Boundary conditions and cognitive mechanisms of the time–space framing effect: dual-modality evidence based on the dimension comparison model

Abstract

Background

The time–space framing effect describes systematic preference changes when identical travel decisions are described using temporal versus spatial distance representations. Understanding when and why this effect occurs holds theoretical and practical importance for decision science and behavioral interventions in travel contexts.

Methods

Three experiments were conducted to examine boundary conditions and cognitive mechanisms of the time–space framing effect. Experiment 1 employed a within-subjects design and constructed 20 binary decision problems (1,038 participants) to identify when framing effects emerge. Experiment 2 used visual analog scales to measure intradimensional difference comparisons (320 participants, between-subjects design) and tested whether framing effects operate through changes in perceived intradimensional differences. Experiment 3 employed eye-tracking (43 participants, within-subjects design) to objectively assess whether individuals adopt dimension-based processing strategies and whether processing patterns predict choices and choice reversals. Statistical analyses included χ² tests, mediation analyses, mixed-effects regressions, and Bayes factor analyses.

Results

The time–space framing effect exhibited a twofold pattern determined by how frames altered the perceived intradimensional differences: frames that magnified perceived distance differences shifted preferences toward the distance-superior option, whereas frames that reduced these differences shifted preferences toward the outcome-superior option. The effect was absent when perceived intradimensional differences remained unchanged across frames. Mediation analyses indicated that changes in perceived intradimensional differences mediated the relationship between frame manipulation and choice preference, and that the presence or absence of such changes constituted a key boundary condition for the occurrence of framing effects. Eye-tracking showed that 95% of participants employed dimension-based strategies, with processing differences predicting both choices and choice reversals across frames.

Conclusions

Time–space framing effects arise from systematic shifts in dimensional comparison processes rather than superficial presentation differences. This mechanistic understanding enables prediction of framing effect direction, providing theoretically grounded guidance for precision nudging in travel contexts.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40359-026-04477-7.

Introduction

People often make spatial choices in which they weigh distance against other valued outcomes [1]. For instance, job seekers weigh distant positions offering higher compensation against proximal positions with lower salaries. Consumers choose between nearby stores with limited selection and distant retailers with greater variety. Spatial distance is often associated with temporal costs, as traveling greater distances requires more time [2]. The physical relationship between distance and time at constant velocity (d = vt) permits direct conversion between these dimensions. Psychological research demonstrates that individuals routinely employ spatial metaphors to represent temporal concepts, describing time as “near” or “far” [3–5]. These physical and psychological links suggest that spatial choices and intertemporal choices may be closely related.

The interchangeability of spatial and temporal representations enables flexible information presentation in real-world contexts. Ancient hunters could describe foraging sites using spatial terms (“two valleys away”) or temporal terms (“half a day’s time”). Modern navigation systems likewise present identical driving routes either as spatial distances (“8.3 kilometers”) or as travel times (“15 minutes”). This raises a fundamental question: When identical options are framed in spatial versus temporal terms, do preferences remain invariant as normative decision theory prescribes, or do systematic framing effects emerge?

Framing effects: from classic examples to the time–space framing

Framing effects occur when logically equivalent information presented in different formats alters decision preferences [6]. Classic framing effects operate within a single dimension and within the same decision domain. For instance, Tversky and Kahneman’s gain-loss framing manipulates outcome valence (presenting outcomes as “200 people will be saved” vs. “400 people will die”) to shift risk preferences [6]. Similarly, attribute framing manipulates product descriptions (e.g., “25% fat” vs. “75% lean”) to influence consumption evaluations [7]. Date-delay framing manipulates temporal representation (e.g., “October 17” vs. “six months”) to affect intertemporal choices [8]. Spatial distance or monetary unit framing manipulates numerical scales (e.g., “1 mile” vs. “1,760 yards”; “240 euro” vs. “32,376 yen”) to influence spatial choices [9].

Time–space framing differs fundamentally from these examples. Rather than reformulating information within a single dimension, it transforms spatial information into temporal terms. This transformation simultaneously shifts the decision domain (from spatial choice to intertemporal choice) and the psychological representation (from spatial distance to temporal delay). Understanding whether such cross-dimensional reframing alters preferences has both theoretical significance and practical value, with potential implications for designing effective nudges in travel decisions [10–12].

Empirical work has begun to document the time–space framing effect. Kuang et al. [13] constructed travel decision problems across four transportation scenarios (walking, subway, car, and high-speed rail), manipulating whether distance information was presented in spatial terms (e.g., “3 km subway trip”) or temporal terms (e.g., “5 min subway trip”) while holding outcome information (e.g., salary amounts) constant. Their results revealed significant choice shifts between frames across multiple scenarios, a pattern they defined as the time–space framing effect. In a simulated driving experiment, Kang et al. [14] further showed that the time–space framing of road sign information significantly affected drivers’ wayfinding performance.

Theoretical mechanisms: dimension comparison versus utility comparison

To elucidate the underlying mechanisms of the time–space framing effect, Kuang et al. [13] examined two competing theoretical frameworks. Dimension comparison models, exemplified by the equate-to-differentiate model [1, 15] and the tradeoff model [16], propose that decision-makers first assess the subjective differences between two options (A and B) along the temporal/spatial distance dimension (ΔDistance_A,B) and the outcome dimension (ΔOutcome_A,B), then compare the relative magnitude of these intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B). The option superior on the dimension with the larger perceived difference is selected [1, 16, 17]. In contrast, utility comparison models, exemplified by the discounted utility model [18] and its extensions, assume that decision-makers independently calculate each option’s discounted utility by devaluing outcomes based on their distance or delay, then select the option with higher overall utility [19, 20].

These models yield divergent predictions regarding framing effects. Dimension comparison models predict that framing influences choices by altering the perceived relative magnitude of intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B). Utility comparison models predict that framing influences choices by altering the relative magnitude of the two options’ utility values across frames. Kuang et al. [13] found that the dimension comparison model, but not the utility comparison model, successfully accounted for the observed framing effects.

Research gaps and the present study

Despite these initial findings, two critical gaps constrain both theoretical understanding and practical application of the time–space framing effect. First, we lack a systematic account that specifies when and why the effect occurs. Second, existing evidence relies on self-reports, which cannot distinguish actual decision processes from post-hoc rationalization. Understanding boundary conditions requires knowing the underlying mechanism; validating this mechanism requires objective process measures.

