Obsessive‑compulsive disorder (OCD) is characterized by an insight‑action dissociation, in which people with OCD recognize that their behavior is irrational but still struggle to inhibit habitual responses. This dissociation may be related to abnormally strong motivational biases, reflected in excessive tendencies to approach reward and avoid punishment. We employed a motivational Go/NoGo learning task, combined with computational modeling and electroencephalography (EEG), to investigate how 36 people with OCD and 37 healthy controls (HC) regulate maladaptive biases during motivated action. People with OCD showed stronger Pavlovian bias and lower learning rates. Similar to HC, people with OCD also showed increased midfrontal theta power related to conflict detection and to the generation of a control demand to increase the weighting of instrumental action values during choice, suggesting that they were able to detect the mismatch between their behavior and task goals. However, in OCD, conflict‑related theta enhancement overlapped with the response window, indicating that control signals emerged or arrived too late to effectively influence choice. Midfrontal‑motor theta phase synchrony provided the strongest model evidence for the modulation of maladaptive biases in OCD, yet this pathway showed no significant conflict‑related enhancement and failed to effectively modulate motivational biases under conflict. Taken together, these findings suggest a neural mechanism underlying the insight‑action dissociation in OCD and identify midfrontal‑motor theta phase synchrony as a potential treatment target.

Task performance: Motivated action was biased by cue and outcome valence in OCD

We employed a motivational Go/NoGo learning task with multiple active response options (Fig 1). Participants learned via trial and error to respond to visual cues by executing a Go (left or right button press) or NoGo response to gain rewards (“win” cues) and avoid losses (“avoid” cues). Because the task included multiple Go response options, it could distinguish Pavlovian response tendencies driven by cue valence from instrumental learning bias shaped by outcome feedback.

To examine whether participants learned the instrumental actions and to determine whether motivational valence biased behavioral activation, we first analyzed Go response probability. In these logistic mixed‑effects models, required action (Go versus NoGo) and valence (“win” versus “avoid” cues) were entered as within‑subject predictors, and these models were fitted separately within the healthy controls (HC) and OCD groups. Behavioral analyses showed that both groups successfully learned the task rules (Fig 2): go responses occurred more often for Go cues than NoGo cues in both groups (HC: β = 1.86, OR = 6.42, χ²(1) = 334.05, p < 0.001; OCD: β = 1.20, OR = 3.32, χ²(1) = 94.44, p < 0.001). However, relative to “avoid” cues, participants overall made more Go responses for “win” cues (HC: β = 0.34, OR = 1.40, χ²(1) = 19.76, p < 0.001; OCD: β = 0.39, OR = 1.48, χ²(1) = 41.44, p < 0.001), which indicated that motivational valence strongly biased Go responding. To test whether these effects differed between groups, we then fitted a combined logistic mixed‑effects model in which Group (HC versus OCD) was added as a between‑subject predictor, together with required action, valence, and their interactions. This model revealed a significant group × required action interaction (β = −0.65, OR = 0.52, χ²(1) = 17.07, p < 0.001). Compared with HC participants, the OCD group made more Go responses to NoGo cues (β = 0.68, OR = 1.98, z = 3.62, p < 0.001) but fewer Go responses when Go responses were required (β = −0.61, OR = 0.54, z = −2.76, p = 0.006). Furthermore, to determine whether reduced Go responding in OCD was accompanied by impaired performance when Go responses were required, we conducted an additional logistic mixed‑effects model restricted to Go cues. In this model, the dependent variable was Go‑cue accuracy, and valence (“win” versus “avoid” cues), group (HC versus OCD), and their interaction were entered as predictors. Consistent with the pattern above, accuracy on Go cues was lower in the OCD group than in the HC group (β = −0.75, OR = 0.47, χ²(1) = 8.89, p = 0.003). Finally, to assess learning dynamics under motivational conflict, we extracted condition‑specific learning slopes from the trial‑by‑trial Go response probability model described above. These slopes captured the change in Go response probability over trials. For example, for NGW cues, in which the correct response was to withhold a Go response, a more negative slope would indicate faster acquisition of response inhibition (i.e., a rapid reduction in erroneous Go responses). The OCD group showed slower acquisition of response inhibition only for NGW cues (HC_slope = −0.011; OCD_slope = −0.008; t(71) = −2.41, p = 0.019, Cohen’s d = −0.56), but not for GA cues.

Compared with healthy controls, people with OCD showed heightened Pavlovian bias and reduced learning rates

Previous studies have shown that motivational biases in Go/NoGo responding come from both cue‑valence‑driven Pavlovian response bias and outcome‑feedback‑driven instrumental learning bias [50]. As shown in Table 1, we built a Behavioral Model Family (M1–M3c) to separate the roles of these two mechanisms in motivated action selection. We compared model evidence using the Watanabe‑Akaike Information Criterion (WAIC), which provides a complexity‑penalized estimate of model fit and reduces the likelihood that improved fit merely reflects over‑parameterization. M1 was a baseline reinforcement‑learning model with only learning rate (ε) and feedback sensitivity (ρ). M2 added a general Go bias (b). M3a further added a Pavlovian bias (π) to capture response tendencies driven by cue valence. M3b added an instrumental learning bias (κ) to capture asymmetric learning shaped by outcome valence and required action. M3c combined all of these parameters to test whether motivational biases could be explained by the combined effects of Pavlovian response bias and instrumental learning bias.

As shown in Fig 3A and 3C, and in Table 1, in both groups, Model M3c, which incorporated both Pavlovian bias (π) and instrumental learning bias (κ), provided the best fit (HC: WAIC = 18585.78, ΔWAIC = −1353.48, R² = 59.75%; OCD: WAIC = 24543.96, ΔWAIC = −2239.49, R² = 42.41%) when compared with models without either or both of those parameters (M1, M2, M3a, and M3b). As shown in Fig 3B and 3D, actual average participant behavior was close to the predictions of the winning model. Altogether, our results indicated that instrumental responding was biased by both cue valence and outcome valence, consistent with previous research [50]. Moreover, as shown in Fig 3E, group‑level posterior comparisons from M3c (Δ = HC − OCD) indicated a stronger Pavlovian bias in OCD (Δπ ≈ −0.56, 95% highest‑density interval (HDI) [−1.04, −0.04], P(Δπ < 0) = 0.991), along with a higher learning rate in HC than OCD (Δϵ ≈ +0.012, 95% HDI [0.003, 0.022], P(Δϵ > 0) = 0.986).

