TABLE 2.

Analysis of CPS data using the reduced and proposed models (1000 women)

	Reduced Model (Without Between-Subject Random Effects)			Proposed Model (With Between-Subject Random Effects)
Parameter	Mean	SD	95% CI	Mean	SD	95% CI
Intercept
β1	0.68	0.15	(0.51, 1.03)	0.58	0.05	(0.47, 0.67)
β2	1.74	0.49	(0.51, 2.32)	2.52	0.19	(2.18, 2.81)
Δ	−2.12	0.43	(−2.89, −1.44)	−2.05	0.30	(−2.52, −1.32)
c	5.18	0.89	(3.93, 7.20)	3.32	0.61	(1.97, 4.24)
Parity
${\beta }_{1_{\text{Parity}}}$	0.00	0.01	(−0.01, 0.01)	0.00	0.01	(−0.01, 0.03)
${\beta }_{2_{\text{Parity}}}$	0.41	0.08	(0.13, 0.51)	0.40	0.04	(0.31, 0.46)
ΔParity	−0.23	0.05	(−0.33, −0.14)	−0.26	0.07	(−0.38, −0.12)
cParity	0.04	0.11	(−0.18, 0.26)	0.29	0.08	(0.10, 0.44)
Gaptime
${\beta }_{1_{\text{No}\hspace{0.17em}\text{data}}}$	−0.05	0.02	(−0.09, −0.01)	−0.04	0.02	(−0.09, 0.00)
${\beta }_{1_{\text{Below}\hspace{0.17em}\text{median}}}$	0.00	0.02	(−0.05, 0.05)	0.01	0.02	(−0.04, 0.05)
${\beta }_{2_{\text{No}\hspace{0.17em}\text{data}}}$	−0.43	0.18	(−0.89, −0.12)	−0.60	0.15	(−0.86, −0.34)
${\beta }_{2_{\text{Below}\hspace{0.17em}\text{median}}}$	−0.42	0.25	(−0.89, 0.04)	−0.32	0.14	(−0.59, −0.03)
ΔNo data	−0.11	0.20	(−0.51, 0.24)	−0.31	0.25	(−0.90, 0.15)
ΔBelow median	−0.61	0.25	(−1.08, −0.13)	−0.70	0.24	(−1.16, −0.22)
cNo data	0.62	0.24	(0.14, 1.09)	0.95	0.36	(0.31, 1.64)
cBelow median	0.39	0.31	(−0.18, 1.00)	0.59	0.37	(−0.08, 1.31)
Labor induced
${\beta }_{1_{\text{Induced}\hspace{0.17em}\text{labor}}}$	−0.30	0.13	(−0.58, −0.17)	−0.22	0.03	(−0.28, −0.17)
${\beta }_{2_{\text{Induced}\hspace{0.17em}\text{labor}}}$	0.93	0.45	(0.43, 2.28)	0.46	0.10	(0.30, 0.64)
ΔInduced labor	0.94	0.26	(0.47, 1.43)	0.87	0.23	(0.35, 1.25)
cInduced labor	2.37	0.82	(0.22, 3.51)	3.59	0.46	(2.89, 4.67)
Between variance
${\mathrm{\Sigma }}_{1{\beta }_1}$	—	—	—	0.02	0.00	(0.01, 0.02)
${\mathrm{\Sigma }}_{1{\beta }_2}$	—	—	—	0.13	0.04	(0.07, 0.23)
Σ1Δ	—	—	—	0.30	0.16	(0.10, 0.70)
Σ1c	—	—	—	0.27	0.12	(0.10, 0.57)
Within variance
${\mathrm{\Sigma }}_{2{\beta }_1}$	0.05	0.02	(0.03, 0.09)	0.03	0.00	(0.03, 0.04)
${\mathrm{\Sigma }}_{2{\beta }_2}$	2.54	0.45	(2.08, 3.99)	2.51	0.21	(2.00, 2.87)
Σ2Δ	13.46	2.28	(9.51, 17.05)	15.98	1.16	(13.82, 18.29)
Σ2c	6.59	1.33	(3.85, 9.03)	6.70	1.05	(3.48, 8.28)
Intracluster correlation
${\rho }_{12{\beta }_1}$	—	—	—	0.31	0.03	(0.25, 0.38)
${\rho }_{12{\beta }_2}$	—	—	—	0.05	0.02	(0.03, 0.09)
ρ12Δ	—	—	—	0.02	0.01	(0.01, 0.04)
ρ12c	—	—	—	0.04	0.02	(0.01, 0.08)
Error variance
${\sigma }_e^2$	0.65	0.07	(0.57, 0.80)	0.59	0.03	(0.56, 0.69)
Goodness of fit
DIC		656130.3			145326.9
Bayesian P-value		0.499			0.500

Note:${\mathrm{\Sigma }}_{1{\beta }_1}$, ${\mathrm{\Sigma }}_{1{\beta }_2}$, Σ_1Δ, Σ_1c are the diagonal elements of matrix Σ₁, ${\mathrm{\Sigma }}_{2{\beta }_1}$, ${\mathrm{\Sigma }}_{2{\beta }_2}$, Σ_2Δ, Σ_2c are the diagonal elements of matrix Σ₂; ${\rho }_{12{\beta }_1}=\frac{{\mathrm{\Sigma }}_{1{\beta }_1}}{{\mathrm{\Sigma }}_{1{\beta }_1}+{\mathrm{\Sigma }}_{2{\beta }_1}}$${\rho }_{12{\beta }_2}=\frac{{\mathrm{\Sigma }}_{1{\beta }_2}}{{\mathrm{\Sigma }}_{1{\beta }_2}+{\mathrm{\Sigma }}_{2{\beta }_2}}$, ${\rho }_{12\mathrm{\Delta }}=\frac{{\mathrm{\Sigma }}_{1\mathrm{\Delta }}}{{\mathrm{\Sigma }}_{1\mathrm{\Delta }}+{\mathrm{\Sigma }}_{2\mathrm{\Delta }}}$,${\rho }_{12c}=\frac{{\mathrm{\Sigma }}_{1c}}{{\mathrm{\Sigma }}_{1c}+{\mathrm{\Sigma }}_{2c}}$.