Table 1.

Simulation estimates of performance characteristics including mean and Monte Carlo Standard Error in parantheses of different models using each DGP.

Model	DGP 1: ${\displaystyle {\beta }_3}$ = 0		DGP 2: ${\displaystyle {\beta }_3}$ = −3		DGP 3: ${\displaystyle {\beta }_3}$ = −3		DGP 4: ${\displaystyle {\beta }_3}$ = −3
Estimate
MLM	1.1	(0.0024)	−1.36	(0.0023)	−0.26	(0.0024)	−0.23	(0.0025)
ML Tobit	−0.0056	(0.0038)	−3.03	(0.0037)	−3.04	(0.0037)	−3.01	(0.0037)
ML Tobit ${\displaystyle {\sigma }_{ϵ}^2}$ = 5	−0.13	(0.0044)	−3.01	(0.0042)	−3.13	(0.0046)	−2.57	(0.0038)
ML Tobit ${\sigma }_{ϵ}^2$ = 10	−0.093	(0.0044)	−3.09	(0.0042)	−3.14	(0.0045)	−3.05	(0.0041)
ML Tobit ${\sigma }_{ϵ}^2$ = 15	−0.057	(0.0044)	−3.09	(0.0042)	−3.12	(0.0045)	−3.11	(0.0043)
ML Tobit ${\sigma }_{ϵ}^2$ = 20	−0.04	(0.0044)	−3.08	(0.0042)	−3.11	(0.0045)	−3.12	(0.0044)
ML Tobit ${\sigma }_{ϵ}^2$ = 25	−0.031	(0.0044)	−3.07	(0.0042)	−3.1	(0.0045)	−3.11	(0.0044)
ML Tobit ${\sigma }_{ϵ}^2$ = 30	−0.026	(0.0044)	−3.07	(0.0042)	−3.09	(0.0045)	−3.1	(0.0045)
OLS SACS	1.1	(0.0024)	−1.36	(0.0023)	−0.26	(0.0024)	−0.23	(0.0025)
OLS ANCOVA	−0.31	(0.0022)	−1.36	(0.002)	−1.69	(0.0021)	−2.43	(0.0019)
OLS Post	−1.36	(0.0023)	−1.36	(0.0022)	−2.72	(0.0023)	−2.69	(0.0018)
Tobit SACS	−0.72	(0.0044)	−3.04	(0.0041)	−3.78	(0.0044)	−4.83	(0.0048)
Tobit ANCOVA	−0.5	(0.0046)	−3.09	(0.0042)	−3.61	(0.0045)	−5.5	(0.0042)
Tobit Post	−3.07	(0.0049)	−3.06	(0.0047)	−6.13	(0.005)	−6.14	(0.004)
Coverage
MLM	0	(0)	0	(0)	0	(0)	0	(0)
ML Tobit	94.8	(0.7)	95.3	(0.67)	93.9	(0.76)	95.4	(0.66)
ML Tobit ${\sigma }_{ϵ}^2$ = 5	67.5	(1.48)	86.7	(1.07)	71.6	(1.43)	4.6	(0.66)
ML Tobit ${\sigma }_{ϵ}^2$ = 10	83.5	(1.17)	85	(1.13)	77.4	(1.32)	92.2	(0.85)
ML Tobit ${\sigma }_{ϵ}^2$ = 15	91.1	(0.9)	87.7	(1.04)	85.7	(1.11)	86.8	(1.07)
ML Tobit ${\sigma }_{ϵ}^2$ = 20	92.7	(0.82)	90	(0.95)	88.2	(1.02)	87.1	(1.06)
ML Tobit ${\sigma }_{ϵ}^2$ = 25	93.4	(0.79)	91.6	(0.88)	89.5	(0.97)	88.2	(1.02)
ML Tobit ${\sigma }_{ϵ}^2$ = 30	93.6	(0.77)	91.9	(0.86)	91.1	(0.9)	88.9	(0.99)
OLS SACS	0	(0)	0	(0)	0	(0)	0	(0)
OLS ANCOVA	0.8	(0.28)	0	(0)	0	(0)	0	(0)
OLS post	0	(0)	0	(0)	2.4	(0.48)	0	(0)
Tobit SACS	0.1	(0.1)	94.4	(0.73)	0	(0)	0	(0)
Tobit ANCOVA	7.2	(0.82)	89.7	(0.96)	1.2	(0.34)	0	(0)
Tobit post	0	(0)	93.3	(0.79)	0	(0)	0	(0)
Model SE
MLM	0.074	(2E-05)	0.074	(2E-05)	0.077	(2E-05)	0.078	(2E-05)
ML Tobit	0.12	(3E-05)	0.12	(3E-05)	0.12	(3E-05)	0.12	(3E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 5	0.1	(3E-05)	0.1	(3E-05)	0.11	(3E-05)	0.11	(4E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 10	0.12	(3E-05)	0.12	(3E-05)	0.13	(4E-05)	0.12	(3E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 15	0.13	(4E-05)	0.13	(4E-05)	0.14	(4E-05)	0.13	(3E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 20	0.13	(5E-05)	0.13	(5E-05)	0.14	(5E-05)	0.14	(4E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 25	0.14	(5E-05)	0.13	(5E-05)	0.14	(6E-05)	0.14	(5E-05)
ML Tobit ${\sigma }_{ϵ}^2$ = 30	0.14	(5E-05)	0.13	(5E-05)	0.15	(6E-05)	0.14	(5E-05)
OLS SACS	0.074	(2E-05)	0.074	(2E-05)	0.077	(2E-05)	0.078	(2E-05)
OLS ANCOVA	0.07	(2E-05)	0.065	(2E-05)	0.072	(2E-05)	0.059	(2E-05)
OLS post	0.07	(2E-05)	0.07	(2E-05)	0.072	(2E-05)	0.055	(2E-05)
Tobit SACS	0.13	(5E-05)	0.13	(5E-05)	0.14	(6E-05)	0.15	(6E-05)
Tobit ANCOVA	0.14	(6E-05)	0.14	(6E-05)	0.15	(6E-05)	0.13	(6E-05)
Tobit post	0.15	(7E-05)	0.15	(6E-05)	0.16	(7E-05)	0.13	(6E-05)

ANCOVA, analysis of covariance; DGP, data generating process; MLM, multilevel model; OLS, ordinarily least squares; SACS, Simple Analysis of Change Scores.