Midfrontal theta in OCD supports conflict detection and modulation of motivational biases

After confirming that motivational biases in people with OCD were affected by both Pavlovian bias and instrumental learning bias, we next examined the neural mechanisms that modulate these biases during motivational conflict. In previous studies, conflict detection has most often been measured using event‑related potentials, especially the N2 component [55, 56]. However, the results of studies examining the N2 in OCD have been inconsistent [57– 60], making it difficult to reach a clear conclusion about conflict detection in this group. In contrast, midfrontal theta is considered a more reliable time‑frequency marker of conflict detection [49 61, 62] and may also play a role in the dynamic regulation of downstream cognitive control processes [54, 63]. Based on this, we examined midfrontal theta activity in people with OCD during motivational conflict and tested whether midfrontal theta was involved in modulating motivational biases. We hypothesized that, compared with motivationally congruent cues (Go‑to‑Win, NoGo‑to‑Avoid), motivationally incongruent cues (Go‑to‑Avoid, NoGo‑to‑Win) would elicit stronger midfrontal theta power. We further hypothesized that this increase would be especially strong in trials where motivational conflict was correctly resolved. To test these hypotheses, we performed a time‑based permutation test on correct trials over predefined midfrontal channels.

The first step in the electroencephalography (EEG) analysis was to investigate whether midfrontal theta reflects the detection of conflict as found in previous research [50]. If midfrontal theta is involved in conflict detection, it should not only distinguish motivationally incongruent from congruent cues, but also increase as Pavlovian‑instrumental conflict becomes stronger under incongruent conditions. Therefore, we first assessed whether cue‑locked midfrontal theta differentiated motivationally incongruent from congruent cues across groups. More specifically, we performed a time‑based permutation test on cue‑locked, trial‑averaged midfrontal theta power in the 4–8 Hz band to identify time windows showing significant differences between motivationally incongruent and congruent cues. This analysis was restricted to correct trials to minimize the potential contribution of error‑related theta activity. As shown in Fig 4A and 4B, cluster‑based permutation tests confirmed that both groups showed robust conflict‑related theta power increases within cue‑locked windows (HC: 400–650 ms, cluster‑corrected p = 0.002; OCD: 424–800 ms, cluster‑corrected p = 0.002). Cluster‑window averaged contrasts confirmed large effects in both the HC group (HC: t(36) = 6.67, p < 0.001, Cohen’s d_z = 1.10) and the OCD group (OCD: t(35) = 4.73, p < 0.001, Cohen’s d_z = 0.79). We next tested the relationship between midfrontal theta power and Pavlovian‑instrumental conflict strength. In this study, Pavlovian‑instrumental conflict was defined as the extent to which the instrumental value of NoGo exceeded that of Go in win trials, and the extent to which the instrumental value of Go exceeded that of NoGo in avoid trials (Equation 7). As shown in Fig 4C and 4E, trial‑by‑trial analyses further revealed that midfrontal theta power positively correlated with Pavlovian‑instrumental conflict strength in both groups (HC: t(36) = 2.54, p = 0.016, Cohen’s d_z = 0.42; OCD: t(35) = 4.80, p < 0.001, Cohen’s d_z = 0.80). Consistent with these findings, an exploratory event‑related potential (ERP) analysis showed significantly enhanced midfrontal N2 responses to incongruent relative to congruent cues in both groups, with no reliable group difference during incongruent trials (see Text B and Figs A–B in S1 File) [57, 58, 64– 69]. Together, these findings suggested that midfrontal theta in the OCD group not only distinguished motivational conflict conditions, but also increased with conflict strength, with convergent N2 evidence further supporting preserved cue-level conflict detection.

To examine whether the magnitude of conflict‑related theta enhancement differed between groups, we extracted the theta contrast (incongruent–congruent) from the significant cue‑locked time window and compared this contrast between HC and OCD participants. Between‑group comparisons showed no significant difference in conflict‑related theta amplitude (incongruent–congruent contrast: t(71) = 1.19, p = 0.237, Cohen’s d = 0.28), but temporal profiles differed between groups. As shown in Fig 4A, in the HC group, cue‑locked theta enhancement preceded mean reaction time (679 ± 204 ms), and a subsequent response‑locked analysis identified a robust pre‑response component (−550 to −126 ms; cluster‑corrected p = 0.002). The cluster‑window averaged contrast further confirmed stronger theta power for Go‑to‑Avoid than Go‑to‑Win trials (t(36) = 4.28, p < 0.001, Cohen’s d_z = 0.70). However, in the OCD group the cue‑locked theta window partially overlapped mean reaction time (700 ± 208 ms), and no reliable pre‑response theta component was observed (Fig 4B). Notably, trial‑level linear mixed‑effects analyses showed that the between‑group difference in conflict‑related pre-response theta remained reliable after controlling for trial‑level RT, subject‑level RT variability, and trial order (see Text C and Fig C in S1 File). Furthermore, mean reaction times did not differ significantly between HC and OCD groups (t(71) = −0.44, p = 0.661, Cohen’s d = −0.10). Thus, although both groups showed robust cue-locked midfrontal theta related to motivational conflict, only the HC group showed a reliable conflict-related theta enhancement before successful response execution.

We further tested whether pre‑response theta was directly related to behavioral performance. A single-trial generalized linear mixed model (GLMM) showed that pre‑response theta significantly predicted accuracy (β = 0.33, SE = 0.03, z = 11.86, p < 0.001, OR = 1.39, 95% CI [1.31, 1.46]). However, the slope of theta predicting accuracy was significantly lower in the OCD group than in the HC group (HC − OCD slope difference: β = 0.33, SE = 0.06, z = 6.00, p < 0.001, OR = 1.39, 95% CI [1.25, 1.55]). Importantly, these findings suggested that pre‑response theta activity remained behaviorally relevant in people with OCD, but unlike in HC participants, it was not selectively enhanced by motivational conflict before response execution. Full fixed‑effect estimates, confidence intervals, odds ratios, and model-fit statistics for these logistic mixed‑effects models were provided in S1 Table.

After showing that midfrontal theta in the OCD group reflected conflict detection, we next tested whether the conflict‑related signal was involved in reducing motivational biases in behavior. We extended our computational modeling framework and constructed a theta modulation model family (M4a–M4d) based on the winning behavioral model M3c [50,70]. Before incorporating trial-by-trial theta estimates into the computational models, we examined whether they were consistent with the trial‑averaged findings. Single-trial mixed‑effects analyses confirmed significant conflict‑related increases in midfrontal theta power in both groups (see Text D in S1 File) [2,44,49]. Trial‑by‑trial midfrontal theta power (θ_t) was added to the model as a modulation signal, and the parameter β was used to test how theta acted on different components of the model. Specifically, these models tested whether midfrontal theta modulated the Pavlovian response tendencies (M4a), the instrumental contribution, reflecting the weighting of instrumental action values during choice (M4b), and/or the balance between the Pavlovian bias and instrumental contribution (M4c). M4d further tested whether theta modulated instrumental learning bias, that is, whether theta activity during decision-making influenced later learning updates. We then compared these models to determine how midfrontal theta modulated motivational biases in the OCD group.

