Investigating travelers’ heterogeneous attitudes toward losses: insights from a stated preference experiment

Figures & data

Table 1. Attribute details of bus lines.

Attributes	Definitions	Levels
In-vehicle Time	time in a bus (min)	35, 45, 55, 65
Wait Time	time waiting for a bus, excluding the transfer time (min)	2, 6, 10, 14
Walk Time	time walking out of a bus, excluding the transfer time (min)	2, 6, 10, 14
Standing Duration	ratio of standing time over in-vehicle time in a bus	0, 0.33, 0.67, 1
Ticket Price	price of the ticket (¥)	0.5, 1, 1.5, 2
Transfer Time	time for transfer (min)	0, 3, 6, 9

Figure 1. An example of stated choice tasks (translated from Chinese).

Table 2. Distribution of sample characteristics.

Socio-demographic attribute	Level	Percentage
Gender	Male	45.07%
	Female	54.93%
Marital Status	Single	56.73%
	Married	43.27%
Age	≤ 20	13.68%
	21 ~ 30	54.70%
	31 ~ 40	22.20%
	41 ~ 50	5.61%
	51 ~ 65	2.91%
	≥ 66	0.90%
Driving Experience (Year)	0	43.05%
	(0, 1]	15.92%
	(1, 3]	19.06%
	(3, 5]	12.11%
	(5, 10]	6.95%
	> 10	2.91%
Income (Yuan/Month)	≤ 3499	42.83%
	3500 ~ 6999	32.96%
	7000 ~ 9999	15.47%
	10,000 ~ 14,999	6.05%
	15,000 ~ 19,999	2.02%
	≥ 20,000	0.67%
Education Level	High school or lower	9.42%
	Bachelor	76.23%
	Master/PhD	14.35%

Table 3. The parameter values to generate synthetic data.

	Data 0	Data 1
Alternative-specific attributes
In-vehicle time	−2.6	−2.6
Wait time	−3.2	−3.2
Walk time	−2.2	−2.2
Standing duration	−0.8	−0.8
Ticket price	−0.4	−0.4
Transfer time	−3.6	−3.6
Loss attitude parameters (exponential form)
In-vehicle time	0.0	−0.2
Wait time	0.0	−0.2
Walk time	0.0	0.0
Standing duration	0.0	0.0
Ticket price	0.0	0.2
Transfer time	0.0	0.2
Threshold 1	−2.5	−2.5
Threshold 2	−1.2	−1.2
Threshold 3	−0.2	−0.2
Threshold 4	1.6	1.6

Table 4. Estimation results based on synthetic data (t values in the parenthesis).

	base data | base model	base data | loss-attitude model	loss-attitude data | base model	loss-attitude data | loss-attitude model
Alternative-specific attributes
In-vehicle time	-2.6396	-2.6271	-2.3866	-2.6361
	(-2.1725)	(-0.7033)	(11.8488)	(-0.9362)
Wait time	-3.1764	-3.2775	-2.8720	-3.2622
	(0.5388)	(-0.8030)	(7.5233)	(-0.6448)
Walk time	-2.2283	-2.1502	-2.2320	-2.1313
	(-0.6524)	(0.5959)	(-0.7400)	(0.8224)
Standing duration	-0.7924	-0.7841	-0.8030	-0.7854
	(0.8617)	(0.8560)	(-0.3434)	(0.7824)
Ticket price	-0.3952	-0.4040	-0.4438	-0.4035
	(0.8305)	(-0.3396)	(-7.5211)	(-0.2993)
Transfer time	-3.5863	-3.6409	-3.7713	-3.6119
	(0.2364)	(-0.3177)	(-2.9660)	(-0.0922)
Loss attitude parameters (exponential form)
In-vehicle time	0 (fixed)	0.0124	0 (fixed)	-0.1881
		(0.5391)		(0.4697)
Wait time	0 (fixed)	-0.0689	0 (fixed)	-0.2643
		(-1.3147)		(-1.1004)
Walk time	0 (fixed)	0.0734	0 (fixed)	0.0878
		(1.1454)		(1.3672)
Standing duration	0 (fixed)	0.0244	0 (fixed)	0.0309
		(0.6013)		(0.7679)
Ticket price	0 (fixed)	-0.0418	0 (fixed)	0.1571
		(-0.8104)		(-0.9149)
Transfer time	0 (fixed)	-0.0310	0 (fixed)	0.1803
		(-0.5080)		(-0.3542)
Threshold 1	-2.4951	-2.4920	-2.5188	-2.4971
	(0.5499)	(0.4763)	(-2.0933)	(0.1693)
Threshold 2	-1.1934	-1.1897	-1.2098	-1.1891
	(1.0709)	(0.6684)	(-1.5801)	(0.7100)
Threshold 3	-0.1989	-0.1951	-0.2182	-0.1976
	(0.1965)	(0.3255)	(-3.3652)	(0.1583)
Threshold 4	1.5978	1.6011	1.5755	1.5982
	(-0.3303)	(0.0710)	(-3.6341)	(-0.1148)
Convergent LL	-225444.9	-225442.6	-226129.9	-226080.5
RMSE	0.014277	0.039498	0.147223	0.039979