Gap 1: when does time–space framing change preferences?

Classic framing manipulations produce consistent directional effects (e.g., gain frames consistently promote risk aversion). However, time–space framing differs. Kuang et al. [13] found that the time frame (versus space frame) enhanced preference for the distance-superior option in the walking scenario but decreased this preference in other contexts. This inconsistency reveals a deeper problem: Current research has shown that preferences shift but has not identified when or in what direction shifts occur.

To account for this variability, we propose that framing operates through a causal sequence. The time–space framing manipulation alters the perceived magnitude of distance differences (ΔDistance_A,B) while leaving the perceived magnitude of outcome differences (ΔOutcome_A,B) unchanged. This asymmetry occurs because only the distance dimension undergoes representational transformation. By modulating ΔDistance_A,B, framing alters how decision-makers judge the relative magnitude of these two intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B), which then determines the dimension on which they base their decisions.

Data from Kuang et al. [13] provided indirect evidence for the above speculation. In the walking scenario, converting from space to time frame magnified the perceived ΔDistance_A,B (e.g., “13 min vs. 40 min walking trip difference” felt larger than “1 km vs. 3 km walking trip difference”). This amplification made ΔDistance_A,B appear larger than ΔOutcome_A,B in dimensional comparison, leading decision-makers to favor the distance-superior option. Other scenarios showed an opposite pattern. The time frame reduced the perceived ΔDistance_A,B (e.g., “5 min vs. 16 min subway trip difference” felt smaller than “3 km vs. 10 km subway trip difference”), prompting individuals to perceive ΔDistance_A,B as smaller than ΔOutcome_A,B and leading decision-makers to favor the outcome-superior option.

However, this “magnification-reduction” account remains post-hoc rather than predictive. Current understanding can explain why the effect occurred but cannot predict when it will occur or in what direction. More critically, it overlooks a third possibility: the “null” case where framing fails to significantly alter ΔDistance_A,B. Under this condition, the relative magnitude of intradimensional differences would remain unchanged, and no framing effect would occur.

To address these limitations, we clarify the boundary conditions for the time–space framing effect. Building on the dimension comparison framework, we specify when the effect will occur, when it will not, and in which direction it will operate. This framework enables one to predict whether a given framing manipulation will shift preferences and to design more effective behavioral interventions. Specifically, we propose:

• H1: The emergence of the time–space framing effect depends on whether the framing manipulation significantly alters the perceived relative magnitude of intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B).

This hypothesis entails two testable conditions. When framing shifts intradimensional difference comparisons, it leads to a corresponding change in preference, thereby producing the framing effect (H1a: mediating mechanism). When framing leaves intradimensional difference comparisons unchanged, preference remains stable, and the framing effect is suppressed (H1b: boundary condition). Kuang et al. [13] have demonstrated H1a, whereas H1b remains untested.

Gap 2: What cognitive process drives the effect?

Self-reports cannot definitively establish that dimensional comparison drives decisions, as they may reflect post-hoc rationalization rather than actual processing [21]. Eye-tracking offers a direct window into processing strategies [22]. If dimensional comparison governs decisions, we should observe dimension-based eye movement transitions, asymmetric attention favoring the determinant dimension, and processing asymmetries predicting both choices and reversals. Utility comparison would predict alternative-based transitions and balanced attention across dimensions [23, 24]. Objective process tracing is indispensable for distinguishing dimensional comparison from alternative strategies.

The present study

To address these issues, the present study systematically investigates the boundary conditions and cognitive mechanisms of the time–space framing effect. To test H1 systematically, we conducted three experiments. Experiment 1 employed three conditions in which the time–space framing manipulation was designed to magnify, reduce, or leave unchanged the perceived ΔDistance_A,B, which in turn should alter (or fail to alter) the relative magnitude of ΔDistance_A,B versus ΔOutcome_A,B. This design allows us to examine whether the effect occurs under each condition, thereby mapping the complete boundary conditions of the effect. Experiments 2 and 3 employed subjective evaluation and objective eye-tracking techniques, respectively, to test the dimension comparison model’s explanatory power regarding when the time–space framing effect occurs or fails to occur. This dual-modality approach provides convergent evidence supporting H1a and H1b across subjective and objective, static and dynamic measurement approaches.

Experiment 1

Method

Participants

Based on Kuang et al.’s [13] within-subjects findings showing 21% of participants made different choices across frames (proportion discordant pairs = 0.21), we conducted a priori power analysis for McNemar χ² test via G*Power 3.1 software [25]. Assuming α = 0.05, power (1 − β) = 0.80, OR = 0.25 (medium effect size, φ = 0.35), the analysis indicated a minimum required sample size of 200 participants per scenario.

Data were collected via a large-scale online experiment administered on the Sojump platform (https://www.wjx.cn). To reduce participant burden, we distributed the four travel-scenario decision tasks across four parallel survey versions. Each version contained one travel-scenario decision task, several filler questions unrelated to the present study, and instructional manipulation check (IMC) items. Participants were randomly assigned to complete one survey version. The system automatically excluded those who failed the IMC, a procedure that enhances data quality and reliability in online experiments [26, 27].

After exclusions, the final valid samples included 284 participants (137 female, M_age= 30.58 years, SD = 9.69) for walking, 248 participants (102 female, M_age = 30.22 years, SD = 9.49) for subway, 253 participants (140 female, M_age = 29.24 years, SD = 10.87) for car, and 253 participants (139 female, M_age = 28.98 years, SD = 9.78) for high-speed rail. All participants provided informed consent and received ¥11 as compensation.

Materials

We constructed 20 binary travel decision problems across four common travel scenarios (walking, subway, car, and high-speed rail; see Appendix, Table S1). Each problem presented two options with a clear tradeoff structure: One offered shorter distance but lower outcome value (the distance-superior option); the other offered higher outcome value but longer distance (the outcome-superior option). Each problem was framed in spatial (e.g., “6-km subway ride”) and temporal terms (e.g., “10-min subway ride”), with spatial and temporal representations made mathematically equivalent by assuming a constant velocity. Taking the subway scenario as an example, the decision problem described in the space [time] frame was presented as follows:

“Suppose you are looking for a job. Two companies are available. The only way to go to both companies from your home is by subway. Note: The average speed of the subway is approximately 0.60 km/min (36 km/h). Which one would you favor?

