Table 3.

Estimated coefficients (standard errors) of the fitted models on DCE_TTO data

	Conditional logit model (after combination)			Mixed logit model						Conditional logit model (after combination)			Conditional logit model Anchored utility
	Coef.	SE	p value	Coef.	SE	p value	SD	SE	p value	Coef.	SE	p value	Coef.	95% CI
Year	0.365	0.009	< 0.001	0.465	0.013	<0.001	0.247	0.006	< 0.001	0.370	0.008	< 0.001	–	–
Physical functioning × year
PF2	− 0.009	0.005	0.052	− 0.008	0.006	0.168	0.068	0.012	0.060	− 0.010	0.005	0.043	− 0.027	− 0.0011 to − 0.0520
PF3	− 0.018	0.005	< 0.001	− 0.022	0.006	< 0.001	0.046	0.013	0.075	− 0.019	0.004	< 0.001	− 0.050	− 0.0267 to − 0.0736
PF4	− 0.054	0.005	< 0.001	− 0.069	0.005	< 0.001	0.005	0.020	0.791	− 0.054	0.005	< 0.001	− 0.145	− 0.1206 to − 0.1688
PF5	− 0.150	0.005	< 0.001	− 0.217	0.007	< 0.001	0.171	0.009	< 0.001	− 0.150	0.005	< 0.001	− 0.404	− 0.3774 to − 0.4308
Role limitation × year
RL2	− 0.011	0.004	0.010	0.001	0.006	0.965	0.006	0.020	0.760	− 0.011	0.004	0.010	− 0.029	− 0.0073 to − 0.0516
RL3	− 0.011	0.005	0.017	− 0.023	0.006	< 0.001	0.066	0.011	0.078	− 0.011	0.005	0.018	− 0.030	− 0.0056 to − 0.0552
RL4	− 0.030	0.004	< 0.001	− 0.024	0.006	< 0.001	0.043	0.016	0.006	− 0.030	0.004	< 0.001	− 0.081	− 0.0589 to − 0.1034
RL5	− 0.041	0.005	< 0.001	− 0.009	0.006	0.137	0.005	0.058	0.926	− 0.041	0.005	< 0.001	− 0.112	− 0.0880 to − 0.1354
Social functioning × year
SF2	− 0.013	0.005	0.004	− 0.010	0.006	0.071	–	–	–	− 0.013	0.005	0.004	− 0.035	− 0.0114 to − 0.0586
SF3	− 0.014	0.004	0.001	− 0.027	0.006	< 0.001	–	–	–	− 0.014	0.004	0.001	− 0.038	− 0.0151 to − 0.0613
SF4	− 0.039	0.004	< 0.001	− 0.051	0.006	< 0.001	–	–	–	− 0.039	0.004	< 0.001	− 0.104	− 0.0819 to − 0.1266
SF5	− 0.042	0.004	< 0.001	− 0.048	0.006	< 0.001	–	–	–	− 0.042	0.004	< 0.001	− 0.114	− 0.0923 to − 0.1348
Pain × year
PN2	− 0.027	0.005	< 0.001	− 0.032	0.006	< 0.001	0.037	0.014	0.068	− 0.027	0.005	< 0.001	− 0.072	− 0.0446 to − 0.0996
PN3	− 0.029	0.005	< 0.001	− 0.013	0.007	0.054	0.058	0.014	0.213	− 0.029	0.005	< 0.001	− 0.079	− 0.0536 to − 0.1054
PN4	− 0.057	0.005	< 0.001	− 0.061	0.007	< 0.001	0.032	0.014	0.020	− 0.057	0.005	< 0.001	− 0.155	− 0.1295 to − 0.1802
PN5	− 0.173	0.006	< 0.001	− 0.216	0.007	< 0.001	0.078	0.012	0.093	− 0.173	0.006	< 0.001	− 0.466	− 0.4382 to − 0.4948
PN6	− 0.200	0.005	< 0.001	− 0.263	0.007	< 0.001	0.127	0.011	< 0.001	− 0.200	0.005	< 0.001	− 0.541	− 0.5126 to − 0.5688
Mental health × year
MH2	0.002	0.004	0.686	0.004	0.006	0.543	–	–	–	0.000	–	–	0.000	–
MH3	− 0.003	0.004	0.568	− 0.026	0.006	< 0.001	–	–	–	− 0.004	0.004	0.341	− 0.010	0.0104 to − 0.0303
MH4	− 0.053	0.005	< 0.001	− 0.075	0.006	< 0.001	–	–	–	− 0.054	0.004	< 0.001	− 0.146	− 0.1266 to − 0.1656
MH5	− 0.072	0.005	< 0.001	− 0.099	0.006	< 0.001	–	–	–	− 0.073	0.004	< 0.001	− 0.197	− 0.1750 to − 0.2193
Vitality × year
VT2	0.007	0.005	0.145	0.019	0.006	0.001	–	–	–	0.000	–	–	0.000	–
VT3	− 0.027	0.005	< 0.001	− 0.011	0.006	0.058	–	–	–	− 0.031	0.004	< 0.001	− 0.083	− 0.0611 to − 0.1040
VT4	− 0.029	0.005	< 0.001	− 0.044	0.006	< 0.001	–	–	–	− 0.033	0.004	< 0.001	− 0.089	− 0.0702 to − 0.1085
VT5	− 0.058	0.005	< 0.001	− 0.070	0.006	< 0.001	–	–	–	− 0.062	0.004	< 0.001	− 0.167	− 0.1475 to − 0.1871
Log likelihood	− 35,563.72			− 29,583.62						− 35,430.03
AIC	71,179.45			59,228.25						70,914.06
BIC	71,395.13			59,427.93						71,119.74

For the mixed logit model, a dimension was specified as having random coefficients (with a normal distribution) as long as the SD of one response level was statistically significant (p < 0.05). 500 Halton draws were used for the simulation. Among all six dimensions, the SDs of SF, MH, and VT were consistently insignificant. As such, these three dimensions were set as fixed coefficients. Although the mixed logit model estimates had a better model fit according to AIC and BIC information criteria, the conditional logit model was selected as the final model given that (1) among all estimations, less non-monotonic coefficients were found; (2) only four dimension levels had statistically significant SDs (as such, the preference heterogeneity was not substantial). Coefficients presented in bold represent the non-monotonicity

AIC Akaike information criterion, BIC Bayesian information criterion, CI confidence interval , Coef. coefficient, DCE_TTO discrete-choice experiments with a duration dimension, MH mental health, PF physical functioning, PN pain, RE random effects, RL role limitation, SD standard deviation, SE standard error, SF social functioning, VT vitality