Dysfunctional reward processing amplifies stress-related smartphone overuse: Evidence from ERPs and ecological momentary assessment

Abstract

Background and aims

Problematic Smartphone Use (PSU) has become a major public health issue, with stress identified as a key factor. Pathological technology use is often linked to dysfunctional reward processing, which is characterized by hyperactivity during reward anticipation and hypoactivity during reward receipt, both closely tied to emotion regulation. This study aimed to investigate the association between PSU and event-related potentials (ERP) linked to reward anticipation and feedback processing, while elucidating the role of reward processing dysfunction in the escalation of daily life stress into PSU through ecological momentary assessment.

Methods

We recorded the ERPs of 44 PSU participants and 50 HC participants during the monetary incentive delay task. Meanwhile, we assessed the momentary stress, PSU levels, and screen time of these participants three times a day for 14 days.

Results

ERP results showed that the PSU group, compared to the HC group, had significantly larger P3 amplitude (but not N2 amplitude) during reward anticipation (cue-P3: η² = 0.066, p = 0.012; cue-N2: η² = 0.004, p = 0.567). In contrast, during feedback, their amplitudes were reduced in both RewP and fb-P3 components (RewP: η² = 0.092, p = 0.003; fb-P3: η² = 0.043, p = 0.048). These findings indicate that PSU is linked to heightened neural activity during reward anticipation but reduced responsiveness during feedback, indicating potential dysfunction in reward processing. Ecological momentary assessment linked momentary stress to increased PSU (β = 0.17, HPD 95% CI [0.129, 0.218]) and screen time (β = 0.18, HPD 95% CI [0.135, 0.227]). Importantly, RewP amplitude moderated these associations, with blunted RewP responses amplifying stress-related increases in both PSU (β = −0.19, HPD 95% CI [−0.352, −0.036]) and screen time (β = −0.20, HPD 95% CI [−0.394, −0.003]).

Conclusion

These findings indicate that reward-related ERPs may serve as potential neural markers for identifying PSU, while dysfunctional reward processing may exacerbate stress-related PSU behaviors. This work provides novel insights for developing prevention and intervention strategies in digital addiction.

Introduction

By early 2024, 5.61 billion people (69.4% of the global population) were using smartphones (We are Social, 2024). Smartphones enhance daily efficiency, but their pervasive use has led to problematic smartphone use (PSU), marked by compulsive behavior and psychological distress during abstinence (Elhai, Dvorak, Levine, & Hall, 2017, p. 251). The global prevalence of PSU is 37.1% (Lu, An, & Chen, 2024), and it is associated with decreased sleep quality, academic difficulties, and affective disorders (Hao, Jin, Huang, & Wu, 2022; Stanković, Nešić, Čičević, & Shi, 2021; Vahedi et al., 2018; West et al., 2021; Zhao et al., 2021). Stress is a key antecedent of PSU, as individuals often turn to their smartphones to relieve stress (e.g., Hao et al., 2022; Stanković et al., 2021). This maladaptive coping strategy may stem from dysregulated reward processing, a key mechanism in emotional regulation. For instance, a diminished hedonic response to rewards is associated with the anhedonia observed in depression, while excessive reward anticipation may contribute to manic mood elevation (Ng, Alloy, & Smith, 2019; Nusslock & Alloy, 2017). Nevertheless, how abnormalities in reward processing transform everyday stress into persistent PSU remains unclear. To address this gap, this study examines how reward processing dysfunction moderates the conversion of stress into PSU using momentary assessments of daily stress and PSU.

Stress and problematic smartphone use

Stress is classically defined as a perturbation of our mental and physical equilibriums that results from unpredictable and/or uncontrollable adversity (Hermans, Hendler, & Kalisch, 2025, p. 331). According to the compensatory internet use theory (Kardefelt-Winther, 2014), individuals under stress or experiencing negative emotions often turn to activities like social media, videos, or online games to restore positive feelings. Over time, this coping mechanism can reinforce smartphone use, leading to excessive dependence. Wang, Wang, Gaskin, and Wang (2015) demonstrated that stress increases the tendency to escape reality through smartphones, supporting this view. Moreover, stress has been identified as a stronger predictor of PSU than anxiety or depression (Stanković et al., 2021). Stress may increase PSU risk by either reducing self-control or triggering negative emotions such as anxiety and depression. Most research has focused on chronic stress, overlooking the immediate effects of daily stress on PSU and screen time (e.g., Cho, Kim, & Park, 2017). In contrast, ecological momentary assessment (EMA) gathers real-time, repeated data in natural settings, capturing daily fluctuations in stress and PSU with notable ecological and temporal precision (Myin-Germeys et al., 2018). This study aims to address this gap by using EMA to observe the real-time effects of stress on PSU.

Reward processing dysfunction and problematic smartphone use

Reward processing includes two phases: anticipation (preparing for rewards) and feedback (evaluating rewards) (Luo, Jiang, Chen, Zhang, & You, 2019). Prior studies show that behavioral addictions, such as social media use, short-form video consumption, and gaming, exhibit a dual sensitivity pattern akin to substance addiction: heightened reward anticipation and diminished feedback responsiveness (He, Zheng, Nie, & Zhou, 2018; Kim et al., 2021; Li, Wang, et al., 2020; Webber et al., 2024). According to incentive sensitization theory (Robinson & Berridge, 2001), chronic engagement with addictive stimuli induces hypersensitivity to reward-predicting cues through neuroplastic changes in striatal circuits. Neuroimaging evidence supports this theory, showing amplified nucleus accumbens and caudate activation in individuals with internet gaming disorder during gaming cue exposure and monetary reward anticipation (Kim et al., 2021; Li, Wang, et al., 2020; Yao, Zhang, Fang, Liu, & Potenza, 2022). These populations show attenuated neural responses and reduced hedonic experience during reward feedback, a phenomenon also observed in substance addiction (Webber et al., 2024).