As shown in Table 1 (M4a–M4d) and Fig 4D and 4F, this model family was designed to adjudicate between alternative computational mechanisms through which trial‑by‑trial midfrontal theta relates to biased action selection. In both groups, M4b, which used learned Q value as internal variable tracking instrumental action values and allowed theta power to scale their contribution to choice, provided the strongest model evidence (HC: WAIC = 18454.40, ΔWAIC = −131.38, R² = 60.04%; OCD: WAIC = 24419.47, ΔWAIC = −124.49, R² = 42.83%). Within M4b, the theta‑modulation parameter (β_θ‑power) showed negative subject‑level posterior median estimates in both groups (HC: 89.19% of participants < 0; OCD: 72.22% < 0), with no between‑group difference (Δ_HC−OCD ≈ −0.21, P(Δ < 0) = 0.786). The winning model suggested that conflict‑related midfrontal theta signals primarily modulated motivational biases in action by increasing the weighting of instrumental action values during choice. Additionally, given that instrumental learning is updated following feedback, we examined feedback-locked midfrontal theta activity for evidence of modulation related to instrumental learning bias. Consistent with the model comparison, feedback-locked theta primarily reflected feedback outcome and showed no significant modulation associated with instrumental learning bias (see Text E and Figs D–E in S1 File) [71–73].

Specific impairment of midfrontal network coupling is associated with ineffective modulation of motivational biases in OCD

In the OCD group, we found that motivationally incongruent trials induced a significant increase in midfrontal theta, and that stronger theta activity was associated with stronger instrumental contribution to choice, suggesting that conflict‑related control signals were still present. However, people with OCD still showed maladaptive behavior, suggesting that an increase in local midfrontal theta activity alone may not be sufficient for effective modulation of motivational biases. Moreover, compared with healthy controls, the increase in midfrontal theta did not mainly occur before the correct response in the OCD group, but instead overlapped more with the behavioral response. Therefore, we asked whether the core deficit in OCD lies not in generating conflict‑related control signals, but in ineffective transmission to downstream executive systems through network coupling. Previous studies have shown that increased theta phase synchrony between the midfrontal cortex and task‑relevant regions (i.e., lPFC and motor cortex) is associated with conflict processing [50,74]. We next examined whether motivational conflict affected ISPS between midfrontal channels and task‑related sites, in order to test whether delayed conflict‑related control in OCD influenced modulation of motivational biases at the network level. To prevent execution‑related motor activation from biasing synchrony estimates [44], analyses of motor targets focused on non‑executing sites (ipsilateral Go and NoGo). This approach minimized confounding from overt motor responses, allowing us to dissociate conflict‑related coupling from execution‑driven effects.

To examine conflict‑related network coordination, we extracted theta‑band ISPS values from correct trials within the significant cue‑locked theta window and used repeated-measures analyses of variance (ANOVAs) with valence (“win” versus “avoid” cues) and required action (Go versus NoGo) as within‑subject factors to test whether MFC‑lPFC and MFC‑motor phase synchrony increased for motivationally incongruent relative to congruent cues. As shown in Fig 5A and 5B, theta phase synchrony analyses showed reliable conflict‑related increases in the MFC‑lPFC phase synchrony in both groups (incongruent > congruent; HC: F(1,36) = 10.69, p = 0.002, η_p² = 0.23; OCD: F(1,29) = 27.32, p < 0.001, η_p² = 0.49). However, MFC‑motor phase synchrony differed between groups. HC participants showed increased conflict‑related phase synchrony between the MFC and nonexecuting motor sites (ipsilateral Go and bilateral NoGo responses; F(1,36) = 14.76, p < 0.001, η_p² = 0.29), consistent with inhibitory control over non‑target actions. In contrast, MFC‑nonexecuting motor phase synchrony did not differ between conflict and non‑conflict conditions in OCD (F(1,29) = 0.25, p = 0.621, η_p² = 0.01). Taken together, people with OCD showed no significant conflict‑related effect in phase synchrony between MFC and non‑executing motor regions, suggesting that network coordination related to non‑target action inhibition may be impaired during conflict.

The previous trial‑averaged results showed that the OCD group still had increased conflict‑related theta phase synchrony between MFC and lPFC, but lacked the significant conflict‑related phase synchrony effect between MFC and motor cortex that was observed in healthy controls. However, a key question was whether abnormalities in theta phase synchrony were associated with the modulation of motivational biases during conflict. Therefore, we built an ISPS Modulation Family of models (M5a–M5b) based on the theta modulation model of instrumental contribution (M4b). In these models, single‑trial theta phase synchrony replaced local theta power (θ_t) as the modulation signal, allowing us to test whether MFC‑lPFC synchrony (ISPS_lPFC,t) and MFC‑motor synchrony were involved in the modulation of instrumental contribution. Before fitting these models, we examined whether the trial‑by‑trial synchrony estimates reproduced the corresponding trial‑averaged effects. Single‑trial mixed‑effects analyses confirmed significant conflict‑related modulation of MFC‑lPFC synchrony in both groups, whereas the execution‑dependent conflict effect in MFC‑motor synchrony was evident in healthy controls but not in the OCD group (see Text F in S1 File) [34,44,75–78]. These supplementary results indicated that the trial‑by‑trial synchrony estimates captured the principal subject‑level patterns observed in the trial‑averaged analyses and were therefore suitable for subsequent computational modeling. In addition, the trial‑averaged statistical analyses mainly focused on ipsilateral motor regions in order to reduce motor‑related noise. In the computational models, however, we used contralateral motor signals because the contralateral motor cortex is more directly involved in behavioral output. This allowed us to test whether MFC‑motor synchrony (ISPS_{motor_contra,t}) was associated with the modulation of motivational biases.

As shown in Table 1 (M5a–M5b), we tested whether theta phase synchrony provides greater explanatory power than local theta power in the modulation of motivational biases. In the models testing modulation of the instrumental contribution (Fig 5C, Table 1 M5a and M5b), adding single‑trial theta phase synchrony as the moderator improved model evidence relative to the corresponding theta‑power model. For HC participants, model comparison favored the MFC‑lPFC theta phase synchrony model (M5a; WAIC = 18435.32; ΔWAIC=−19.08; R² = 60.07%) over M4b, and β_ISPS-lPFC was stably negative (89.19% of participants < 0), indicating that stronger MFC‑lPFC theta phase synchrony increased the weighting of instrumental action values. In contrast, in the OCD group, the best‑fitting model was the MFC‑motor theta phase synchrony model (M5b; WAIC = 24372.24; ΔWAIC = −47.23; R² = 43.05%), but the group‑level modulation parameter was statistically negligible (β_ISPS‑motor: mean = +0.009; 95% HDI [−0.038, 0.053]; Pr(β < 0) = 0.35), and the Bayes factor favored the absence of a directional effect (BF₁₀ = 0.008). Thus, although MFC‑motor synchrony offered the best account of choice behavior in the OCD group, its group‑level influence on the weighting of instrumental action values was weak or heterogeneous rather than consistently directional.

