Response Inhibition

Understanding the functional anatomy of inhibitory motor and cognitive control processes during RT tasks is the current goal of many studies in cognitive neuroscience (Schmidt, Leventhal, Mallet, Chen, & Berke, 2013; Cai, Oldenkamp, & Aron, 2011; Seiss & Praamstra, 2004; Redgrave, Prescott, & Gurney, 1999; Mink, 1996; Alexander & Crutcher, 1990). Here, we focus on a computational model of the BG (Wiecki & Frank, 2013; Frank, 2006). The model supports (a) stimulus-triggered action selection, (b) selective and nonselective inhibitory control, (c) response–conflict management, and (d) volitional action generation. There are three main pathways linking frontal cortex with the BG (Figure 7): the direct “go” pathway, the indirect “no-go” pathway, and the hyperdirect pathway. The direct “go” pathway (cortex → striatum “go” → GPi → thalamus → cortex) and indirect “no-go” pathway (cortex → striatum “no-go” → GPe → GPi → thalamus → cortex) together implement a selective gating mechanism by facilitating or suppressing each of the candidate motor actions relevant in a given task.

After stimulus onset, sensory cortical representations project to the cortical response units in the SMA, whose activity is modulated by the thalamus. By itself, this SMA activation is not sufficient to initiate response generation immediately because the thalamus is under tonic inhibition from the BG's output nucleus, the GPi (globus pallidus internal segment; Figure 7). The tonic inhibition is removed by activation of striatal go units in the direct pathway, which inhibit the GPi and therefore disinhibit the thalamus. Acting in opposition to the direct go pathway, striatal no-go units in the indirect pathway further excite the GPi indirectly by removing tonic inhibition from GPe (globus pallidus external segment) to GPi. Direct pathway activity thus results in gating of a manual response (go), whereas indirect pathway activity prevents its gating (no-go). One such gating mechanism is assumed to exist for each candidate response. Lateral inhibition between individual responses in SMA (or feedforward inhibition from SMA to M1) in case of response conflict is detected by the ACC (Botvinick, Cohen, & Carter, 2004; van Veen & Carter, 2002) and activates the hyperdirect pathway (ACC → STN → GPi). This prevents premature responses by raising thresholds for all candidate responses. This model is able to gate stimulus-driven responses and to automatically slow down when those responses get into conflict.

However, in most response–conflict tasks, an initial (primed) response gets activated but then needs to be suppressed in favor of a more controlled response. To allow executive control to inhibit and override response activation, Wiecki and Frank (2013) add an executive control layer (assumed to reside in DLPFC). Once DLPFC determines the correct response based on integrating stimuli and task instructions, it (1) projects to the correct SMA response units supporting the controlled response, (2) activates striatal no-go units to prevent gating of the initial response, and (3) activates striatal go units to gate the controlled (correct) response. If due to random noise executive control is slower on some trials, it might be too late to activate the correct rule representation before the primed response is gated (Gratton, Coles, & Donchin, 1992). Note that this leaves the model with two inhibition mechanisms: global threshold adjustment (hyperdirect pathway) and selective response inhibition (indirect pathway; Wiecki & Frank, 2013).

This model is able to explain the PCE in the no-mask conditions of Experiment 1. The prime activates its associated response representation in SMA as well as a response-specific go signal in the direct pathway. If this gating signal crosses the global response threshold, the thalamus is disinhibited, and an overt response is emitted that is exclusively controlled by the prime. This response is always correct when the prime is consistent and always incorrect when it is inconsistent, thus explaining the PCE in the conditional accuracies, that is, fast errors on inconsistent trials. On trials where the global response threshold is initially not crossed, time passes on and the target eventually activates the SMA representation of its associated response. This leads to response conflict when the target is inconsistent with the visible prime and to the temporary decline in *h*(*t*) in the no-mask inconsistent trials due to the temporary global raising of response thresholds by the hyperdirect pathway. The DLPFC eventually recognizes the target as the imperative stimulus and activates SMA and striatal go units for the controlled response and no-go units for the primed response. However, this process cannot yet explain the response-specific, mask-locked NCE because the identity of the target response is not yet known by DLPFC right after mask onset detection.