While initial evidence suggests analogous dysfunctions in the nucleus accumbens and prefrontal cortex among PSU populations (Anbumalar & Binu Sahayam, 2024), electrophysiological confirmation remains lacking. Event-related potential (ERP) studies offer potential markers for such reward dysfunctions. During anticipation, elevated cue-N2 (200–300 ms) amplitudes reflect early attentional evaluation of reward valence, with reward cues typically eliciting more positive N2 responses than loss or neutral cues (Novak & Foti, 2015; Zhang et al., 2023), while enhanced cue-P3 (300–500 ms) amplitudes reflect heightened sensitivity to motivational incentives, as this component is elevated for both potential win and loss cues (Novak & Foti, 2015), indicating broad attentional allocation to incentive-relevant information. In contrast, feedback processing was characterized by attenuated RewP (250–350 ms) amplitude, reflecting reduced reward sensitivity (Proudfit, 2015), along with diminished fb-P3 (300–500 ms) amplitude, indicating decreased motivational salience—specifically, the capacity of rewards to drive goal-directed behavior—particularly for larger reward magnitudes (Zheng et al., 2017). As summarized by Glazer et al. (2018), these components reflect distinct psychological mechanisms: the RewP is primarily associated with immediate hedonic experience (e.g., affective evaluation of reward receipt), while the fb-P3 mediates the integration of motivational salience (e.g., adjusting behavioral strategies based on reward magnitude). Existing studies have shown that behavioral addictions may manifest reward processing dysfunction. For example, during reward anticipation, individuals with behavioral addiction exhibit increased cue-P3 amplitudes to reward-related cues (Peng et al., 2024). During reward feedback processing, these individuals show attenuated RewP amplitudes to gain outcomes (Li, Wang, et al., 2020; West et al., 2021), accompanied by reduced fb-P3 amplitudes (West et al., 2021). Although PSU is classified as a digital addiction subtype (Meng et al., 2020), its electrophysiological profile during reward phases remains unexplored. We hypothesize that PSU populations will exhibit heightened ERP amplitudes (cue-N2/cue-P3) during reward anticipation and diminished amplitudes (RewP/fb-P3) during feedback processing.

The moderating role of the neurodynamics of reward processing

Well-functioning reward processing may be a key pathway for moderating the negative impact of stress on PSU. Hypersensitivity in reward anticipation may increase cravings for instant rewards, such as those from smartphones (Komarnyckyj et al., 2022; Martins et al., 2022), leading individuals under stress to rely on smartphone-mediated rewards for escape. Additionally, insensitivity in reward feedback processing can result in reduced pleasure from daily activities and increased sensitivity to negative stimuli. For example, individuals with depression often exhibit decreased RewP amplitude, which reflects diminished pleasure when receiving rewards and is closely linked to anhedonia (Proudfit, 2015). This diminished reward experience may drive a compensatory tendency to seek immediate gratification through smartphone use (Tsilosani, Chan, Steffens, Bolton, & Kowalczyk, 2023). While understanding how reward processing affects the stress-PSU relationship is valuable, research on its dynamic, real-time role remains limited. Therefore, another objective of this study is to explore the mechanism of the role of reward processing in the conversion of stress into PSU in the context of daily momentary assessment.

The present study

This study integrates ERP and EMA to examine reward processing in PSU and its moderating role in the daily stress-PSU relationship. Specifically, our first objective is to compare ERP markers of reward anticipation (cue-N2, cue-P3) and reward feedback (RewP, fb-P3) between individuals with PSU and healthy controls. Our second objective is to use EMA to capture real-time data on daily stress, PSU, and screen time. It also tests whether individual differences in reward processing moderate the daily stress-PSU association. Based on these aims, we propose the following hypotheses:

Hypothesis 1:

In the reward anticipation phase, individuals with PSU will exhibit higher cue-N2 and cue-P3 amplitudes compared to HC group.

Hypothesis 2:

In the reward feedback phase, individuals with PSU will exhibit lower RewP and fb-P3 amplitudes compared to HC group.

Hypothesis 3:

Increased amplitudes of cue-N2 and cue-P3 will strengthen the effect of stress on PSU.

Hypothesis 4:

Increased amplitudes of RewP and fb-P3 will reduce the effect of stress on PSU.

Method

Participants

The sample size was calculated using G*Power 3 (Faul, Erdfelder, Lang, & Buchner, 2007) for a 2 × 2 interaction, with a medium effect size (f = 0.25), α = 0.05, and power = 0.95, resulting in an estimated sample size of 84 participants. A total of 537 university students were recruited, and 100 were selected for the ERPs study (48 PSU, 52 HC). PSU was assessed using the 10-item Smartphone Addiction Scale-Short Version (SAS-SV; Cheung et al., 2019; Kwon, Kim, Cho, & Yang, 2013), which is scored on a 6-point Likert scale (range: 6–60). Scores ≥31 for males and ≥33 for females indicated PSU (Cronbach's α = 0.84). Additionally, screen time ≥5 hours/day was required, based on national averages (China Internet Network Information Center, 2024; Zhang et al., 2022). Participants were screened for depressive symptoms using the 21-item Chinese Beck Depression Inventory-II (BDI-II; Li, Lok, et al., 2020), which is scored on a 0–3 scale (range: 0–63). Scores <14 indicated no depressive disorder (Cronbach's α = 0.76), and for anxiety symptoms using the 7-item Chinese Generalized Anxiety Disorder Questionnaire (GAD-7; Yu et al., 2018), scored on a 0–3 scale (range: 0–21), with scores <10 indicating no anxiety disorder (Cronbach's α = 0.78). After excluding six participants due to excessive ERP artifacts, 44 PSU and 50 HC participants remained. While power analysis indicated that 84 participants were needed for the ERP study, a larger sample size was chosen to enhance statistical power and robustness (Erceg-Hurn & Mirosevich, 2008). Post hoc analysis using G*Power 3 (Faul et al., 2007) confirmed that 94 participants yielded 99% power for a 2 × 2 ANOVA, demonstrating the adequacy of our sample size.

In the 14-day EMA survey, participants completed three surveys per day (42 total). Ten participants were unreachable or unwilling to continue, and six participants who completed fewer than 20 surveys were excluded (Kemp, Sperry, Hernández, Barrantes-Vidal, & Kwapil, 2023). The final sample consisted of 78 participants (M_age = 19.59, SD = 1.68), providing 3,062 data points. Given the nested structure of EMA data (Kim, Yang, Liu, Gezer, & Wong, 2024), non-normal distributions with potential nonlinear relationships in affective and behavioral variables (Pirla, Taquet, & Quoidbach, 2023), and diverse modeling approaches (Hamaker, 2025), estimating statistical power in EMA research poses significant challenges. This study adopted two complementary evaluation approaches. First, dynamic structural equation modeling (DSEM) simulations (Schultzberg & Muthén, 2018) demonstrated >80% power (proportion of simulations with credible intervals excluding zero) when total observations exceeded 2,000. Our dataset containing 3,276 observations (N = 78 participants, T = 42 measurements) substantially surpasses this threshold. Second, leveraging Pirla et al.’s (2023) real-world EMA database (N = 7,016) with seven psychological-behavioral indicators, resampling analyses of 2,500 datasets showed that 87% power (proportion of resampled datasets demonstrating statistically significant positive correlations with measures in the original dataset) could be achieved at α = 0.05 for detecting medium effects (r = 0.35) with our sample size (N = 78, T = 42). Both methodological approaches confirm that the current study's sample size provides sufficient statistical power for reliably detecting psychological dynamics and supporting robust DSEM parameter estimation.