Option A: The company is approximately a 6-km [10-min] subway ride from your home, with a monthly salary of 7,200 yuan.

Option B: The company is approximately a 15-km [25-min] subway ride from your home, with a monthly salary of 8,000 yuan.”

To test H1 systematically, we first conducted a pilot study (n = 50; 38 female, M_age = 30.82 years, SD = 8.81) in which participants judged whether converting distance information from the space frame to the time frame magnified, reduced, or left unchanged perceived distance difference between the two options (ΔDistance_A,B), which in turn affects the relative magnitude judgment between ΔDistance_A,B and ΔOutcome_A,B. Each problem was assigned to one of three conditions based on the condition that received the highest selection rate in the pilot study. Specifically:

1. Magnified condition (Problems 1–3, 9): Temporal representation magnified perceived distance differences (ΔTemporal Distance_A,B > ΔSpatial Distance_A,B). In these problems, the time frame should increase the relative salience of the distance dimension compared to the outcome dimension, making ΔDistance_A,B appear larger relative to ΔOutcome_A,B. According to H1a, this should increase preference for the distance-superior option.

2. Reduced condition (Problems 6–8, 11, 12, 16–19): Temporal representation reduced perceived distance differences (ΔTemporal Distance_A,B < ΔSpatial Distance_A,B). In these problems, the time frame should decrease the relative salience of the distance dimension, making ΔDistance_A,B appear smaller relative to ΔOutcome_A,B. According to H1a, this should increase preference for the outcome-superior option.

3. Unchanged condition (Problems 4, 5, 10, 13–15, 20): Temporal and spatial representations yielded equivalent perceived distance differences (ΔTemporal Distance_A,B ≈ ΔSpatial Distance_A,B). In these problems, the framing manipulation should leave the relative magnitude judgment between ΔDistance_A,B and ΔOutcome_A,B unchanged. According to H1b, these problems should show no framing effects.

Procedure

Participants completed a within-subjects design with two blocks: all problems in the space frame (Block 1) and all problems in the time frame (Block 2), with block order counterbalanced across participants. To minimize memory-based consistency bias, we inserted unrelated filler questions and IMC items between blocks. This design allows direct assessment of whether the same individual changes preferences across frames, providing a conservative but precise test of framing effects.

Results

Table 1 presents choice patterns under space versus time frames for all 20 problems, tested via McNemar χ² tests.

Table 1.

Choice patterns across space and time frames in Experiment 1

Scenarios	Time frame
Walking (n = 284)			P1		P2		P3		P4		P5
			A	B	A	B	A	B	A	B	A	B
	Space frame	A	123	25	107	37	86	21	92	34	48	24
		B	50	86	33	107	55	122	46	112	19	193
		χ2	7.68**		0.13		14.33***		1.51		0.37
		φ	0.16		0.02		0.22		0.07		0.04
Subway (n = 248)			P6		P7		P8		P9		P10
			A	B	A	B	A	B	A	B	A	B
	Space frame	A	86	60	73	52	42	33	24	16	36	33
		B	14	88	9	114	18	155	20	188	17	162
		χ2	27.37***		28.92***		3.84*		0.25		4.50*
		φ	0.33		0.34		0.12		0.03		0.13
Car (n = 253)			P11		P12		P13		P14		P15
			A	B	A	B	A	B	A	B	A	B
	Space frame	A	43	18	117	37	60	31	25	10	51	31
		B	22	170	17	82	24	138	10	108	17	154
		χ2	0.23		6.69**		0.66		0		3.52
		φ	0.03		0.16		0.05		0		0.12
High-speed rail (n = 253)			P16		P17		P18		P19		P20
			A	B	A	B	A	B	A	B	A	B
	Space frame	A	119	45	139	40	124	41	90	39	91	43
		B	18	71	17	57	27	61	15	109	18	101
		χ2	10.73**		8.49**		2.49		9.80**		9.44**
		φ	0.21		0.18		0.10		0.20		0.19

In each problem, Option A represents the distance-superior option, and Option B represents the outcome-superior option. Italicized values indicate participants who changed choices across frames. ^***p < .001, ^**p < .01, ^*p < .05

Magnified condition (Problems 1–3, 9). Half of these problems (1, 3) exhibited significant framing effects consistent with predictions (both ps < .05, φ = 0.16 and 0.22, respectively). The time frame increased preferences for the distance-superior option relative to the space frame, confirming that magnifying perceived distance differences shifts choices toward distance-based decisions. Problems 2 and 9 yielded non-significant effects (both ps > .05).

Reduced condition (Problems 6–8, 11, 12, 16–19). Seven of these problems (6–8, 12, 16, 17, 19) showed significant effects in the predicted direction (all ps < 0.05, φ ranging from 0.12 to 0.34). The time frame shifted preferences from the distance-superior to the outcome-superior option, demonstrating that reducing perceived distance differences prompted outcome-based decisions. Problems 11 and 18 showed non-significant effects (both ps > .05).

Unchanged condition (Problems 4, 5, 10, 13–15, 20). Five of these problems (4, 5, 13–15) showed non-significant framing effects (all ps > .05), consistent with H1b’s prediction that stable intradimensional difference comparisons yield stable preferences. However, two problems (10, 20) unexpectedly showed significant effects (both ps < .05, φ = 0.13 and 0.19, respectively) following the reduction pattern.

Overall, 14 of 20 problems (70%) behaved as predicted, supporting H1. The magnified condition showed 2 of 4 predicted effects (50%), the reduced condition showed 7 of 9 predicted effects (78%), and the unchanged condition showed 5 of 7 predicted null effects (71%). These results indicate that the classification procedure was generally valid and effective, although it may be ineffective in some cases.

The remaining six problems (30%) deviated from predictions. Four problems (Problems 2 and 9 in the magnified condition, Problems 11 and 18 in the reduced condition) failed to show predicted effects. In the unchanged condition, two problems (Problems 10 and 20) unexpectedly showed significant effects. These deviations can be attributed to two potential limitations of the present experiment. First, the pilot sample (n = 50) was relatively small, which may have yielded unstable selection rate estimates, particularly for problems where responses were distributed across conditions. For instance, in Problem 2 and 9, the plurality-assigned condition (magnified) led the next most-endorsed condition (unchanged) by merely 8% points (40% vs. 32% and 42% vs. 34%, respectively); in Problem 20, the plurality-assigned condition (unchanged) led the next most-endorsed condition (reduced) by only 4% points (44% vs. 40%). Given these narrow differences, the classifications of these problems carry inherent uncertainty, and their null or unexpected results in the formal experiment are more plausibly attributed to classification uncertainty than to theoretical failure. Second, the within-subjects design may have reduced sensitivity to detect subtle effects [28]. For instance, Problems 11 and 18, for which pilot classifications were comparatively clear with the reduced condition endorsed by 48% and 60% of participants respectively, most plausibly reflect design insensitivity rather than classification error.

