. 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 2.

Summary Statistics of Results from Testing Questions 1–3 Using MSEMs as Highlighted in the Simulation Design Section.

Known β membership, T = 1 and n = 500

Q1: Proportion of MC runs with significant LRT from freeing LO(low β → high) and LO(low β → low) = 1.00

Q2:

Proportion (AIC favors less restrictive 3-R Model to 2-R Model) = 1.00

Proportion (BIC favors less restrictive 3-R Model to 2-R Model) = .51

Proportion (aBIC favors less restrictive 3-R Model to 2-R Model) = .95

Proportion (Entropy favors cusp-inspired 3-R model among all models considered) = .97

Q3: Proportion of MC runs with significant LRT with equal b_β across regimes = 1.00

Proportion (cases free of SE estimation problems for logit parameters in Model 2) =.94

Known β membership, T = 1 and n = 200

Q1: Proportion of MC runs with significant LRT from freeing LO(low β → high) and LO(low β → low) = .96

Q2:

Proportion (AIC favors less restrictive 3-R Model to 2-R Model) = .93

Proportion (BIC favors less restrictive 3-R Model to 2-R Model) = .17

Proportion (aBIC favors less restrictive 3-R Model to 2-R Model) = .90

Proportion (Entropy favors cusp-inspired 3-R model among all models considered) = .89

Q3: Proportion of MC runs with significant LRT with equal b_β across regimes = 1.00

Proportion (cases free of SE estimation problems for logit parameters in Model 2) =.54

Unknown β membership, T = 1 and n = 500

Q1: Proportion of MC runs with significant LRT from freeing LO(low β → high) and LO(low β → low) = .97

Q2:

Proportion (AIC favors less restrictive 3-R Model to 2-R Model) = .99

Proportion (BIC favors less restrictive 3-R Model to 2-R Model) = .35

Proportion (aBIC favors less restrictive 3-R Model to 2-R Model) = .93

Proportion (Entropy favors cusp-inspired 3-R model among all models considered) = .88

Q3: Proportion of MC runs with significant LRT with equal b_β across regimes = 1.00

Proportion (cases free of SE estimation problems for logit parameters in Model 2) =.69

Unknown β membership, T = 1 and n = 200

Q1: Proportion of MC runs with significant LRT from freeing LO(low β → high) and LO(low β → low) = .68

Q2:

Proportion (AIC favors less restrictive 3-R Model to 2-R Model) = .87

Proportion (BIC favors less restrictive 3-R Model to 2-R Model) = .06

Proportion (aBIC favors less restrictive 3-R Model to 2-R Model) = .84

Proportion (Entropy favors cusp-inspired 3-R model among all models considered) = .82

Q3: Proportion of MC runs with significant LRT with equal b_β across regimes = .99

Proportion (cases free of SE estimation problems for logit parameters in Model 2) =.38