. Author manuscript; available in PMC: 2015 Jul 17.

Published in final edited form as: Psychol Methods. 2015 Mar;20(1):142–164. doi: 10.1037/a0038962

Table 1.

Summary of Models Used in the Simulation Study.

MSEM	Descriptions	Questions to address
Model 1	The cusp-inspired MSEM in Eqs 11–12, with $a_{1_{1}} = a_{2_{1}} = - 10$ and $b_{21_{1}, α} = b_{22_{1}, α} = 0$ to prevent cases in the low-β regime from moving into the high and low regimes.
Model 2	Same specifications as Model 1, with the exceptions that the values of $a_{1_{1}}$ , $a_{2_{1}}$ , $b_{21_{1}, α}$ and $b_{22_{1}, α}$ were all freely estimated.	Q1: Can the MSEM be used to detect the unique transition patterns of the cusp system? What proportion of MC replications shows significant LRT results in comparing Model 1 to Model 2?
Model 3	A 2-regime model with no explicit constraint.	Q2: Can IC measures detect the existence of 3 regimes?
Model 4	Same specifications as Model 2, with the exception that b_β,high = b_β,low in Eq (11).	Q3: Can evidence of bifurcation be detected? What proportion of MC replications shows significant LRT results comparing Model 2 to Model 4?
Model 5–Model 8	Identical to Models 1–4, respectively, but β was latent; membership in the high- vs. low-β regime was unknown.	Relative differences in performance between Models 1–4 (with known β membership) compared to Models 5–8.
MSEM-RS
Model 1	The cusp-inspired MSEM-RS described in Eqs 11 (with time index to denote repeated measurements), 13 and 14
Model 2	Less restrictive 3-R model: same specifications as MSEM-RS Model 1, with the exception that b_α,high,low = b_α,med in Eq (11).	Q4: Can the differential effects of α on y_it be detected? What proportion of MC replications shows significant LRT results in comparing MSEM-RS Model 1 to 2?
Model 3	The longitudinal analog of the 2-regime MSEM Model 3	Q5: Can IC measures detect the higher-order Markov dependency on C_i₀?
Model 4	The longitudinal analog of MSEM Model 4, with b_β,high = b_β,low in Eq. (11).	Q6: Can evidence of bifurcation be detected? What proportion of MC replications shows significant LRT results comparing Model 1 to Model 4?
Model 5–Model 8	Identical to Models 1–4, respectively, but β was latent; membership in the high- vs. low-β regime was unknown.	Relative differences in performance between Models 1–4 compared to Models 5–8 when longitudinal data are used.