Table 4.

Summary Statistics of Parameter Estimates from MSEM Model 6, T = 1 and n = 500 across 500 MC Replications.

	True θ	Mean $\widehat{\theta }$	SD	2.5 %tile	97.5%tile	$a\widehat{SE}$
λβ,1	1.20	1.20	0.01	1.19	1.22	0.01
λβ,2	0.90	0.90	0.01	0.89	0.91	0.01
${\psi }_{\mathit{\epsilon },{\beta }_1}^2$	0.09	0.09	0.01	0.07	0.11	0.01
${\psi }_{\mathit{\epsilon },{\beta }_2}^2$	0.09	0.09	0.01	0.07	0.11	0.01
${\psi }_{\mathit{\epsilon },{\beta }_3}^2$	0.09	0.09	0.01	0.08	0.10	0.01
μβ,high	2.50	2.50	0.05	2.41	2.59	0.05
ψβ,high	0.49	0.49	0.05	0.40	0.58	0.05
μβ,low	−2.50	−2.50	0.05	−2.60	−2.41	0.05
ψβ,low	0.49	0.49	0.05	0.39	0.59	0.05
τhigh		1.06	0.10	0.83	1.21	0.07
bα,high&low		0.12	0.01	0.09	0.15	0.01
bβ,high		0.20	0.03	0.17	0.27	0.02
ψζ,high&low		0.12	0.01	0.09	0.14	0.01
τlow		−1.06	0.10	−1.22	−0.84	0.07
bβ,low		−0.20	0.03	−0.28	−0.16	0.02
τmed		−0.00	0.24	−0.52	0.47	0.15
bα,med		0.18	0.08	0.01	0.31	0.06
ψζ,med		0.19	0.07	0.04	0.31	0.06
$a_{1_0}$, logit intercept for Rhigh β	0.00	−0.00	0.00	−0.01	0.01	0.09
$b_{{11}_1,\mathrm{\Delta }}$, Δ LO(high β → high)		2.84	3.99	−2.02	13.93	2.24
$b_{{12}_1,\mathrm{\Delta }}$, Δ LO(high β → low)		2.74	3.76	−2.21	11.84	2.34
$a_{1_1}$, logit intercept for LO(low β → high)		−1.99	3.84	−11.75	2.93	2.09
$a_{2_1}$, logit intercept for LO(low β → low)		−1.93	3.63	−10.85	3.02	2.23
$b_{{11}_1,\alpha }$, α → ΔLO(high β → high)		1.74	1.01	0.48	4.17	0.65
$b_{{12}_1,\alpha }$, α → ΔLO(high β → low)		−1.75	1.11	−3.94	−0.45	0.66
$b_{{21}_1,\alpha }$, α → LO(low β → high)		1.01	1.12	−0.69	3.95	0.69
$b_{{22}_1,\alpha }$, α → LO(low β → low)		−0.88	1.10	−3.72	0.81	0.69
Pr(high β → high)a		0.41	0.11	0.18	0.60	0.10
Pr(high β → low)		0.39	0.11	0.19	0.58	0.10
Pr(high β → med)		0.20	0.09	0.05	0.42	0.09
Pr(low β → high)		0.19	0.15	0.00	0.55	0.12
Pr(low β → low)		0.20	0.16	0.00	0.55	0.12
Pr(low β → med)		0.62	0.24	0.02	0.98	0.18

MSEM-RS = mixture structural equation model with regime-switching; MC = Monte Carlo; True θ = True parameter values; Mean $\widehat{\theta }$ = Average point estimate for each parameter across MC runs; 2.5%tile and 97.5%tile = 2.5th and 97.5th percentiles for each parameter across MC runs; $a\widehat{SE}=\mathrm{SE}$ estimate for a parameter across MC runs.

^aThe class and transition probabilities were computed using Equations 8, 9 and 12 with α_i set to 0.