Parameter estimates from the baseline model (M3c; Fig 3E) confirmed that people with OCD exhibited an increased Pavlovian bias. We next sought to determine whether this exaggerated Pavlovian bias was linked to abnormal modulation at the network level. Specifically, we examined whether functional coordination between midfrontal and task‑related regions was associated with the modulation of Pavlovian bias during motivational conflict, providing a more comprehensive network‑level account of OCD pathology. We fitted a parallel set of extended models in which ISPS was used as the modulation parameter. These models tested whether theta phase synchrony between MFC and lPFC (M5c) or motor cortex (M5d) modulated the Pavlovian bias parameter on a trial‑by‑trial basis as motivational conflict varied.

In the models with the Pavlovian bias parameter π (Fig 5D, Table 1 M5c and M5d), compared with M4a, the model in which the MFC‑motor phase synchrony scaled π (M5d) provided a better fit in both groups (HC: WAIC = 18476.93, ΔWAIC = −14.79, R² = 60.07%; OCD: WAIC = 24339.93, ΔWAIC = −93.97, R² = 43.13%). The synchrony‑scaling parameter (β_ISPS‑motor) was negative (89.19% of participants < 0), indicating that stronger synchrony was associated with reduced Pavlovian bias in the HC group. Notably, the β_ISPS‑motor parameter estimate in the OCD group had a slightly negative posterior mean, but the posterior distribution showed no consistent directionality (mean = −0.005; 95% HDI [−0.708, 0.682]; Pr(β < 0) = 0.51; BF₁₀ = 0.12). Although MFC‑motor phase synchrony improved model fit relative to theta power, it did not provide evidence for a reliable group‑level inhibitory effect on Pavlovian bias in the OCD group.

Heterogeneous regulatory orientations of midfrontal‑motor coupling and their clinical relevance in OCD

Previous results showed that, in the OCD group, the MFC‑motor cortex theta phase synchrony model was the best‑fitting model for modulation of both the instrumental contribution (Fig 5C, right panel; M5b) and Pavlovian bias (Fig 5D, right panel; M5d). Although these two effects were estimated in separate models, they correspond to two theoretically complementary routes through which motivational conflict can be modulated by increasing the weighting of instrumental action values and suppressing Pavlovian response tendencies. However, the group‑level modulation effects did not show a consistent direction in those models. These results suggested that the underlying regulatory mechanism of phase synchrony was characterized by substantial inter‑individual heterogeneity. Consequently, we shifted from group‑averaged analyses to an exploratory individual‑level approach to examine how these two synchrony‑related modulation estimates were distributed across participants.

As shown in Fig 5C and 5D, we extracted the beta parameters from the winning synchrony models quantifying how theta phase synchrony scaled the weighting of instrumental action values and Pavlovian bias, and plotted them in a common coordinate space as a descriptive individual‑differences visualization of regulatory orientation (Fig 6A and 6B). When Pavlovian response tendencies conflicted with instrumental demands, healthy controls modulated motivational biases through a complementary pattern of theta phase synchrony between MFC and task‑relevant regions. In Fig 6A and 6C, most healthy controls fell into the lower‑left-hand quadrant, indicating stronger MFC‑lPFC theta phase synchrony associated with increased weighting of instrumental action values during choice, together with stronger MFC‑motor theta phase synchrony associated with inhibition of Pavlovian response tendencies. By contrast, in people with OCD, MFC‑motor theta phase synchrony emerged as the predominant pathway associated with modulation of motivational biases, while individual regulatory orientations showed a broader and more heterogeneous distribution within the regulatory-orientation space (Fig 6B and 6C). As shown in Fig 6B, people with OCD falling in the upper‑left quadrant tended to inhibit Pavlovian response tendencies at the cost of reduced instrumental weighting, whereas those falling in the lower‑right quadrant showed increased instrumental weighting accompanied by amplified Pavlovian response tendencies. This divergent distribution highlights marked inter‑individual heterogeneity in OCD, where opposing regulatory tendencies may have offset directional effects at the group level. To address the possibility that the separately estimated synchrony effects on instrumental weighting and Pavlovian bias might reflect overlapping variance, we additionally fitted joint models in which both modulation effects were estimated simultaneously within the same model likelihood. The jointly estimated parameters reproduced both the group‑specific regulatory‑orientation patterns and the association between regulatory orientation and obsessive‑thought severity observed in the primary analysis. These supplementary analyses supported the robustness of the individual-level regulatory‑orientation findings (see Text G and Figs F–G in S1 File).

To test whether this heterogeneity was clinically meaningful, we combined each OCD participant’s β estimates for scaling Pavlovian bias and instrumental contribution into a single angular index (Regulatory orientation angle, Φ_reg). Importantly, Φ_reg was treated as a continuous measure of regulatory orientation rather than as a categorical subgroup label. The direction of the angle reflects the preference for modulating motivational biases by upregulating instrumental action values or suppressing Pavlovian bias. We found that Φ_reg was positively correlated with obsessive‑thought severity (Fig 6C, right), and this association remained significant after controlling for anxiety and depression (r = 0.38, p = 0.022), and after additionally controlling for trait impulsivity (r = 0.34, p = 0.042). These results indicated a clinically meaningful link between regulatory orientation and symptoms. Higher severity of obsessive thoughts was associated with a stronger tendency to prioritize increased instrumental contribution when modulating maladaptive biases under motivational conflict, but this tendency was accompanied by a simultaneous amplification of Pavlovian bias.

Ethics statement

The study was conducted in accordance with the principles expressed in the Declaration of Helsinki and was approved by the Ethics Committee of the School of Psychology, South China Normal University (approval number: SCNU‑PSY‑2022‑343). All participants were right‑handed and provided verbal informed consent prior to participation.

Participants

Sample size estimation was conducted using G*Power 3.1.9.7 [132]. Because exact power estimation for the mixed‑effects models, permutation-based EEG analyses, and hierarchical computational models used in the present study is not directly implemented in G*Power, power was approximated using the corresponding subject‑level repeated‑measures designs. For the primary within‑participant valence × required action effect, a repeated-measures design with four measurements indicated that 36 participants were required to achieve 95% power to detect a medium effect (f = 0.25, α = 0.05), assuming a correlation of 0.50 among repeated measures and ε = 1. Both groups met this requirement (37 healthy controls and 36 people with OCD). For the primary group × valence × required action interaction, a two‑group repeated‑measures within‑between interaction indicated that 62 participants were required to achieve 99% power under a more stringent α = 0.01, assuming the same effect size (f = 0.25), correlation among repeated measures (0.50), and ε = 1. For the secondary individual-difference analyses examining associations between regulatory orientation and Y‑BOCS obsessive-thought severity within the OCD group, a correlation‑based a priori power analysis indicated that 32 participants were required to detect a large correlation (ρ = 0.50) with 85% power at α = 0.05 using a two‑tailed test.

We recruited 40 people with OCD from the Affiliated Kangning Hospital of Ningbo University and 40 healthy controls matched to the OCD group on age, sex, and years of education. After excluding seven participants (HC = 3, OCD = 4) with excessive artifacts in EEG preprocessing, data from 36 participants with OCD and 37 healthy controls were included in subsequent analysis. All participants were right‑handed and provided verbal informed consent prior to participation. The study was approved by the Ethics Committee of the School of Psychology, South China Normal University (approval number: SCNU‑PSY‑2022‑343) and was conducted in accordance with the Declaration of Helsinki.