Procedures and ERP task

Participants meeting PSU or HC criteria were invited to complete the ERP task. We used an adapted Monetary Incentive Delay Task (Novak & Foti, 2015) to measure brain activity during reward anticipation and feedback phases (see Fig. 1). Each trial began with a cue indicating a reward (money symbol) or neutral (empty circle) condition, followed by a fixation mark for 2000–2500 ms. Then, a target stimulus (white square) appeared, and participants had to respond by pressing the “space” key. The target duration started at 200 ms and was adaptively adjusted to maintain a 50% success rate based on response speed (Landes et al., 2018). A fixation mark was shown for 1,300 ms before feedback, which lasted 1 s. In the reward condition, participants earned 1 Renminbi (RMB, the official currency of China) for a correct response, and lost 0.5 RMB for failure or exceeding 1,300 ms. In the neutral condition, no reward or punishment was given. Before the experiment, participants completed 10 practice trials (7 reward, 3 neutral) to familiarize themselves with the task. The formal experiment included 140 trials in 2 blocks of 70 trials (50 reward, 20 neutral), with trial types presented in a pseudo-random order. After the first block, participants were informed of their earnings and given a brief break. Afterward, they were asked about their willingness to join a two-week follow-up survey later, providing contact information if they agreed.

Fig. 1.

Trial structure of the monetary incentive delay task

Momentary state assessments

The EMA data were collected through daily smartphone message reminders over a two-week period, with all participants starting on the same day. Participants completed three daily EMA surveys over 14 days, assessing stress, PSU, and screen time at fixed intervals: 9:00–12:00, 14:00–17:00, and 19:00–22:00. Participants received a 2-yuan reward per survey and additional rewards for completing more than 80% of the surveys.

The daily questionnaire assessed stress and PSU using EMA. Momentary stress was measured using a 4-item EMA scale developed by Murray et al. (2023), which comprised the following exhaustive set of items: Each item began with the phrase “In the past 30 min, I felt…” and included: (1) “…that I was unable to control the important things in my life,” (2) “…nervous and stressed,” (3) “…I could not cope with all the things I had to do,” and (4) “…difficulties were piling up so high that I could not overcome them.” Items were rated on a 9-point Likert scale (1 = “strongly disagree” to 9 = “strongly agree”). The 30-min timeframe was chosen to reduce recall bias and to capture more life events over a longer period (Murray et al., 2023). The within-person reliability of this measure was good (ω = 0.75), and the between-person reliability was excellent (ω = 0.91), as calculated using Cooke et al.’s (2022) method.

The EMA version of the PSU measure was adapted from the Smartphone Addiction Scale–Short Version (SAS-SV; Cheung et al., 2019; Kwon et al., 2013). Five items were selected based on their relevance to momentary assessment and their ability to capture key aspects of PSU in a concise manner. Each item began with “In the past 30 min, I…” and included: (1) “…thought about my smartphone even when I wasn't using it,” (2) “…missing planned work due to smartphone use,” (3) “…found it hard to focus on tasks due to smartphone use,” (4) “…constantly checked my smartphone to avoid missing social media interactions,” and (5) “…felt like I spent more time on my smartphone than planned.” Items were rated on the same 9-point scale. Participants were informed that survey reminders would appear randomly during specific time windows to avoid misjudgment about interference. The within-person reliability of this measure was good (ω = 0.79), and the between-person reliability was excellent (ω = 0.95).

After completing the 9 items, participants uploaded screenshots of their smartphone usage duration, and screen time within each 5-h interval was calculated by subtracting the previous session's time from the current session's time. Following each upload, three researchers verify whether the submission falls within the designated 30-min timeframe by examining the displayed timestamp on the screen capture. Should temporal inaccuracies be identified or image anomalies detected (e.g., absence of critical information), researchers will promptly notify participants to initiate re-upload procedures. The intraclass correlation coefficients (ICC), representing the proportion of between-person variance to total variance (Hove, Jorgensen, & van der Ark, 2022), were 0.69 for stress, 0.65 for PSU, and 0.64 for screen time, indicating substantial between-person variability while also confirming meaningful within-person fluctuations.

ERP data analysis

EEG data were recorded using a 64-channel SynAmps system (Neuroscan) with FCz reference and AFz ground, sampled at 500 Hz (0.01–100 Hz bandpass, electrode impedance <5 kΩ). Preprocessing was conducted in EEGLAB v2021.0 (Delorme & Makeig, 2004) within MATLAB 2023b. Steps included re-referencing to averaged mastoids (M1/M2), 0.1–30 Hz filtering, ICA-based ocular artifact correction, and rejection of artifacts exceeding ±100 μV or 50 μV/ms voltage slope. ERP components were defined using spatiotemporal criteria from Novak and Foti (2015) and Threadgill and Gable (2016): cue-N2 (275–325 ms; Fz/FC1/FC2/Cz), cue-P3 (350–450 ms; Cz/CP1/CP2/Pz), RewP (250–350 ms; Fz/FC1/FC2/Cz), and feedback-P3 (350–450 ms; Cz/CP1/CP2/Pz). Behavioral metrics (reaction time) and ERP amplitudes were analyzed via repeated-measures ANCOVA with anxiety and depression covariates, Bonferroni-corrected. Reward processing indices (Δcue-N2/Δcue-P3: reward-neutral contrast; ΔRewP/Δfb-P3: gain-loss contrast) were computed through differential waveform analysis and compared using ANCOVA.