These limitations also complicate the interpretation of null results. For the nine problems showing null results (Problems 2, 4, 5, 9, 11, 13–15, 18), we could not determine whether intradimensional difference comparisons remained unchanged, as H1b predicts, or whether the null findings reflected low classification discriminability or insufficient design sensitivity. Resolving this ambiguity requires both a more sensitive design and a direct measure of intradimensional difference comparisons, neither of which was available in Experiment 1.

Experiment 2

Experiment 2 addressed these limitations through two modifications. First, we employed a between-subjects design with increased sample size (N = 320), providing greater sensitivity for detecting framing effects that may have been obscured by the within-subjects design in Experiment 1. Second, we directly measured intradimensional difference comparisons using a visual analog scale (VAS), which allowed us to assess whether the framing manipulation altered perceived dimensional differences and to test whether such changes mediated choice preferences. Together, these modifications provide a basis for testing both H1a and H1b that goes beyond the indirect evidence available in Experiment 1. We focused on the nine problems from Experiment 1 that showed no significant framing effect, as these constitute the most direct test of the boundary condition specified by H1b.

Method

Participants

The minimum sample size required for this experiment was determined based on applicable statistical testing methods: (1) For independent sample chi-square tests, setting α = 0.05, power (1 − β) = 0.80, and medium effect (φ) = 0.3, we calculated the required minimum sample size of 88 participants using G*Power 3.1 software [25]; (2) For mediation effect analysis, Schönbrodt and Perugini [29] and Golec de Zavala et al. [30] recommend setting the initial sample size above 250 to ensure result stability. Similar to Experiment 1, Experiment 2 incorporated IMC items to identify valid participants. Ultimately, 320 participants were recruited through the Sojump platform (189 female, M_age = 31.28 years, SD = 8.06), with 160 participants each in the space and time frame conditions. Each participant received ¥5 compensation upon completing the experiment.

Materials and procedure

Participants were randomly assigned to either the space or time frame condition and completed a choice task followed by an intradimensional difference comparison (IDC) task. The choice task consisted of the nine problems from Experiment 1 that showed non-significant framing effects (Problems 2, 4, 5, 9, 11, 13–15, 18).

The IDC task employed a visual analog scale (VAS) developed by Jiang et al. [31], which has been widely used in related research [13, 17, 23]. The scale measured participants’ subjective evaluations of the relative magnitude of ΔDistance_{A, B} and ΔOutcome_{A, B} between two options (Fig. 1). Participants indicated their judgment on a six-point VAS labeled A through F and coded from 1 to 6, with left-tilting options A to C indicating ΔDistance_A,B > ΔOutcome_A,B and right-tilting options D to F indicating ΔOutcome_A,B > ΔDistance_A,B. Greater tilt indicated a larger perceived relative difference between the two ends of the balance.

Fig. 1.

Schematic illustration of the six-point VAS used in the IDC task (space frame condition shown). Options A–C indicate that the distance difference exceeds the outcome difference (to a significant, moderate, or slight degree, respectively), whereas options D–F indicate the reverse (to a slight, moderate, or significant degree, respectively)

To ensure that participants understood the IDC task, written instructions explaining the meaning of the VAS were provided prior to the formal experiment. A comprehension check was also included, requiring participants to select the balance option that matched the instructional requirements. Only participants who passed the check proceeded to the experiment; those who failed were excluded.

Results

Choices

Table 2 presents descriptive statistics and independent chi-square test (χ²) results for the choice task. Five of nine problems (2, 4, 5, 9, 14) replicated Experiment 1, showing no significant difference in choice preferences across frames (all ps > .05), indicating no time–space framing effect. However, the remaining four problems (11, 13, 15, 18) diverged from Experiment 1, showing significant differences in choice preferences across frames (all ps < .05, φ ranging from 0.12 to 0.28), indicating detection of the time–space framing effect. These results partially demonstrate the influence of experimental design (within-subjects vs. between-subjects) on framing effect detection.

Table 2.

Results of choice and IDC tasks in Experiment 2

Problem	Frame	Choice task				VAS ratings in IDC task
		A	B	χ2	φ	M (SD)	t	d
2	Space	49	111	0.23	0.03	3.89 (1.32)	−0.24	−0.03
	Time	53	107			3.93 (1.43)
4	Space	66	94	0.81	0.05	3.46 (1.44)	−0.90	−0.10
	Time	74	86			3.61 (1.55)
5	Space	35	125	0.97	0.06	4.13 (1.25)	−0.86	−0.10
	Time	28	132			4.24 (1.23)
9	Space	17	143	0.59	0.04	4.28 (1.24)	−1.48	−0.17
	Time	13	147			4.48 (1.17)
11	Space	29	131	4.37*	0.12	4.24 (1.31)	−2.60**	−0.29
	Time	16	144			4.60 (1.13)
13	Space	91	69	24.67***	0.28	3.32 (1.21)	−3.62***	−0.41
	Time	47	113			3.79 (1.11)
14	Space	17	143	0.59	0.04	4.30 (1.10)	−1.66	−0.19
	Time	13	147			4.49 (0.98)
15	Space	87	73	22.75***	0.27	3.30 (1.13)	−5.11***	−0.57
	Time	45	115			3.94 (1.13)
18	Space	113	47	15.05***	0.22	3.03 (1.23)	−2.40*	−0.27
	Time	79	81			3.36 (1.24)

In each problem, Option A represents the distance-superior option, and Option B represents the outcome-superior option. ^***p < .001, ^**p < .01, ^*p < .05

Mediation analysis of intradimensional difference comparison

We first conducted separate t-tests for each problem to determine whether the VAS ratings changed due to the time–space frame manipulation. As expected, for all five problems where no time–space framing effect was detected (Problems 2, 4, 5, 9, 14), the VAS ratings showed no significant difference between space and time frame conditions (all ps > .05), indicating that time–space frame manipulation failed to induce significant changes in ΔDistance_{A, B} versus ΔOutcome_{A, B}. For all four problems where the time–space framing effect was detected (Problems 11, 13, 15, 18), the VAS ratings differed significantly between frames (all ps < .05, d ranging from 0.27 to 0.57), indicating that time–space frame manipulation induced significant changes in ΔDistance_{A, B} versus ΔOutcome_{A, B}.

