Table 1.

Parameter settings and results for two simulations comparing the LRR model to the LME model. Simulation 1 generated data based on the LRR model with a random effect for the intercept and slope. The variance for LME model was adjusted using the sandwich estimator to ensure appropriate size in simulation 1. Simulation 2 generated data based on the LME model with a random effect for the intercept and linear time. For both simulations, a cubic polynomial equation was used to model time and bivariate covariate was used to estimate differences in the rate of change of the outcome.

	Simulation 1	Simulation 2
True Model Structure	LRR	LME
Sample Size	100	100
Time Structure ( ${\beta }_1^{\ast },{\beta }_2^{\ast },{\beta }_3^{\ast }$)	0.11, −0.0002, −0.00005	0.12, −0.002, −0.00002
Intercept and Main Effect (α0, α1)	4, −0.06	4, 0.02
Difference in Rates (θ)	−0.1	−0.05
Random Effects Covariance ( ${\tau }_0^2,{\tau }_1^2$, ρ)	0.005,0.05*,−.78	0.006,0.00001**,0
Measurement Error Variance (σ2)	0.005	0.07
Size of Test (LRR, LME)	.047, .051	.044, .041
Power of Test (LRR, LME)	.637, .455	.941, .848
Failure Rate (LRR, LME)	0, 0	.012,.008

^*Variance for the random effect for slope.

^**Variance for the random effect for linear time.