EMA data analysis

A multilevel bivariate model was implemented using the Dynamic Structural Equation Modeling (DSEM) framework in Mplus 8.3. DSEM employs Bayesian estimation, treating model parameters as random rather than fixed, and combines prior distributions with data to update posterior distributions, offering flexibility for small samples and complex models (Speyer, Murray, & Kievit, 2024). DSEM captures within-person dynamics (e.g., daily fluctuations) and between-person differences (e.g., stable traits), making it suitable for examining cross-lagged relationships between stress and PSU/screen time and testing the moderating effects of ERP components (∆cue-N2, ∆cue-P3, ∆RewP, ∆fb-P3) at the between-person level (Zhou, Wang, & Zhang, 2021). Eight separate DSEM models were constructed to avoid complexity and ensure interpretability (Enting, Jongerling, & Reitz, 2024). Group, anxiety, and depression levels were included as covariates, directed toward stress and PSU/screen time at the between-person level (Asparouhov, Hamaker, & Muthén, 2018) (see Fig. 2).

Fig. 2.

Dynamic structural equation model. Within-person: ϕ12 and ϕ21 = cross-lagged effects between stress and PSU/screen time; ϕ11 and ϕ22 = autocorrelations of stress and PSU/screen time; ςstress, ςPSU, ςST = residual errors. Between-person: ERPs components (Δcue-N2, Δcue- P3, ΔRewP, Δfb-P3) moderate cross-lagged effects. Covariates: group, anxiety, depression. ST = screen time; PSU = problematic smartphone use

Estimates used default diffuse priors, with 25,000 iterations per chain. Point scale reduction values (<1.005) indicated convergence. Missing data (6.53%) were handled via DSEM's Markov Chain Monte Carlo procedure (Hamaker et al., 2018). The TINTERVAL feature controlled for unequal time intervals by setting intervals to 5 h (McNeish & Hamaker, 2020). Reported estimates represent the medians of posterior parameter distributions, accompanied by their 95% highest posterior density (HPD) credible interval (CI; McNeish, 2019). When 95% CI excluded zero, parameters were interpreted as having substantial evidence for a non-zero effect (i.e., the posterior distribution assigned low probability to values near zero).

Ethics

The Ethics Committee of School of Psychology at Shaanxi Normal University approved the study (HR2022-12-001). All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as received in 2000. We obtained informed consent from all participants to include them in the study.

Results

Sample characteristics

As shown in Table 1, the two groups showed significant differences in PSU scores but no significant differences in age or gender. The PSU group scored significantly higher than the HC group on anxiety and depression. The samples for ERP and EMA analyses were consistent in these characteristics. In the EMA data, each participant was scheduled for 42 observations, resulting in a planned total of 3,276 observations. The actual completed observations totaled 2,906, with participants averaging 39.27 observations each (SD = 3.52; Median = 41; min = 23, max = 42). Table 2 presents the minimum, maximum, median, and mean values of the EMA variables (PSU, stress, screen time). The mean values of these variables showed positive correlations with age, gender, group, anxiety, and depression.

Table 1.

Sample characteristics (M ± SD)

Variables	ERP sample (N = 94)						EMA sample (N = 78)
	PSU (N = 44)	HC (N = 50)	t/x 2	p	Cohen's d	95% CI for Cohen's d	PSU (N = 31)	HC (N = 47)	t/x 2	p	Cohen's d	95% CI for Cohen's d
Gender (M/F)	6/38	8/42	0.1	0.748	–		3/28	7/40	0.46	0.500	–
Age (years)	19.93 ± 1.97	19.66 ± 1.70	0.72	0.474	0.15	[−0.26, 0.55]	19.58 ± 1.71	19.60 ± 1.68	0.039	0.969	0.01	[−0.46, 0.45]
PSU	42.30 ± 4.65	27.34 ± 3.21	18.32	<0.001	3.79	[3.10, 4.46]	41.81 ± 4.98	27.13 ± 2.91	16.44	<0.001	3.80	[3.04, 4.55]
Screen time	9.35 ± 2.42	3.13 ± 1.00	16.63	<0.001	3.44	[2.71, 3.97]	8.78 ± 2.55	3.07 ± 1.00	13.85	<0.001	3.21	[2.52, 3.88]
Depression	9.95 ± 1.95	6.76 ± 3.54	5.31	<0.001	1.1	[0.66, 1.53]	9.87 ± 1.75	6.70 ± 3.61	4.54	<0.001	1.05	[0.56, 1.53]
Anxiety	6.25 ± 1.53	5.14 ± 1.91	3.09	0.003	0.64	[0.22, 1.05]	6.48 ± 1.50	5.15 ± 1.93	3.25	0.002	0.75	[0.28, 1.22]

Note. PSU, problematic smartphone use; HC, healthy control; EMA, ecological momentary assessment; 95% CI = 95% credible intervals.

Table 2.

Descriptive statistics and between-person/within-person mean correlations (N = 78)

variables	M ± SD	Median	Min	Max	Age	Gender	Group	Depression	Anxiety	PSU	Screen time	Stress
Age (between-person level)	19.59 ± 1.68	19	18	26	–
Gender (between-person level)	–	–	–	–	r = 0.12 95% CI = [−0.108, 0.331]	–
Group (between-person level)	–	–	–	–	r = 0.01 95% CI = [−0.227, 0.218]	r = −0.08 95% CI = [−0.294, 0.149]	–
Depression (between-person level)	7.96 ± 3.38	8.50	0	13.00	r = −0.07 95% CI = [−0.292, 0.151]	r = 0.08 95% CI = [−0.141, 0.301]	r = 0.46*** 95% CI = [0.267, 0.621]	–
Anxiety (between-person level)	5.68 ± 1.88	6.00	0	9.00	r = 0.10 95% CI = [−0.128, 0.313]	r = −0.02 95% CI = [−0.238, 0.207]	r = 0.35** 95% CI = [0.137, 0.531]	r = 0.06 95% CI = [−0.163, 0.280]	–
PSU (within-person level)	22.21 ± 11.36	23.00	0	45.00	r = 0.08 95% CI = [−0.107, 0.262]	r = −0.04 95% CI = [−0.183, 0.100]	r = 0.32** 95% CI = [0.127, 0.522]	r = 0.33** 95% CI = [0.139, 0.521]	r = 0.16 95% CI = [−0.027, 0.356]	–	r = 0.88*** 95% CI = [0.823, 0.929]	r = 0.43*** 95% CI = [0.370, 0.495]
Screen time (within-person level)	97.13 ± 47.14	102.00	3	295.00	r = 0.05 95% CI = [−0.147, 0.254]	r = −0.03 95% CI = [−0.170, 0.110]	r = 0.33** 95% CI = [0.130, 0.523]	r = 0.34*** 95% CI = [0.150, 0.537]	r = 0.16 95% CI = [−0.027, 0.343]	r = 0.98*** 95% CI = [0.972, 0.996]	–	r = 0.42*** 95% CI = [0.362, 0.480]
Stress (within-person level)	14.76 ± 9.58	14.00	0	36.00	r = 0.03** 95% CI = [−0.157, 0.211]	r = 0.01** 95% CI = [−0.133, 0.139]	r = 0.35*** 95% CI = [0.147, 0.561]	r = 0.26* 95% CI = [0.056, 0.470]	r = 0.21* 95% CI = [0.034, 0.394]	r = 0.80*** 95% CI = [0.691, 0.907]	r = 0.84*** 95% CI = [0.400, 0.705]	–