To further test the effect of description frame (space vs. time) on choice preference through the evaluation of intradimensional difference comparison (VAS rating), we performed a mediation analysis. Following recommendations from previous researchers [32, 33], when the dependent variable is binary, it is appropriate to apply the RMediation package in R, testing the significance of Za ×Zb through the product of coefficients method. If the 95% confidence interval (CI) for Za ×Zb does not include 0, the mediation effect is significant.

Table 3 shows the results of mediation analysis. In all four problems where the time–space framing effect was detected, the 95% CI for Za × Zb did not contain 0, indicating that the intradimensional difference comparison results significantly mediated the relationship between time–space frame manipulation and choice preference, thus supporting H1a. In all five problems where no time–space framing effect was detected, all the 95% CIs for Za × Zb contained 0, indicating non-significant mediation effects. Notably, in these five problems, although the intradimensional difference comparison results did not significantly change across frames (Path a: X→M, all ps > .05, consistent with t-test results), they still significantly predicted choice preference (Path b: M→Y, all ps < .001), supporting H1b.

Table 3.

Mediation effects of intradimensional difference comparison results (M) on the relationship between time–space frame (X) and choice preference (Y)

Problem	X→M			M→Y			X→M→Y	Mediation model path diagram
	a	SE	Za	b	SE	Zb	95% CI for Za× Zb
11	0.36**	0.14	2.60	1.42***	0.19	7.46	[0.12, 0.94]	Significant effect:
13	0.47***	0.13	3.62	2.03***	0.23	8.79	[0.42, 1.54]
15	0.64***	0.13	5.11	1.86***	0.22	8.53	[0.69, 1.77]
18	0.33*	0.14	2.40	1.30***	0.15	8.47	[0.08, 0.81]
2	0.04	0.15	0.24	0.99***	0.12	8.18	[-0.26, 0.34]	Non-significant effect:
4	0.15	0.17	0.90	1.13***	0.12	9.17	[-0.20, 0.55]
5	0.12	0.14	0.86	0.88***	0.13	6.51	[-0.13, 0.36]
9	0.20	0.13	1.48	1.21***	0.19	6.43	[-0.08, 0.59]
14	0.19	0.12	1.66	1.76***	0.26	6.74	[-0.06, 0.78]

a denotes linear regression coefficients, b denotes logistic regression coefficients, and Za and Zb denote standardized coefficients. In the path diagram, solid arrows indicate significant paths, whereas dashed arrows indicate non-significant paths. ^***p < .001, ^**p < .01, ^*p < .05

Overall, these results support H1a and H1b: when frame manipulation altered intradimensional difference comparisons, choice preferences changed; when comparisons were not altered, preferences remained stable.

Experiment 3

Experiment 2 provided subjective evidence supporting the dimension comparison mechanism underlying the time–space framing effect. However, self-reports cannot definitively establish that dimensional comparison occurs during the decision process itself rather than serving as post-hoc rationalization. Experiment 3 employed eye-tracking methodology to provide objective, process-level validation of the dimensional comparison mechanism. We tested whether individuals’ decision processes conform to the dimensional comparison strategy under both frame conditions and whether eye movement indices predict choice and choice reversal behavior.

Method

Participants

Following Brysbaert and Stevens’s [34] recommendations for cognitive experiments with repeated measures, we required a minimum of 1600 total trials. With 64 trials per participant in the experiment, this yielded a minimum sample of 25 participants. A total of 47 participants with normal or corrected-to-normal vision were recruited from university pools, four of whom withdrew due to calibration failure. Ultimately, 43 valid participants (25 female, M_age = 24.88 years, SD = 2.10) were recorded, each compensated ¥50.

Apparatus

The experiment employed an EyeLink 1000 Plus tower-mounted eye tracker (1000 Hz sampling rate, nine-point calibration; fixation position error < 0.5° after calibration). All experimental stimuli appeared on a 24-inch monitor (1920 × 1080 resolution, 144 Hz refresh rate). A chin rest fixed participants’ heads 70 cm from the screen, producing a visual angle of 41° × 24°.

Materials

A pilot experiment (n = 161; 94 female, M_age = 20.78 years, SD = 1.89) screened materials using walking and subway versions of commute decision problems (see Experiment 1 for an example). Each version generated 40 pairs of logically equivalent space- and time-frame problems. Parameter settings followed the logic of Experiment 1, with half the problems designed to satisfy conditions for producing or not producing the time–space framing effect. Based on the pilot results, we selected eight problem pairs with the largest and smallest effect sizes from each travel mode (32 pairs total: 32 space-frame and 32 time-frame problems) as the formal trial materials (see Appendix, Table S2). Eight additional problems served as practice trials, and four problems contained strongly dominant options for quality checks.

Procedure

The experiment required participants to choose their preferred option (distance-superior vs. outcome-superior) while eye movements were recorded. After calibration, participants first completed 8 practice trials. Figure 2 illustrates formal trial procedure. Each trial began with presentation of a walking or subway scenario. After reading, participants pressed the Spacebar to trigger a central fixation dot for drift calibration. Once fixation was achieved, two options appeared onscreen. Participants viewed options without time constraint but responded immediately upon deciding by pressing “F” for the left option or “J” for the right option. Following the response, a 1,000 ms blank screen preceded the next trial. Following the guidelines of Holmqvist et al. [35], four non-overlapping Areas of Interest (AOIs; indicated by red boxes in Figs. 2 and 582 × 462 pixels) were defined in a 2 × 2 grid on the choice task screen to capture participants’ fixations on the distance and outcome dimensions of the two options. Neighboring AOIs were separated by 1° of visual angle to ensure the spatial accuracy and reliability of the eye-tracking data. AOI boundaries were invisible to participants.

Fig. 2.