Note: the t values are to test if an estimated value is statistically different from its target value

Note: the column name ‘X data – Y model’ means the results in this column are from estimating Y model using X data

Figure 2. Final log-likelihoods based on various numbers of scrambled Halton draws.

Table 5. Estimation results for the base model.

	Estimate	Std. Error	p-value
Alternative-specific attributes
In-vehicle time	−2.6156	0.1677	0.0000 ***
Wait time	−3.2072	0.4152	0.0000 ***
Walk time	−2.2040	0.4178	0.0000 ***
Standing duration	−0.8028	0.0804	0.0000 ***
Ticket price	−0.3700	0.0534	0.0000 ***
Transfer time	−3.5556	0.5281	0.0000 ***
Threshold 1	−2.4581	0.0866	0.0000 ***
Threshold 2	−1.2491	0.0621	0.0000 ***
Threshold 3	0.1685	0.0498	0.0007 ***
Threshold 4	1.6398	0.0642	0.0000 ***
Initial log-likelihood	−2871.237
Final log-likelihood	−2537.777
Rho-squared	0.1161
Adjusted Rho-squared	0.1127
Number of parameters	10
Number of observations	1784

*** p-value <0.01; ** p-value <0.05; * p-value <0.1

Table 6. Estimation results for the loss-attitude model.

	Estimate	Std. Error	p-value
Alternative-specific attributes
In-vehicle time	−1.3585	0.3611	0.0002 ***
Wait time	−3.3398	0.4467	0.0000 ***
Walk time	−2.3214	0.4448	0.0000 ***
Standing duration	−0.7686	0.1072	0.0000 ***
Ticket price	−0.4015	0.0570	0.0000 ***
Transfer time	−3.2457	0.6000	0.0000 ***
Threshold 1	−3.0652	0.1830	0.0000 ***
Threshold 2	−1.6503	0.1120	0.0000 ***
Threshold 3	−0.1280	0.0836	0.1258
Threshold 4	1.3788	0.0897	0.0000 ***
Loss attitude to in-vehicle time^†
Constant	0.9480	0.3323	0.0043 ***
std. deviation	0.6764	0.1774	0.0001 ***
Income (Yuan/Month)
≥ 7000	0.3810	(referenced level)
≤ 3499	−0.2719	0.1130	0.0162 **
3500 ~ 6999	−0.1091	0.0997	0.2741
Marital status
Married	−0.2203	(referenced level)
Single	0.2052	0.0847	0.0154 **
Loss attitude to standing duration
std. deviation	−0.8536	0.2739	0.0018 ***
Initial log-likelihood	−2871.237
Final log-likelihood	−2516.739
Rho-squared	0.1235
Adjusted Rho-squared	0.1179
Number of parameters	16
Number of scrambled Halton draws	1000
Number of observations	1784

*** p-value <0.01; ** p-value <0.05; * p-value <0.1

^†All socio-demographic attributes are effects coded

Figure 3. Changes in attribute utility in terms of in-vehicle time.

Figure 4. Changes in attribute utility in terms of standing duration.

Figure 5. Responses to gains and losses in terms of in-vehicle time.

Figure 6. Responses to gains and losses in terms of standing duration.