Note. Between-person correlations are shown below the diagonal, while within-person correlations are presented above the diagonal. PSU, problematic smartphone use; 95% CI = 95% credible intervals. *p < 0.05, **p < 0.01, ***p < 0.001.

Behavioral data

A repeated-measures ANCOVA of average RTs for hit trials (Cue: reward vs neutral; Group: PSU vs HC) showed no significant effect of Cue type (F (1, 90) = 0.01, p = 0.937, η² < 0.001, 95% CI = [−0.001, 0.005]), but a significant effect of Group (F (1, 90) = 17.22, p < 0.001, η² = 0.161, 95% CI = [0.045, 0.294]). The Group × Cue interaction was not significant (F (1, 90) = 0.03, p = 0.854, η² < 0.001, 95% CI = [−0.001, 0.014]). Simple effects analysis showed that the PSU group (264.84 ± 32.16 ms) responded significantly faster than the HC group (308.17 ± 40.05 ms) under the reward cues (t = 5.73, p < 0.001, Cohen's d = 1.86, 95% CI = [0.74, 1.62]). The average hit rate under the reward condition was 0.48 (SD = 0.03), consistent with the experimental procedure's ∼50% target, with no significant group differences (t = 1.51, p = 0.133, Cohen's d = 0.313, 95% CI = [−0.095, 0.720]).

ERPs data of reward anticipation processing

Figure 3A and 3B display the overall average ERPs waveforms for each cue type in the PSU and HC groups, respectively. A 2 × 2 ANCOVA of cue-N2 amplitude (Cue: reward vs neutral; Group: PSU vs HC) revealed no significant effects (Cue: F (1, 90) = 0.94, p = 0.335, η² = 0.010, 95% CI = [−0.001, 0.085]; Group: F (1, 90) = 0.85, p = 0.360, η² = 0.009, 95% CI = [−0.001, 0.083]; Cue × Group: F (1, 90) = 0.32, p = 0.574, η² = 0.004, 95% CI = [−0.001, 0.064]). Depression and anxiety were also not significant (Depression: F (1, 90) = 0.03, p = 0.862, η² < 0.001, 95% CI = [−0.001, 0.014]; Anxiety: F (1, 90) = 0.10, p = 0.753, η² = 0.001, 95% CI = [−0.001, 0.045]). The intergroup ANCOVA of ∆cue-N2 amplitude also showed no significant differences (F (1, 90) = 0.33, p = 0.567, η² = 0.004, 95% CI = [−0.001, 0.065]).

Fig. 3.

Cue-N2 and cue-P3 results during the reward anticipation phase. (A) Total average ERPs waveforms and scalp maps for the PSU and HC groups at Fz, FC1, FC2, and Cz (275–325 ms). The color-shaded error bars represent the standard error of the individual means, and the gray shaded vertical bars indicate the time window of cue-N2. (B) Total average ERPs waveforms and scalp maps for the PSU and HC groups at Cz, CP1, CP2, and Pz (350–450 ms). The color-shaded error bars represent the standard error of the individual means, and the gray shaded vertical bars indicate the time window of cue-P3. (C) Violin plots for cue-N2 and cue-P3 in the PSU and HC groups. The density plot shows the distribution, the box plot indicates the median and the first and third quartiles, and the circles and dots represent individual participants and the group mean, respectively. The error bars represent the standard error

In contrast, the 2 × 2 ANCOVA of cue-P3 amplitude showed a significant main effect of Cue type (F (1, 90) = 11.76, p = 0.001, η² = 0.116, 95% CI = [0.021, 0.244]) and a significant Group × Cue interaction (F (1, 90) = 9.87, p = 0.002, η² = 0.099, 95% CI = [0.013, 0.224]), but no significant Group effect (F (1, 90) = 2.45, p = 0.121, η² = 0.026, 95% CI = [−0.001, 0.120]). Simple effects analysis indicated that the PSU group (5.46 ± 3.89 μV) had a significantly larger cue-P3 amplitude than the HC group (3.00 ± 3.65 μV) under the reward condition (t = 3.17, p = 0.002, Cohen's d = 0.655, 95% CI = [0.237, 1.069]). Depression and anxiety were also not significant (Depression: F (1, 90) = 0.03, p = 0.959, η² < 0.001, 95% CI = [−0.001, 0.014]; Anxiety: F (1, 90) = 0.86, p = 0.357, η² = 0.009, 95% CI = [−0.001, 0.083]). Furthermore, the PSU group exhibited a significantly larger ∆cue-P3 amplitude (3.30 ± 3.16 μV) than the HC group (1.56 ± 3.42 μV) (F (1, 90) = 6.52, p = 0.012, η² = 0.066, 95% CI = [0.003, 0.183]), suggesting that the differences in ∆cue-P3 were primarily driven by reward cues (see Fig. 3C).

ERPs data of reward feedback processing

Figure 4A and 4B display the overall average ERPs waveforms for each feedback type in the PSU and HC groups, respectively. A 2 × 3 ANCOVA (Group: PSU vs HC; Feedback: gain, loss, neutral) revealed a significant main effect of Feedback type on RewP amplitude (F (1, 90) = 4.65, p = 0.011, η² = 0.049, 95% CI = [0.001, 0.157]) and a significant Group × Cue interaction (F (1, 90) = 5.12, p = 0.007, η² = 0.054, 95% CI = [0.001, 0.164]), but no significant Group effect (F (1, 90) = 2.07, p = 0.154, η² = 0.022, 95% CI = [−0.001, 0.112]). Simple effects analysis indicated that the PSU group (14.34 ± 7.27 μV) had a significantly smaller RewP amplitude than the HC group (8.63 ± 1.22 μV) under the gain condition (t = 3.09, p = 0.003, Cohen's d = 0.638, 95% CI = [0.221, 1.052]). Depression and anxiety were not significant (Depression: F (1, 90) = 0.53, p = 0.468, η² = 0.006, 95% CI = [−0.001, 0.073]; Anxiety: F (1, 90) = 0.22, p = 0.218, η² = 0.002, 95% CI = [−0.001, 0.059]). The PSU group (2.41 ± 4.33 μV) also exhibited significantly smaller ∆RewP than the HC group (5.75 ± 4.77 μV) (F (1, 90) = 9.17, p = 0.003, η² = 0.092, 95% CI = [0.011, 0.216]).