### Active, Selective Response Inhibition as the Cause of the NCE

In the stop signal task (Aron, 2011; Aron & Poldrack, 2006), a signal is presented at a variable delay after an imperative go stimulus, instructing the participant to withhold responding. Wiecki and Frank (2013) simulated this task by including the right VLPFC (also known as the right inferior frontal cortex) with direct projections to the subthalamic nucleus (STN), the key structure of the hyperdirect pathway (Figure 7). Specifically, the stop signal excites the right VLPFC, which excites the STN, which raises all response thresholds. Furthermore, in addition to this fast and nonselective mechanism, the right VLPFC selectively inhibits the active response via activating the corresponding population of striatal no-go units (perhaps via DLPFC as in Figure 7). Critically, to account for empirical observations, this selective mechanism is slower but remains active after the STN returned to baseline in the model of Wiecki and Frank (2013). We propose that this active dual reaction of VLPFC to a stop signal can explain the emergence of the NCE in masked priming, as follows.

We assume that the prime triggers a fast automatic response, that the mask acts as a stop signal detected by VLPFC, and that the target triggers the controlled response through DLPFC. The first mask-triggered mechanism, a fast, nonselective, and transient raising of response thresholds (hyperdirect pathway), can explain why response hazards tend to drop after the earliest prime-triggered responses in conditions L-S and L-L in Experiment 2 (see Figures S6–S11); in conditions S-S and S-L and the three masked prime conditions in Experiment 1, this mask-triggered transient global inhibition prevents observing an overt PCE. The second mechanism, a slower, but lasting and selective activation of striatal no-go units can explain why the NCE emerges: It selectively inhibits the primed response, leading to disinhibition of the antiprime response due to lateral inhibition in SMA—in other words, thrust reversal (Schmidt et al., 2015). When the target signal then activates the gating of the controlled response, this antiprime activation will have created a head-start in correct response activation in inconsistent trials but leads to temporary response conflict in consistent trials in SMA. The special feature of the masked priming paradigm is thus that the cues for activating the primed and controlled response are separated in time, compared with other response inhibition tasks such as the antisaccade task, the Simon task, and the Stroop task. A neural stop signal response might also be invoked by target onset in both unmasked prime conditions of Experiment 1, which would explain why hazard eventually increases at a slower rate and reaches a lower peak when the prime is visible (see Figure 5).

In summary, our results are in line with the mask-triggered inhibition account (Jaśkowski, 2007, 2008; Jaśkowski et al., 2008; Jaśkowski & Przekoracka-Krawczyk, 2005), which holds that the mask stimulus can trigger selective response inhibition directed specifically against the initial response. Active selective inhibition via the indirect pathway of the BG is different from mere lateral inhibition in SMA (or feedforward inhibition from SMA to M1), because it occurs even if prime and target afford the same response and never generate a response conflict (Schmidt et al., 2015). We conclude that the NCE is due to active, selective, stimulus-triggered inhibition of a premature response, likely involving the indirect pathway of the BG.

## Acknowledgments

We would like to thank Christina Arnold for help with data collection.

Reprint requests should be sent to Sven Panis, Experimental Psychology Unit, Faculty of Social Sciences, University of Kaiserslautern, Kaiserslautern, Germany, or via e-mail: sven.panis@sowi.uni-kl.de.

## Notes

Although we used a fixed response collection period of 800 msec in each trial of Experiment 1, most responses occurred before 600 msec after target onset. For analysis purposes, we therefore censored all trials at 600 msec after target onset. This means that trials without a response in the first 600 msec after target onset were treated as right-censored observations that are not ignored but contribute to each bin's risk set—see Table 1.

Standard errors for *h*(*t*), *P*(*t*), and *ca*(*t*) can be estimated using the formula for a proportion *p*—the square root of {*p*(1 − *p*)/*N*}—where *N* equals, respectively, the risk set for bin *t*, the total number of trials, and the number of observed responses in bin *t*. The standard errors for *S*(*t*) were estimated using the formula of Singer and Willett (2003, p. 350).

The complementary log–log link is preferred over the logit link for a discrete time hazard model when the events can in principle occur at any time during each time bin, which is the case for RT: cloglog[*h*(*t*)] = ln{−ln[1 − *h*(*t*)]}; logit[*ca*(*t*)] = ln[*ca*(*t*)/1 − *ca*(*t*)]. Inverses of the links: *h*(*t*) = 1 − exp{−exp{cloglog[*h*(*t*)]}}; *ca*(*t*) = exp{logit[*ca*(*t*)]}/(1 + exp{logit[*ca*(*t*)]}).

Proactive control can involve more than top–down attentional facilitation and inhibition of task-relevant sensory channels. For example, in the model of Wiecki and Frank (2013), speed–accuracy adjustments are implemented by increasing functional connectivity between frontal motor regions and striatum to decrease the decision threshold under speed emphasis. Also, response caution can be increased by increasing the baseline VLPFC activity to slow responding via the VLPFC-STN hyperdirect pathway (see Figure 7).