For the OCD group, inclusion criteria were: (1) a primary diagnosis of obsessive‑compulsive disorder confirmed by licensed psychiatrists according to the Chinese version of DSM-5; (2) a Yale-Brown Obsessive Compulsive Scale total score ≥ 16; and (3) age between 18 and 50 years. Participants with any current or lifetime psychiatric diagnosis other than OCD were excluded, including depressive disorders such as major depressive disorder, anxiety disorders such as generalized anxiety disorder, substance use disorders, bipolar disorder, post‑traumatic stress disorder, and personality disorders. Additional exclusion criteria were a history of brain injury or any neurological disorder and receipt of electroconvulsive therapy within the three months prior to enrollment. Thus, everyone included in the final OCD sample had OCD as the primary diagnosis and did not meet criteria for current or lifetime psychiatric comorbidities. Furthermore, those in the OCD group were not medication‑free at the time of testing and remained on stable psychotropic medication during the experiment. Medications included selective serotonin reuptake inhibitors (SSRIs; n = 23), serotonin-norepinephrine reuptake inhibitors (SNRIs; n = 1), atypical antipsychotics (n = 8), benzodiazepines (BZDs; n = 5), non-benzodiazepine hypnotics/anxiolytics (n = 2), and antimanic agents (n = 1). Medication categories were not mutually exclusive, and some people with OCD received more than one class of drug. HC participants had no current or lifetime psychiatric disorder and no first‑degree family history of OCD. For the HC group, additional inclusion criteria were age between 18 and 50 years, and exclusion criteria were a history of brain injury or any neurological disorder and use of any psychotropic medication within the three months prior to study participation. Demographic characteristics and clinical scores appear in Table 2.

Motivational Go/NoGo learning task

To dissociate Pavlovian response tendencies from instrumental learning processes, we employed a motivational Go/NoGo learning task [50]. In this task, participants learned by trial and error to make optimal responses to different cues in order to maximize rewards for win cues and minimize punishments for avoid cues. As illustrated in Fig 1, the learning phase used eight gem‑shaped cues as stimuli, each of which was presented 60 times. Each trial began with a cue presented for 1,300 ms followed by a fixation cross for 700 ms. Feedback was then displayed for 1,000 ms based on the participant’s performance. Each trial concluded with an inter‑trial interval ranging from 1,000–1,750 ms in steps of 250 ms. After learning, participants completed a forced‑choice transfer task in which pairs of previously learned cues were presented in counterbalanced positions (upper and lower) on the screen and they selected the cue they believed was more likely to obtain reward. Cues were always paired across categories (i.e., Go‑to‑Win/Go‑to‑Avoid/NoGo‑to‑Win/NoGo‑to‑Avoid), and there were 48 trials in total. Behavioral results of the forced-choice transfer task confirmed successful learning of cue valence and revealed a systematic preference for Go over NoGo cues that could not be explained by differences in cumulative outcomes, indicating enhanced subjective valuation of Go relative to NoGo cues (see Text A in S1 File).

EEG data acquisition

While participants performed the task, EEG data were recorded using a 128‑channel EGI system (GSN‑HydroCel‑128; Electrical Geodesics, Eugene, OR, USA) and Net Station software. The online reference was set to Cz. Continuous EEG was recorded at a sampling rate of 500 Hz, with all electrode impedances maintained below 50 kΩ.

EEG preprocessing

All preprocessing was conducted in MATLAB (version R2022b) [133] and EEGLAB (version 2022.0) [134]. Continuous EEG data were first filtered with a 0.5 Hz high‑pass filter and a 50 Hz low‑pass filter, and were then re‑referenced offline to the weighted average of the bilateral mastoids while restoring the reference electrode signal. The data were epoched into segments starting 1.75 s before cue onset and ending 1.5 s after feedback offset, and baseline‑corrected using the 200 ms pre‑cue interval. These relatively long epochs were used to minimize edge artifacts during subsequent time‑frequency decomposition. The epoched data were then visually inspected for trial rejection. Trials were rejected if they contained electromyographic activity or other non‑neural artifacts unrelated to brain activity, whereas trials containing eye blinks were retained for subsequent independent component analysis (ICA) correction. ICA was subsequently performed using EEGLAB’s runica algorithm in extended mode, with dimensionality reduced to 64 components using principal component analysis (PCA). Components related to blinks, eye movements, muscle activity, or other artifacts clearly distinguishable from brain activity were manually identified and removed. Across participants, 4–17 components were removed, with an average of 9 components removed per participant. After ICA, bad channels were identified by visual inspection and repaired using spherical spline interpolation. The number of interpolated channels ranged from 2 to 11 per participant, with an average of 5 interpolated channels. The cleaned EEG data were then spatially filtered using surface Laplacian estimation to reduce volume‑conduction effects and emphasize local cortical activity [135,136]. This procedure reduces spurious connectivity driven by spatial smearing and thereby improves the reliability of subsequent intersite phase synchrony estimates [137].

Participants were excluded from EEG analyses if more than 35% of their trials were rejected because of excessive artifacts. Based on this criterion, seven participants were excluded, including three healthy controls and four people with OCD. Among the retained participants, the proportion of rejected trials ranged from 0.47% to 33.96%, with a mean rejection rate of 6.97%. The final EEG analyses therefore included 37 healthy controls and 36 people with OCD. The task employed a 2 × 2 factorial design crossing valence (“win” versus “avoid” cues) and required action (Go versus NoGo), yielding four experimental conditions. For the retained participants, the analyzed trial counts across the four conditions were Go‑to‑Win (85.40 ± 20.09), NoGo‑to‑Avoid (83.00 ± 17.41), NoGo‑to‑Win (70.22 ± 26.76), and Go‑to‑Avoid (74.10 ± 21.22). These trial counts indicate that EEG and computational variables were estimated from adequate numbers of observations across conditions.

Time–frequency decomposition

Time–frequency decomposition for cue‑ and response‑locked EEG data was conducted in MATLAB with complex Morlet wavelets from the FieldTrip toolbox (version 20211209) [138]. Specifically, the time series were convolved with Morlet wavelets, which can be conceptualized as sinusoidal carriers windowed by a Gaussian function and implemented as multiplication in the frequency domain. Frequencies ranged from 1 to 50 Hz in 39 logarithmically spaced steps, with the Gaussian width fixed at 4 cycles. Wavelet convolution yielded complex‑valued signals from which power and phase were extracted at each time‑frequency point and then down‑sampled to 40 Hz. For each condition, power values were averaged across trials and converted to decibel units using a condition‑averaged baseline interval from −250 to −50 ms relative to cue onset. Based on our hypotheses, we focused on midfrontal (Fz, FCz, Cz) theta‑band activity (4–8 Hz). Cue‑locked theta enhancement was defined as the time window after cue onset in which midfrontal theta power was stronger for incongruent than congruent trials. To identify the time window, we employed a time‑based permutation test (500 permutations) on cue‑locked, trial‑averaged midfrontal theta power, with congruency (congruent versus incongruent) as the within‑subject factor. Congruent trials included Go‑to‑Win and NoGo‑to‑Avoid cues, whereas incongruent trials included NoGo‑to‑Win and Go‑to‑Avoid cues. The significant time window identified by this test was then used as the theta extraction window. The resulting group‑specific windows were 400–650 ms in the HC group and 424–800 ms in the OCD group.