Fig. 4.

RewP and fb-P3 results during the reward feedback phase. (A) Total average ERPs waveforms and scalp maps for the PSU and HC groups at Fz, FC1, FC2, and Cz (250–350 ms). The color-shaded error bars represent the standard error of the individual means, and the gray shaded vertical bars indicate the time window of RewP. (B) Total average ERPs waveforms and scalp maps for the PSU and HC groups at Cz, CP1, CP2, and Pz (350–450 ms). The color-shaded error bars represent the standard error of the individual means, and the gray shaded vertical bars indicate the time window of fb-P3. (C) Violin plots for RewP and fb-P3 in the PSU and HC groups. The density plot shows the distribution, the box plot indicates the median and the first and third quartiles, and the circles and dots represent individual participants and the group mean, respectively. The error bars represent the standard error

Similarly, a 2 × 3 ANCOVA of fb-P3 amplitude showed a significant main effect of Group (F (1, 90) = 6.09, p = 0.015, η² = 0.063, 95% CI = [0.002, 0.177]) and a significant Group × Feedback interaction (F (1, 90) = 4.64, p = 0.011, η² = 0.049, 95% CI = [0.001, 0.157]), but no significant Feedback type effect (F (1, 90) = 1.84, p = 0.162, η² = 0.020, 95% CI = [−0.001, 0.107]). Simple effects analysis indicated that the PSU group (16.17 ± 7.39 μV) had a significantly smaller fb-P3 amplitude than the HC group (21.69 ± 8.41 μV) under the gain condition (t = 3.36, p = 0.001, Cohen's d = 0.694, 95% CI = [0.275, 1.110]), and the PSU group (15.14 ± 6.98 μV) also had a smaller fb-P3 amplitude than the HC group (18.38 ± 7.31 μV) under the loss condition (t = 2.19, p = 0.031, Cohen's d = 0.452, 95% CI = [0.041, 0.862]). Depression and anxiety were not significant (Depression: F (1, 90) = 0.02, p = 0.904, η² < 0.001, 95% CI = [−0.001, 0.009]; Anxiety: F (1, 90) = 0.58, p = 0.449, η² = 0.063, 95% CI = [−0.001, 0.074]). The PSU group (0.66 ± 4.15) also showed significantly smaller ∆fb-P3 than the HC group (3.31 ± 4.23) (F (1, 90) = 4.03, p = 0.048, η² = 0.043, 95% CI = [0.001, 0.147]). These findings suggest that differences in ∆RewP and ∆fb-P3 were driven by both gain and loss feedback (see Fig. 4C).

Dynamic structural equation model results

The standardized dynamic structural equation model results for stress, PSU, and screen time are detailed in Table 3. All Beta coefficients are standardized. The 95% confidence intervals of the posterior distributions for cross-lagged effects from stress to PSU (β = 0.17, Post. SD = 0.02, HPD 95% CI = [0.129, 0.218]) and screen time (β = 0.18, Post. SD = 0.02, HPD 95% CI = [0.135, 0.227]) did not include zero. Similarly, the 95% confidence intervals for cross-lagged effects from PSU (β = 0.15, Post. SD = 0.02, HPD 95% CI_range = [0.99, 0.191]) and screen time (β = 0.11–0.12, Post. SD = 0.02, HPD 95% CI = [0.067, 0.154]) to stress also did not include zero. T-tests showed that the effect of stress on PSU/screen time was significantly stronger than the reverse (t = 6.25–21.86, p < 0.001, Cohen's d = 0.752–1.756, 95% CI = [0.334, 2.006]) (See Appendix Table A1), indicating stress has a greater influence on PSU/screen time than vice versa.

Table 3.

Standardized dynamic structural equation model results for stress, PSU/screen time, and ERPs components (N = 78)