Schematic illustration of the experimental procedure for a single trial (walking scenario shown). Red boxes indicate the Areas of Interest (AOIs)

The 64 experimental trials were divided into two blocks (32 trials each: one space frame, one time frame) with a 2-minute rest between blocks. Each block included two randomly positioned quality checks. The presentation positions of option outcome and distance information were counterbalanced within blocks, and block order was counterbalanced across participants.

Eye movement indices and hypotheses

To test the dimension comparison model’s explanatory power for the time–space framing effect, we examined decision processing under both frame conditions and its relationship with choice behavior. Three categories of eye movement indices were analyzed:

1. Scanpath similarity score [36]. This index quantifies scanpath similarity between any two trials (ranging [0, 1]; higher values indicate more similar information search strategies). Following Zhou et al. [36], we computed pairwise similarities for each participant across three conditions: within time frame tasks, within space frame tasks, and between tasks. We hypothesized:

   • H2a: Average similarity scores within the same frame show no difference from the between-frame scores, indicating similar information search strategies across frames [36].

2. SM value [37]. SM is the preferred index for measuring whether individuals’ information search strategies lean more toward alternative-based or dimension-based approaches [38, 39]. The SM function is as follows:

Where A and D represent the numbers of alternatives and dimensions (in this experiment A = D = 2), r_a and r_d represent the number of alternative-based and dimension-based transitions respectively, and N represents the total number of transitions. According to Pfeiffer et al. [38] and Huang et al. [23], SM < 0 indicates dimension-based strategies dominate, while SM > 0 indicates alternative-based strategies dominate. We hypothesized:

• H2b: SM values in both space and time frame tasks are significantly less than 0, supporting the dimension comparison model.

• (3)Dimensional processing difference indices [24]: fixation duration difference (FDD), fixation count difference (FCD), and saccade count difference (SCD). Each index measures the processing difference between distance and outcome dimensions, calculated as: FDD/FCD/SCD = (Distance dimension value) – (Outcome dimension value). These indices reflect processing depth and complexity, evaluating how dimensional processing affects choice behavior. Liu et al. [17] demonstrated that greater fixation counts and duration on a certain dimension led to more evidence accumulation for that dimension, increasing the likelihood of selecting the option superior on that dimension. Accordingly, we hypothesized:

• H2c: Larger dimensional processing differences (FDD/FCD/SCD) increase the likelihood of selecting the distance-superior option.

• H2d: Greater changes in dimensional processing differences between frames (ΔFDD/ΔFCD/ΔSCD = |Time frame value – Space frame value|) increase the likelihood of choice reversal.

Results

All participants passed quality checks. The experiment yielded 2752 valid trials containing 55,846 fixations. After excluding fixations outside interest areas or shorter than 50 ms, 49,039 valid fixations remained for analysis. We applied mixed-effect models (MEMs) using the lme4 and lmerTest packages in R, treating participants and task trial (pair) numbers as random factors to enhance the generalizability of results [40]. For non-significant effects (p > .05), we computed Bayes factors (BF₀₁) using the BayesFactor package to quantify evidence for the null hypothesis [41].

Choices

McNemar χ² tests were conducted for the 32 problem pairs (see Appendix, Table S2). Results largely replicated the pilot study. Fifteen pairs showed significant choice preference differences between space and time frame conditions (all ps < .05), indicating the time–space framing effect. The remaining 17 pairs showed non-significant differences (all ps > .05), indicating no framing effect.

Scanpath similarity score

To test H2a, we conducted linear mixed-effects regression with scanpath similarity score as the dependent variable and trial source (within time frame vs. within space frame vs. between frames) as fixed factor (participants as random intercepts). Bayes factors quantified evidence for the null hypothesis. Results revealed no significant differences among conditions. The within time frame group (M = 0.604, SD = 0.038) did not differ from the between-frames group (M = 0.598, SD = 0.036; b = 0.0062, SE = 0.004, p = .434; BF₀₁ = 3.41). Similarly, the within space frame group (M = 0.604, SD = 0.039) did not differ from the between-frames group (b = 0.0057, SE = 0.004, p = .528; BF₀₁ = 3.56), nor did the two within-frame groups differ (b = 0.0005, SE = 0.004, p > .999; BF₀₁ = 4.43). These findings indicate that individuals’ information search strategies did not differ between space and time frame tasks, with moderate evidence (BF₀₁ > 3) supporting H2a.

SM

We conducted linear mixed-effects regression with SM value as dependent variable and frame type (space vs. time) as fixed factor (participants and trial pairs as random factors). Bayes factor analysis complemented the regression. Results showed no significant effect of frame type on SM value (b = − 0.05, SE = 0.05, t(42) = − 1.06, p = .297; BF₀₁= 9.28), indicating that information search strategies did not differ between frame conditions. This finding provides moderate evidence for H2a, consistent with the scanpath similarity results. Additionally, random effects revealed large between-participant variation in baseline SM values (variance = 0.20), but small variation in the effects of frame type across participants (variance = 0.05) or trial pairs (variance = 0.04). Given this individual variability, we conducted participant-level analyses to test H2b.

One-sample t-tests examined whether each participant’s mean SM value across all 64 trials differed from 0. Among 43 participants, 41 had SM values significantly below 0 (all ps < .001), supporting H2b. One participant (ID 26) showed a negative but non-significant SM (M = − 0.09, SD = 0.72; t(63) = − 0.98, p = .337); and one participant (ID 2) showed a significantly positive SM (M = 0.38, SD = 0.87; t(63) = 3.47, p < .001). These results indicate that the vast majority of participants (95%, except IDs 2 and 26) employed dimension-based search strategies, supporting H2b. Figure 3 displays the distribution of SM values across trials and participants.

Fig. 3.

Individual-level heatmap of SM values. Blue indicates SM < 0 (dimension-based processing), red indicates SM > 0 (alternative-based processing), with color intensity reflecting |SM| magnitude

Dimensional processing difference indices

When examining how dimensional processing differences predict choice and choice reversal (H2c and H2d), we conducted analyses both including and excluding two participants (IDs 2 and 26) who showed atypical decision strategies. The results were unchanged. We therefore report the more conservative analyses excluding these participants, providing a purer test of dimensional comparison predictions among the 41 participants who clearly employed dimension-based strategies.