For the single-trial analyses used in the computational models, Laplacian‑filtered EEG data were first broadband filtered in the theta range (4–8 Hz) and Hilbert transformed. This yielded power time series, which were z-transformed and then averaged within the corresponding group-specific time windows. For the channels of interest, values were t‑weighted based on the main contrast (incongruent minus congruent). Mean theta power was then extracted from single‑trial data within the corresponding group‑specific window and used as a trial‑level EEG predictor in the computational models. The resulting power values were inverse-transformed before being entered into the computational models.

ISPS was computed from theta‑band phase angles to quantify phase coupling between the midfrontal seed cluster and two target clusters. Phase angles (φ) were used to compute intersite phase synchrony, which is taken to reflect functional connectivity between electrode sites [103,139,140]. In the theta band (4–8 Hz), ISPS was calculated at each time‑frequency point according to the following formula:

(1)

Here, N is the number of trials, i is the imaginary unit, and j and k index the seed and target electrodes, respectively. ISPS values range from 0, indicating no phase synchrony, to 1, indicating identical phase angles. The lateral prefrontal target cluster comprised bilateral frontal electrodes approximately corresponding to AF3/F3/F5/AF7 and AF4/F4/F6/AF8, whereas the motor target cluster comprised bilateral central electrodes approximately corresponding to C3/CP3 and C4/CP4. Because ISPS is sensitive to trial number, an equal number of trials was randomly selected from each condition before ISPS computation. This procedure was repeated 100 times, and ISPS values were averaged across repetitions. Condition cells with fewer than 20 trials were excluded, resulting in the exclusion of six participants from the OCD group for the ISPS analysis. ISPS values were baseline‑transformed using the −250 to −50 ms pre‑cue interval. Specifically, ISPS values were converted to percent signal change relative to the same condition-averaged baseline interval.

For the single-trial ISPS analyses used in the computational models, phase angles from the Hilbert-transformed theta-band signals were extracted to compute phase synchrony between the midfrontal seed electrodes and the lateral prefrontal and motor target electrodes within the same group-specific time windows as follows:

(2)

Here, T denotes the number of time points within the analysis window, and n indexes time points.

The seed electrodes were weighted in the same way as the power time series, whereas the target electrodes were t‑weighted according to the corresponding main ISPS contrast (lateral prefrontal: valence × required action; motor channels: congruency × motor execution). The resulting power and ISPS values were inverse‑transformed before being entered into the computational models.

In all analyses, we first defined electrode clusters of interest based on previous studies and then refined these clusters in a data‑driven manner, in a way that was orthogonal to the main contrasts of interest, because scalp potential topographies can vary substantially across participants and studies. To assess midfrontal theta power, we initially selected two central electrodes approximately corresponding to Cz and FCz in the 10–20 system, which have been shown in prior work to be particularly sensitive to conflict‑related midfrontal theta activity [136,140]. The midfrontal cluster was then refined using condition-averaged cue-locked data, which were orthogonal to the main contrast, by adding an additional frontal electrode approximately corresponding to Fz, yielding the final Fz/FCz/Cz midfrontal seed cluster. Post hoc t tests were used to determine which electrodes contributed significantly to the group‑level cluster effect, and these significant electrodes were t‑weighted according to the main contrast (incongruent minus congruent). T‑weighting was applied only after the effect of interest had been established at the group level and therefore could not bias identification of the effect. Performing t‑weighting at the group rather than individual level also reduced susceptibility to noise and improved the generalizability of the resulting trial‑wise measures.

For the connectivity analyses, a t‑weighted midfrontal seed time series was constructed from these significant midfrontal electrodes. The lateral prefrontal target cluster was selected to include dorsolateral peak electrodes observed in the condition‑averaged cue‑locked data and to extend laterally to sites near F5/F6, which are traditionally regarded as lateral prefrontal electrodes [141,142]. The motor target cluster was selected based on clear hand-related lateralization independent of cue valence.

Statistical analyses

Behavioral data were analyzed using mixed‑effects models in R (version 4.4.3) [143] with the lme4 (version 1.1-37) [144], psych (version 2.5.6) [145], and lmerTest (version 3.1−3) [146] packages. To examine the effects of motivational valence on behavioral activation and potential group differences, generalized linear mixed models (GLMMs) were first used to analyze choice preference (Go versus NoGo), with valence (“win” versus “avoid” cues) and required action (Go versus NoGo) as within‑subject factors. Group (HC versus OCD) was added as a between‑subject factor to assess whether the influence of motivational valence on behavioral activation differed between healthy controls and people with OCD. Second, to determine whether the effects on Go responding were explained by correct or incorrect Go responses, additional analyses were restricted to Go cues. In these analyses, valence (“win” versus “avoid” cues) was the within-subject predictor, and Group (HC versus OCD) was included as a between‑subject factor to examine group differences in the observed effects. All models included the full set of relevant main effects and interactions and implemented a maximal random‑effects structure. Unless otherwise specified, all inferential statistical tests were two‑sided, with α = 0.05. Exact p values were reported for p ≥ 0.001, whereas smaller values were reported as p < 0.001.

For the EEG analysis, we employed a cue‑locked time‑based permutation test (500 permutations) to identify a time window in which midfrontal theta power (4–8 Hz) differed between congruent and incongruent trials for the OCD and HC groups, separately. Go‑to‑Win and NoGo‑to‑Avoid cues were classified as motivationally congruent because the Pavlovian response tendencies aligned with the instrumental requirements, whereas NoGo‑to‑Win and Go‑to‑Avoid cues were classified as motivationally incongruent. Post hoc t‑tests were subsequently conducted to determine which of the three midfrontal channels contributed significantly to the time window identified by the permutation test (Bonferroni‑corrected α = 0.017). Considering that (ⅰ) midfrontal theta power increases significantly after errors [147,148], and (ⅱ) errors occur more frequently on motivationally incongruent than congruent trials, we restricted this analysis to correct trials to minimize the influence of error processing on the midfrontal theta signal. Error trials were examined separately, and the corresponding results were reported in Text D in S1 File.

To assess the behavioral relevance of pre-response theta, we tested whether trial‑level theta power predicted response accuracy. Because both correct and error responses were required, response‑locked permutation analyses were repeated across all Go trials. A significant pre‑response theta window was identified in the HC group (−536 to −274 ms), whereas no significant cluster was found in the OCD group. An exploratory interval showing descriptively greater theta for Go‑to‑Avoid than Go‑to‑Win trials was therefore used for the OCD group (−655 to −324 ms). Within these intervals, midfrontal theta power (4–8 Hz) was averaged and standardized within participant. Accuracy (correct = 1, incorrect = 0) was analyzed using a binomial GLMM with pre‑response theta, group, and their interaction as fixed effects, trial-level RT and trial order as covariates, and participant as a random intercept.