		Estimate	Post. SD	HPD 95% CI
				Lower	Upper
Model 1	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.29*	0.03	0.240	0.336
	ϕ22 (PSUt−1 → PSUt)	0.36*	0.02	0.313	0.406
	ϕ12 (Stresst−1 → PSUt)	0.17*	0.02	0.132	0.212
	ϕ21 (PSUt−1 → Stresst)	0.15*	0.02	0.106	0.191
	Between-person
	∆cue-N2→ϕ12	0.04	0.08	−0.102	0.196
	∆cue-N2→ϕ21	0.08	0.10	−0.119	0.280
Model 2	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.31*	0.02	0.265	0.357
	ϕ22 (STt−1 → STt)	0.31*	0.02	0.265	0.360
	ϕ12 (Stresst−1 → STt)	0.18*	0.02	0.135	0.223
	ϕ21 (STt−1 → Stresst)	0.12*	0.02	0.069	0.154
	Between-person
	∆cue-N2→ϕ12	0.10	0.09	−0.084	0.285
	∆cue-N2→ϕ21	0.06	0.11	−0.153	0.266
Model 3	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.29*	0.02	0.241	0.335
	ϕ22 (PSUt−1 → PSUt)	0.36*	0.02	0.314	0.403
	ϕ12 (Stresst−1 → PSUt)	0.17*	0.02	0.135	0.218
	ϕ21 (PSUt−1 → Stresst)	0.15*	0.02	0.099	0.191
	Between-person
	∆cue-P3→ϕ12	0.05	0.08	−0.115	0.207
	∆cue-P3→ϕ21	−0.04	0.10	−0.227	0.151
Model 4	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.31*	0.02	0.266	0.356
	ϕ22 (STt−1 → STt)	0.31*	0.02	0.265	0.358
	ϕ12 (Stresst−1 → STt)	0.18*	0.02	0.136	0.227
	ϕ21 (STt−1 → Stresst)	0.11*	0.02	0.070	0.153
	Between-person
	∆cue-P3→ϕ12	0.06	0.10	−0.131	0.258
	∆cue-P3→ϕ21	0.02	0.10	−0.168	0.210
Model 5	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.29*	0.02	0.242	0.337
	ϕ22 (PSUt−1 → PSUt)	0.36*	0.02	0.315	0.403
	ϕ12 (Stresst−1 → PSUt)	0.17*	0.02	0.129	0.209
	ϕ21 (PSUt−1 → Stresst)	0.15*	0.02	0.107	0.190
	Between-person
	∆RewP→ϕ12	−0.19*	0.08	−0.352	−0.036
	∆RewP→ϕ21	−0.07	0.10	−0.256	0.117
Model 6	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.31*	0.02	0.267	0.351
	ϕ22 (STt−1 → STt)	0.32*	0.02	0.276	0.360
	ϕ12 (Stresst−1 → STt)	0.18*	0.02	0.138	0.218
	ϕ21 (STt−1 → Stresst)	0.11*	0.02	0.067	0.152
	Between-person
	∆RewP→ϕ12	−0.20*	0.10	−0.394	−0.003
	∆RewP→ϕ21	−0.14	0.09	−0.321	0.048
Model 7	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.29*	0.02	0.241	0.336
	ϕ22 (PSUt−1 → PSUt)	0.36*	0.02	0.316	0.405
	ϕ12 (Stresst−1 → PSUt)	0.17*	0.02	0.132	0.216
	ϕ21 (PSUt−1 → Stresst)	0.15*	0.02	0.101	0.191
	Between-person
	∆fb-P3→ϕ12	−0.09	0.08	−0.248	0.060
	∆fb-P3→ϕ21	−0.03	0.09	−0.208	0.152
Model 8	Within-person
	ϕ11 (Stresst−1 → Stresst)	0.31*	0.02	0.266	0.357
	ϕ22 (STt−1 → STt)	0.31*	0.02	0.266	0.360
	ϕ12 (Stresst−1 → STt)	0.18*	0.02	0.135	0.225
	ϕ21 (STt−1 → Stresst)	0.11*	0.02	0.070	0.153
	Between-person
	∆fb-P3→ϕ12	−0.07	0.10	−0.257	0.123
	∆fb-P3→ϕ21	−0.06	0.10	−0.246	0.128

Note. *Indicates that 0 is not in the Bayesian credible interval. All Beta coefficients are standardized; HPD 95% CI, highest posterior density 95% credible interval; PSU, problematic smartphone use; ST, screen time.

At the between-person level, only ∆RewP amplitude moderated the cross-lagged effects of stress on PSU (β = −0.19, Post. SD = 0.08, HPD 95% CI = [−0.352, −0.036]) and screen time (β = −0.20, Post. SD = 0.10, HPD 95% CI = [−0.394, −0.003]). This indicates that lower ∆RewP amplitude exacerbates the negative impact of stress on PSU and screen time.

Sensitivity analysis

We examined whether group differences influenced ∆RewP's moderating effect in the DESM. Including the group × ∆RewP interaction term, ∆RewP continued to moderate the effects of stress on both PSU (β = −0.20, Post. SD = 0.08, HPD 95% CI = [−0.356, −0.041) and screen time (β = −0.20, Post. SD = 0.10, HPD 95% CI = [−0.400, −0.012), with both credible intervals excluding zero. The interaction term's credible intervals included zero for both PSU (β = −0.10, Post. SD = 0.12, HPD 95% CI = [−0.339, 0.125) and screen time (β = −0.28, Post. SD = 0.14, HPD 95% CI = [−0.563, 0.003), indicating group differences do not significantly alter ∆RewP's moderating role.

Discussion

This study aimed to investigate the reward processing mechanisms in PSU and their moderating role in the daily relationship between stress and PSU. ERP analyses revealed that, compared to the HC group, the PSU group exhibited enhanced neural activity during reward anticipation but reduced activity during reward feedback. Additionally, EMA results demonstrated that lower ∆RewP amplitude increases the likelihood of stress leading to elevated PSU levels and screen time. Thus, our findings support the presence of reward processing dysregulation in PSU and demonstrate that reduced ∆RewP exacerbates daily stress-related smartphone overuse.

Our findings reveal significant differences in reward anticipation and feedback processing between the PSU and HC groups. During reward anticipation, the PSU group exhibited faster response speeds and larger ∆cue-P3 amplitudes to monetary rewards, indicating heightened reward motivation and goal-directed behavior. This aligns with findings in substance use disorders (Martins et al., 2022) and internet gaming disorder (Kim et al., 2021), supporting the incentive sensitization theory that over-reliance on reward-driven behaviors increases addiction risk by enhancing anticipation of addictive stimuli (He et al., 2018; Robinson & Berridge, 2001). In PSU, this may manifest as frequent checking of notifications or browsing short videos to seek immediate feedback, reinforcing reward craving. Contrary to Hypothesis 1, no significant between-group differences were observed in Δcue-N2 amplitudes, suggesting that individuals with PSU may maintain intact attentional processing of reward valence. During the reward anticipation phase, the cue-N2 component reflects early attentional evaluation of reward valence, with reward cues typically eliciting stronger cue-N2 amplitudes than neutral cues (Zhang et al., 2023). Although prior research has reported attentional impairments in individuals with PSU, these deficits are primarily associated with impaired sustained attentional engagement in executive control functions (Choi et al., 2021). In contrast, the attentional processing of reward valence in this study involved a relatively simple discrimination task, which may explain the lack of significant differences between the PSU and HC groups. Thus, during reward anticipation, the motivational effects of monetary rewards may be more prominently reflected in the cue-P3 amplitude—which is linked to motivational activation—rather than in the cue-N2 amplitude, which is associated with attentional processing of reward valence.

During reward feedback processing, the PSU group exhibited significantly reduced ∆RewP and ∆fb-P3 amplitudes compared to the HC group, supporting Hypothesis 2. This suggests blunted reward responsiveness and hedonic deficits in PSU, consistent with negative correlations between PSU severity and reward-related ERP amplitudes (West et al., 2021) and observations in internet gaming disorder (Li, Wang, et al., 2020; Yao et al., 2020). While prior research has rarely examined daily PSU behaviors or reward anticipation processes (e.g., West et al., 2021), our data reveal reward processing dysfunctions across both anticipation and feedback stages, extending current evidence.