To test H2c, we conducted logistic mixed-effects regression with choice as dependent variable (0 = outcome-superior option, 1 = distance-superior option), dimensional processing difference indices (FDD/FCD/SCD) as fixed factors, and participants and 64 trials as random factors.1 All three indices significantly predicted choice (Fig. 4): fixation duration difference (FDD: b = 0.16, SE = 0.07, p = .026, OR = 1.17), fixation count difference (FCD: b = 0.16, SE = 0.07, p = .017, OR = 1.18), and saccade count difference (SCD: b = 0.17, SE = 0.06, p = .006, OR = 1.18). These results support H2c: larger dimensional processing differences (FDD/FCD/SCD), reflecting greater attention to the distance dimension, increased the likelihood of selecting the distance-superior option.

Fig. 4.

Dimensional processing difference indices predict choice preference. Red lines show logistic regression fits with 95% confidence intervals. (a) FDD = fixation duration difference between distance and outcome dimensions; (b) FCD = fixation count difference between distance and outcome dimensions; (c) SCD = saccade count difference between distance and outcome dimensions

To test H2d, we conducted logistic mixed-effects regression with choice reversal as dependent variable (0 = no reversal, 1 = reversal), ΔFDD/ΔFCD/ΔSCD as fixed factors, and participants and 32 trial pairs as random factors. All three change indices significantly predicted choice reversals (Fig. 5): ΔFDD (b = 0.21, SE = 0.07, p = .003, OR = 1.23), ΔFCD (b = 0.17, SE = 0.07, p = .012, OR = 1.19), and ΔSCD (b = 0.17, SE = 0.07, p = .011, OR = 1.19). These results confirmed H2d: greater changes in dimensional processing differences across frames, indicating shifts in the dimension underlying decisions, increased the likelihood of choice reversal.

Fig. 5.

Changes in dimensional processing differences predict choice reversals across frames. Red lines show logistic regression fits with 95% confidence intervals. (a) ΔFDD = changes in fixation duration difference between distance and outcome dimensions across time and space frames; (b) ΔFCD = changes in fixation count difference between distance and outcome dimensions across time and space frames; (c) ΔSCD = changes in saccade count difference between distance and outcome dimensions across time and space frames

General discussion

Understanding when and why framing effects occur is more theoretically and practically informative than merely documenting their existence [42, 43]. The risky choice framing literature illustrates this point. Following Tversky and Kahneman’s [6] initial discovery, subsequent studies showed that framing effects are not universal but vary systematically with task characteristics [42]. Specifically, preferences vary with probability and outcome magnitude, yielding the “fourfold pattern”: risk seeking for small gains and large losses, and risk aversion for large gains and small losses [44–48]. These findings led some researchers to question whether utility comparison models (e.g., prospect theory) can fully account for complex decision phenomena and to propose dimension comparison accounts, such as the equate-to-differentiate model [44, 49].

Our research applies this approach to investigate time–space framing. Prior work documented that representing travel distance in temporal versus spatial terms shifts choice preferences and affects task performance [13, 14]. We extend this evidence by examining the boundary conditions and cognitive mechanisms underlying these effects.

Boundary conditions of the time–space framing effect

Experiments 1 to 3 collectively suggest that the time–space framing effect is conditional rather than universal. The effect emerged when frame manipulation induced significant changes in perceived intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B), but was absent when such manipulation left these comparisons unchanged. Moreover, the effect exhibited a “twofold” pattern: when framing magnified perceived differences along the distance dimension (ΔDistance_A,B), individuals tended to base their decisions on this dimension, favoring distance-superior options; when framing reduced these differences, individuals instead relied on outcome dimension, favoring outcome-superior options.

This pattern represents a theoretically significant advance over classic framing effects that show stable directional tendencies (e.g., gain frames promoting risk aversion). The context dependency reflects the underlying mechanism: framing alters the relative salience of intradimensional differences, which in turn determines the decision-relevant dimension. This mechanistic account enables predictions about the direction of the framing effect based on how a given frame modulates perceived intradimensional differences.

Dual-modality evidence for dimension comparison

We employed two complementary methods to test whether the dimension comparison model accounts for the cognitive mechanism underlying the time–space framing effect. In Experiment 2, a visual analog scale (VAS) measured individuals’ subjective evaluations of intradimensional differences, providing direct outcome-level evidence for the proposed mechanism [17]. In Experiment 3, eye tracking captured the dynamic process of decision-making, offering real-time, objective process-level evidence while minimizing self-report bias [21, 22]. Taken together, the results of both methods provide convergent support for the dimension comparison model.

In Experiment 2, the correspondence between changes in VAS ratings and the presence or absence of framing effects provided outcome-level support for the dimension comparison model. Mediation analyses confirmed that altered intradimensional difference comparisons accounted for observed preference shifts. Even in problems where framing did not alter preferences, intradimensional difference comparisons remained a significant predictor of choice. This suggests that dimensional comparison serves as a stable basis for decision-making, regardless of whether framing succeeds in modifying perceived dimensional differences. In Experiment 3, most participants (95%; 41 of 43) showed dimension-based rather than alternative-based processing patterns, as indicated by negative SM values. Scanpath similarity analyses revealed broadly consistent information search strategies across time and space frames, which is consistent with the prediction that individuals tend to employ dimension-based strategies across frame types. Moreover, indices of dimensional processing differences (fixation duration, fixation count, and saccade count) were associated with choices and predicted choice reversals across frames. This finding suggests that these eye-movement indices may serve as useful markers of the psychological processes underlying decisions, though their status as definitive mechanistic indicators should be interpreted cautiously given the modest sample size of Experiment 3.

These findings are broadly consistent with evidence from other decision domains. Wei et al. [50] found that in continuous risky decision-making, representing risk using single occurrence probability or average risk occurrence time triggers different risk preferences, and the dimension comparison model can explain this phenomenon, suggesting a shared psychological mechanism across probability (risk) and time (intertemporal) decisions. Huang et al. [23] also found that individuals exhibit similar dimension-based decision strategies in risky, intertemporal, and spatial choices. Extending this evidence, the present findings show convergence between subjective evaluations and eye-movement indices, supporting the dimension comparison model across multiple levels of measurement.

Theoretical and methodological contributions

The convergence between subjective evaluations and objective eye-tracking validates the dimension comparison model across multiple analytical levels. Eye-tracking provides process-level evidence that dimensional comparison operates during actual decision-making rather than serving merely as post-hoc rationalization. This addresses a critical limitation of self-report measures and strengthens confidence in the dimensional comparison interpretation.