Separately, to characterize interregional coordination during cue processing, we examined theta‑band phase synchronization between the MFC and target regions within the group‑specific cue‑locked time windows identified by the permutation tests (HC: 400–650 ms; OCD: 424–800 ms). Mean midfrontal theta power was extracted from these windows, and ISPS values between the MFC and target regions (lPFC and motor cortices) were calculated on correct trials. Repeated‑measures ANOVAs with valence (“win” versus “avoid” cues) and required action (Go versus NoGo) as within‑subject factors were conducted in IBM SPSS Statistics (version 22.0.0.0) [149] to evaluate conflict effects on theta power and ISPS. For the motor ISPS analysis, we further examined whether ISPS differed between the executing motor cortex (contralateral to the Go response hand) and the nonexecuting motor cortex (ipsilateral to the Go response hand). Because midfrontal functional connectivity is generally considered to be activity‑dependent [44], such that target regions become more sensitive to midfrontal signals when they are more strongly activated, Go responses were separated into contralateral and ipsilateral responses. This yielded three levels of the required response factor (Go_contra, Go_ipsi, and NoGo_bilateral). Significant valence × required response interactions were followed up with simple‑effects analyses comparing win and avoid conditions separately within each level of required response. For within‑subject factors with more than two levels, sphericity was assessed using Mauchly’s test, and Greenhouse–Geisser corrections were applied when this assumption was violated.

Computational models

We modeled trial‑by‑trial choices in the motivational Go/NoGo learning task within a hierarchical Bayesian reinforcement‑learning framework [50]. In this framework, nested reinforcement‑learning models were used to formally test whether Pavlovian response biases and instrumental learning biases contributed to asymmetric effects of valence on behavioral activation. Individual‑level parameters characterizing learning, choice stochasticity, and motivational biases were estimated while being constrained by group‑level population distributions. This hierarchical structure allowed partial pooling across participants, thereby improving the stability of subject‑level parameter estimates while preserving inter‑individual variability. Consistent with recommended practices in computational cognitive modeling [150,151], we specified theory‑driven candidate models, compared competing model families, inspected convergence diagnostics, and evaluated model adequacy using posterior predictive simulations.

On each trial, participants selected one of three responses (Go‑left, Go‑right, or NoGo) to a given cue (win or avoid), and learned the probabilistic “cue‑response‑outcome” mappings through feedback (win/neutral/loss). The probability of each response (𝑎) was determined from the corresponding action weights (𝑤) using a softmax function (Equation 3). Action values were updated according to prediction error (Equation 4).

(3)(4)

where ε represents the learning rate, ρ denotes feedback sensitivity, and r_t is the trial outcome. Trial outcomes were coded as 𝑟 ∈ {−1,0,1}. Because cue valence could only be inferred after the first reward or punishment outcome, initial Q‑values were set to 𝜌 × 0.5 for win cues and 𝜌 × −0.5 for avoid cues (i.e., the initial expected outcome is 0.5 for win cues and −0.5 for avoid cues), while these Q‑values influenced behavior only once cue valence was known.

To identify the mechanisms of motivational biases in choice, we fitted a baseline model containing learning rate (ε) and feedback sensitivity (ρ) (Equations 3–4; Table 1 M1). Then, Go bias parameter (𝑏) was added to the action weights of Go responses to capture individual differences in the general tendency to make Go responses, independent of cue information (Table 1 M2). M3a then additionally incorporated a Pavlovian response bias (𝜋), such that static Pavlovian values (𝑉) contributed to the action weights (Equation 5; Table 1 M3a).

(5)

In Model 3b (Table 1 M3b), we introduced an instrumental learning bias parameter (𝜅) to test whether rewards preferentially strengthen Go responses relative to NoGo responses, and whether punishments are less effective at reducing NoGo responses than Go responses. Under this formulation, 𝜅 increases the learning rate following rewarded Go responses while decreasing the learning rate following punished NoGo responses (Equation 6).

(6)

In Model 3c (Table 1 M3c), both Pavlovian response bias (π) and instrumental learning bias (𝜅) were included to test whether the observed motivational biases in action arise from the complementary contributions of Pavlovian response tendencies and instrumental learning bias.

We used the winning model (M3c) to compute a trial‑wise Pavlovian‑instrumental conflict index (Equation 7) and tested whether cue‑locked midfrontal theta power tracked this conflict strength on a trial‑by‑trial basis. We operationalized conflict as the difference in Q‑values between the Pavlovian‑congruent and incongruent response options. Specifically, conflict was calculated as Q_NoGo − mean(Q_Go) for win cues and as mean(Q_Go) − Q_NoGo for avoid cues.

(7)

In Equation 7, valenced(s_t) indicates whether the cue valence had been learned. It was initialized to 0 and set to 1 after the first reward or punishment outcome. V(s_t) denotes the cue value and was fixed at +0.5 for “win” cues and −0.5 for “avoid” cues. Q(a,s) represents the instrumental action values, the expected value of choosing action a given cue s, where a₁, a₂, and a₃ correspond to Go‑left, Go‑right, and NoGo, respectively. The factor of 2 rescales V(s_t) from ±0.5 to ±1, such that the conflict index corresponds to Q_NoGo − mean(Q_Go) for win cues and mean(Q_Go) − Q_NoGo for avoid cues. Larger conflict values reflect a greater mismatch between Pavlovian response tendencies elicited by cue‑value and the optimal instrumental action required in the task, which in turn demands stronger cognitive control to inhibit Pavlovian tendencies and execute goal‑directed behavior.

We further extended the winning behavioral model by adding a gain parameter (β), which scales how trial-by-trial theta power modulates the motivational biasing of action, and compared a series of alternative theta-modulated models (M4a–d). Each of these models represented a candidate mechanism through which the midfrontal cortex may modulate motivational biases [70] (Equations 8–11).

In Model 4a, we tested whether midfrontal theta power modulated Pavlovian response tendencies. In this model, theta power scaled the Pavlovian bias (π) on incongruent trials. Given the form of the equation, a negative β value corresponds to theta‑related adaptive suppression of Pavlovian response tendencies during motivational conflict.

(8)

In Model 4b, we tested whether midfrontal theta power modulated the contribution of learned instrumental action values to choice. In this model, theta power acted as a multiplicative gain on the model‑derived Q‑value term, such that the instrumental contribution was scaled by (1 − β × θ_t). Under this specification, a negative β indicates that higher theta power increases the contribution of instrumental action values to choice.