Most importantly, this study is the first to uncover the moderating role of reward processing in the relationship between daily stress and PSU/screen time. Longitudinal analyses showed that ∆RewP negatively moderated the impact of stress on PSU/screen time, but not the reverse. Although these findings partially deviate from Hypotheses 3 and 4, the significant effect of RewP is crucial. Lower ∆RewP amplitudes were associated with stronger stress-related increases in PSU/screen time, potentially reflecting the reward system's regulatory role in stress-behavior dynamics. As a neural marker of reward-related activity with generators in the dorsal striatum (Proudfit, 2015), reduced RewP amplitude reflects attenuated responsiveness in reward sensitivity networks (e.g., ventral striatum, medial prefrontal cortex). Under daily stress, blunted reward responses might drive individuals to rely on high-intensity sensory stimulation (e.g., digital media's immediate feedback) to compensate for deficient endogenous emotion regulation (Ng et al., 2019). For instance, Herzberg & Gunnar (2020) demonstrated that childhood adversity impairs emotional processing, linked to reduced reward sensitivity. Alternatively, attenuated reward sensitivity may undermine motivation for active emotion regulation, as reduced reward sensitivity primarily affects motivational anhedonia in depression progression (Nusslock & Alloy, 2017). Lower RewP might thus reflect deficient motivational aspects of emotion regulation, leading to reliance on low-cognitive-load coping strategies like screen-based interactions. Collectively, reward processing dysfunction may serve as a critical neural marker of PSU, with reward sensitivity playing a pivotal role in translating stress into maladaptive behaviors.

The data did not support the hypothesized moderation effects of N2, cue-P3, and fb-P3 in Hypotheses 3–4, with all 95% credible intervals substantially overlapping zero (N2: [−0.084, 0.258]; cue-P3: [−0.131, 0.258]; fb-P3: [−0.257, 0.123]) and showing wide ranges around 0.30, indicating inconclusive evidence for either null or meaningful effects, potentially due to their limited role in daily stress regulation. While these components are involved in reward processing, their functional specificity suggests dissociation from stress modulation: cue-N2 reflects reward valence evaluation (more negative for loss cues), cue-P3 indexes motivational salience (enhanced amplitudes for gain/loss cues), and fb-P3 represents attentional allocation to feedback outcomes (higher amplitudes for gains/losses vs. neutral; Novak & Foti, 2015), implying these reward-related evaluative mechanisms may not inherently facilitate stress coping. In contrast, RewP directly captures neural reward sensitivity. Prior research has found that heightened RewP is associated with individuals' preference for affective stimuli (e.g., emotional photographs, Brown, Jackson, & Cavanagh, 2022) and avoidance of punishments (e.g., electric shocks, Heydari & Holroyd, 2016), highlighting its unique adaptive value in mitigating daily stress effects through behavioral motivation systems. These findings provide valuable insights for developing interventions targeting reward system recalibration to disrupt the stress-PSU vicious cycle.

Limitations

Several limitations should be considered when interpreting these findings. First, while the cross-sectional and longitudinal data shed light on the role of reward feedback sensitivity in PSU, the sample primarily consisted of youth, limiting the generalizability of results to other age groups. For example, PSU in older adults may stem from factors like loneliness, and whether reward processing neural activity can reduce stress-related PSU in these populations remains to be explored. Second, although we observed a persistent moderating effect of ∆RewP in the dynamic relationship between stress and PSU, the reward task used monetary incentives. PSU individuals may process social rewards (e.g., approval from others) or PSU-related rewards (e.g., phone notifications) differently from monetary rewards. Future research should investigate ∆RewP and similar amplitudes across various reward types to guide interventions targeting specific reward processing abilities. Third, the medium effect sizes in our findings should be considered within multifactorial frameworks. The ERP analyses yielded η² values of 0.043–0.092 (largest for ∆RewP: η² = 0.092), consistent with medium effects (Richardson, 2011). The DSEM moderation effects exhibited relatively wide HPD 95% CIs (e.g., Stress → PSU: β = −0.19, HPD 95% CI = [−0.352, −0.036]). While these results, characterized by medium effects and uncertainty, do not negate the study's significance, they underscore that PSU is more likely driven by multiple factors such as cognitive control and emotion regulation (Elhai et al., 2017; Lu et al., 2024). Future research should explore additional mechanisms and expand sample sizes to improve estimation precision.

Conclusion

This study reveals reward processing dysfunction in PSU individuals, characterized by enhanced ERPs amplitudes (∆cue-P3) during reward anticipation but attenuated amplitudes (∆RewP/∆fb-P3) during reward feedback compared to the HC group. Furthermore, lower ∆RewP amplitudes exacerbate stress-related increases in PSU and screen time. These findings provide novel insights into the mechanisms underlying stress-related PSU and inform the development of targeted interventions.

Appendix

Table A1.

Tests of differences in cross-lagged path coefficients

Model	ϕ12	Post. SD ϕ12	ϕ21	Post. SD ϕ21	t	df	p	Cohen's d	95% CI for Cohen's d
Model 1	0.17	0.02	0.15	0.02	6.25	154	<0.001	0.502	0.334	0.668
Model 2	0.18	0.02	0.12	0.02	18.74	154	<0.001	1.510	1.270	1.730
Model 3	0.17	0.02	0.15	0.02	9.367	154	<0.001	0.752	0.573	0.930
Model 4	0.18	0.02	0.11	0.02	21.86	154	<0.001	1.756	1.502	2.006
Model 5	0.17	0.02	0.15	0.02	6.25	154	<0.001	0.502	0.334	0.668
Model 6	0.18	0.02	0.11	0.02	21.86	154	<0.001	1.756	1.502	2.006
Model 7	0.17	0.02	0.15	0.02	6.25	154	<0.001	0.502	0.334	0.668
Model 8	0.18	0.02	0.11	0.02	21.86	154	<0.001	1.756	1.502	2.006

Funding Statement

Funding sources: Natural Science Basic Research Plan in Shaanxi Province of China [Grant Number: 2024JC-YBMS-147]; the Fundamental Research Funds for the Central Universities [grant numbers GK202201018; 24ZYZD004]; and supported by the ‘111’ center [Grant Number: B25068].

Data availability

The data and code are accessible on the Open Science Framework: https://osf.io/wtahd/?view_only=469ebf6e6d1047c2b84abf01fd1118c8. We have reported the results of the data analysis and the results output.