Our findings also contribute methodologically by showing that dimension-based processing models can be integrated with recent extensions of the drift diffusion model (DDM). Traditional DDM applications assume alternative-based evidence accumulation, but recent work explores dimension-based DDM variants [51]. Our research provides empirical support for this modeling direction while suggesting three extensions: (1) incorporating how different dimensional units (spatial vs. temporal) influence evidence accumulation rates; (2) accounting for how attention allocation patterns predict decision behavior; and (3) extending to multiple decision domains to achieve model generalizability.

Dimension comparison and information leakage

An alternative perspective on framing effects is the information leakage account [52, 53], which posits that logically equivalent frames may nonetheless convey different choice-relevant information: speakers tend to select the frame whose focal attribute has increased relative to a reference point, and listeners draw corresponding inferences. In the present context, it is plausible that temporal and spatial frames may carry different implicit meanings. For instance, temporal descriptions (relative to spatial ones) may prompt individuals to consider subjective experiential cost, such as the physical effort associated with travel may heighten attention to temporal information [54].

At the same time, several features of the present framing design may constrain the extent to which such pragmatic inference alone can account for the observed effects. First, classic information leakage operates within a single dimension or attribute (e.g., “half full” vs. “half empty”, “75% lean” vs. “25% fat”), whereas time–space framing involves cross-dimensional transformations between cognitively asymmetric representations [3], to which the reference point mechanism does not readily generalize. Second, the explicit provision of velocity conversion information in all experiments anchored both frames to an identical objective description, thereby reducing the degree of informational ambiguity on which pragmatic inference typically relies. Third, whereas the information leakage account generally predicts unidirectional, valence-consistent shifts in preference (e.g., a positive frame implies the relative abundance of a desirable attribute, leading to more favorable evaluations) [52], the present effect exhibits a “twofold” pattern: the same frame can either magnify or reduce perceived distance differences depending on travel mode [13]. This pattern is difficult to reconcile with a purely information leakage account but follows naturally from the dimension comparison model.

Nonetheless, the two accounts need not be mutually exclusive. Information leakage may contribute to the formation of perceived intradimensional differences (e.g., if temporal frame implies greater subjective cost, this may modulate perceived distance differences), while the dimension comparison process determines how such altered differences are translated into choice. In this sense, information leakage may explain why a given frame shifts dimensional salience, while the dimension comparison model explains how such shifts affect choice behavior. Future research could systematically test this integrative account.

Implications for precision nudging

The present findings suggest that nudging strategies may need to be reconsidered. Traditional approaches often assume that framing effects are relatively stable. For instance, gain framing, relative to loss framing, is often used to nudge individuals toward more conservative choices in risky contexts. The present research, however, points to a more context-dependent pattern in the case of time–space framing. More specifically, the direction of the framing effect appears to depend on whether a given frame magnifies or reduces perceived distance differences. Frames that magnify these differences are more likely to nudge individuals toward options that involve shorter distance, whereas frames that reduce these differences tend to shift choices toward options that are superior in terms of outcomes. This pattern provides practitioners with greater flexibility in selecting presentation formats, which allows them to make particular dimensions more salient depending on the desired behavioral outcome, rather than relying on a single approach across contexts.

Our findings also have practical implications for the design of intelligent transportation systems. In navigation apps (e.g., AutoNavi Map), route information may be more effective when its framing is adapted to the travel context rather than presented in a uniform format across situations. Specifically, temporal representations (e.g., “13-minute walk”) appear to make differences in distance feel larger than their spatial equivalents (e.g., “1 kilometer”). When the goal is to nudge users toward the nearer route, presenting information in temporal terms may therefore be more effective in short-distance walking scenarios. For medium- to long-distance travel by subway, car, or high-speed rail, however, the pattern in the present study generally points in the opposite direction, with spatial representations appearing more effective than temporal ones in nudging users toward the nearer option. One possible application would be for a navigation app to shift its default display from time-based units (minutes) to distance-based units (kilometers) once a trip exceeds a certain threshold, to keep attention focused on the dimension most likely to support the intended choice.

Another implication is that the framing of travel information may be adapted to individual differences in attentional allocation. In Experiment 3, variation across participants in dimensional processing patterns suggests that individuals may differ in their sensitivity to different dimensions. If gaze-based dimensional preferences are shown to be reliable in larger and more diverse samples, navigation systems could potentially use attention patterns to infer which dimension a user is more sensitive to and adjust presentation formats accordingly. One possible implementation would be to provisionally default to temporal formats for users who consistently attend to temporal information, and to spatial formats for those who focus more on spatial information.

It should be noted that these recommendations are based on the specific scenarios examined in the present study and on evidence from a relatively modest sample size. Further validation across a broader range of travel contexts and more diverse populations is needed before these approaches can be implemented in practice.

Conclusion

This research indicates that time–space framing effects reflect systematic shifts in dimensional comparison processes rather than superficial presentation differences. Three findings support this conclusion: (1) framing effects are conditional and emerge when the framing manipulation significantly alters perceived intradimensional differences (ΔDistance_A,B vs. ΔOutcome_A,B); (2) the effect follows a predictable twofold pattern, depending on whether framing magnifies or reduces perceived distance differences; and (3) converging evidence from subjective evaluations and objective eye-tracking supports the role of dimensional comparison as the underlying mechanism.

Abbreviations

IMC

Instructional manipulation check

IDC

Intradimensional difference comparison

VAS

Visual analog scale

FDD

Fixation duration difference

FCD

Fixation count difference

SCD

Saccade count difference

Authors’ contributions

YK conceptualized the study, collected and analyzed the data, and drafted the manuscript. HZL provided guidance on study design, data analysis, and manuscript preparation. FLW and ZXH contributed to data analysis and manuscript preparation. SL provided guidance during study conceptualization and manuscript preparation and served as the guarantor for the work. All authors have approved the final manuscript.

Funding

This research was partially supported by the National Natural Science Foundation of China (No. 72301096).

Data availability

The datasets and analysis code supporting the conclusions of this study are available in the Science Data Bank website: https://www.scidb.cn/anonymous/bmUyeUVi.

Declarations

Ethics approval and consent to participate

The study was conducted in accordance with the Declaration of Helsinki. Ethical approval for this study was obtained from the Ethics Committee of the Normal School, Hubei University (Approval No. H2023066). Informed consent was obtained from all participants.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.