(9)

In Model 4c, we developed an exploratory arbitration model to test whether midfrontal theta power shifted the balance between Pavlovian and instrumental control, rather than selectively modulating either Pavlovian response tendencies or the instrumental contribution. This model was not intended as an extension of a parameter already selected in the M3 behavioral family; instead, it served as an alternative comparison model to evaluate whether theta acted through a more global Pavlovian‑instrumental trade‑off mechanism. Specifically, M4c used a Pavlovian‑instrumental trade‑off parameter τ, and β captured whether theta power shifted decision weighting toward Pavlovian or instrumental control on motivationally incongruent trials. In this model, a positive β indicates a shift toward stronger Pavlovian tendencies and weaker instrumental contribution, whereas a negative β indicates a shift toward stronger instrumental contribution and weaker Pavlovian tendencies.

(10)

In Model 4d, we tested whether midfrontal theta power modulated instrumental learning bias. In this model, β scaled the biased learning‑rate terms for rewarded Go responses and punished NoGo responses, allowing them to move toward the unbiased learning rate ε₀. Thus, a larger positive β indicates that theta power reduces the instrumental learning bias and makes updating more similar to the unbiased learning rate.

(11)

Existing theories suggest that an important function of the midfrontal cortex is to detect motivational conflict and to “alert” task‑relevant regions to implement control by synchronizing their activity with that of the midfrontal cortex [54]. This view implies that the degree of synchronization with task‑relevant regions, rather than local power alone, may be a better predictor of an individual’s ability to reduce motivational biases. Finally, to assess whether theta‑related modulation of motivational biases depended on long‑range network coordination, we extended the same modeling framework to an intersite phase synchrony modulation family (M5a–M5d). In these models, single‑trial theta‑band phase synchrony estimates replaced local midfrontal theta power (θ_t) as the modulation signal, while the mathematical architecture, parameter constraints, and sign conventions were inherited from the corresponding M4 power‑based models. Specifically, we tested whether trial‑by‑trial MFC‑lPFC theta phase synchrony (ISPS_lPFC,t; M5a, Equation 12) and MFC‑motor theta phase synchrony (ISPS_{motor‑contra,t}; M5b, Equation 13) modulated the instrumental contribution during choice.

(12)(13)

We further tested whether MFC‑lPFC theta phase synchrony (ISPS_lPFC,t; M5c, Equation 14) and MFC‑motor theta phase synchrony (ISPS_{motor‑contra,t}; M5d, Equation 15) modulated Pavlovian bias.

(14)(15)

We used hierarchical Bayesian sampling to estimate parameters at both the group and subject levels. The group‑level parameters 𝑋 served as priors for the individual‑level parameters 𝑥, such that 𝑥∼𝒩(𝑋,𝜎). Hyperpriors on 𝜎 followed a half‑Cauchy distribution with scale 2. The group‑level means 𝑋 were given weakly informative, zero‑centered priors: 𝑋_ε,𝜅∼𝒩(0,2) and 𝑋_{𝜌,𝑏,𝜋,𝛽}∼𝒩(0,3). All parameters were defined on the real line, except for ρ, which was constrained to be positive via an exponential transform, and ε, which was constrained to [0,1] via an inverse‑logit transform. To ensure that the effect of 𝜅 on ε was symmetric in model space (i.e., after inverse‑logit transformation and restriction to [0,1]), ε was computed as specified in Equation 16.

(16)

Model estimation was performed in R using RStan (version 2.32.6; Stan version 2.32.2) with Markov chain Monte Carlo (MCMC) sampling. Four chains were run for each model, with 200 warm‑up iterations followed by 1,000 sampling iterations per chain, yielding 4,000 posterior samples in total. Convergence was considered satisfactory when R‑hat < 1.1 for all parameters, which was achieved for all fitted models. Model comparison was based on the WAIC, with lower WAIC values indicating better expected out-of-sample predictive performance after accounting for model complexity. Differences in WAIC of 2–6, 6–10, and >10 were interpreted as positive, strong, and very strong evidence, respectively, in favor of the model with the lower WAIC. For completeness, we also report the proportion of explained variance (R²) for each model. However, WAIC was used for formal model selection because it explicitly penalizes additional model complexity and accommodates differences in the amount of behavioral variance that individual parameters can potentially explain.

Individual regulatory orientation

To characterize individual differences in theta‑synchrony-dependent regulatory orientation under motivational conflict, we extracted participant‑level posterior estimates of two model‑derived modulation parameters. The first parameter (𝛽_π) quantified the modulation of the Pavlovian bias and was obtained from M5d. The second parameter (𝛽_Q) quantified the modulation of the instrumental action‑value contribution and was obtained from M5a for healthy control participants and M5b for people with OCD. For each participant, the posterior mean of the corresponding individual‑level parameter was used in subsequent analyses. We then represented these two complementary modulation components within a two‑dimensional regulatory strategy space, such that each participant was characterized by a vector jointly determined by the Pavlovian‑bias and instrumental action‑value contribution modulation parameters. This two‑dimensional representation provided the basis for quantifying both the relative orientation and the overall magnitude of each participant’s regulatory profile.

To convert this two‑dimensional regulatory profile into a single continuous index suitable for symptom‑correlation analyses, we defined a regulatory orientation angle, Φ_reg. For interpretability, we re‑expressed the modulation estimates as control indices by setting PCI = −𝛽_π and QCI = −𝛽_Q, such that higher PCI values reflected stronger suppression of Pavlovian response tendencies whereas higher QCI values reflected greater contribution of instrumental action values. PCI and QCI were then separately z‑standardized within each group to obtain PCI_z and QCI_z. We subsequently quantified regulatory orientation as the angular direction of each participant’s vector in the standardized two-dimensional control space defined by PCIz and QCIz, using the four‑quadrant inverse tangent function (Equation 17) [152].

(17)

The rationale for this index is that angular measures can effectively capture trade‑offs between two competing regulatory targets. Shifts in Φ_reg toward different regions of the two‑dimensional control space reflect individual differences in the relative weighting of regulatory modulation across Pavlovian response tendencies and instrumental action‑value contribution. Thus, Φ_reg provides a continuous measure of regulatory orientation, thereby enabling the potential clinical relevance of these individual differences to be examined in relation to OCD symptom severity.

Finally, we examined the association between Φ_reg and OCD symptom severity, indexed by the Y-BOCS total score and its subscales (Obsessions and Compulsions). Because the observed Φ_reg values were well separated from the circular discontinuity at ±180° and did not exhibit wrap‑around across this boundary, we treated Φ_reg as an approximately continuous orientation measure for inferential analyses. Symptom associations were assessed using a residual‑based partial Spearman approach, in which both Φ_reg and the symptom score of interest were residualized with respect to covariates before their residuals were correlated nonparametrically. Analyses controlled for Beck Depression Inventory (BDI) and Beck Anxiety Inventory (BAI) scores, with Barratt Impulsiveness Scale (BIS-11) scores additionally included in a more stringent model. To assess whether the associations depended on the arbitrary angular zero point, we further performed a rotation‑robustness analysis by uniformly shifting Φ_reg over a range that did not introduce wrap-around (0°–30°) and repeating the partial Spearman analyses.