. Author manuscript; available in PMC: 2021 Apr 15.

Published in final edited form as: Stat Med. 2020 Jan 29;39(8):1167–1182. doi: 10.1002/sim.8469

Table 3:

Simulation results for the situation where there is a single change-point in a covariate of a linear, logistic or Poisson regression model for longitudinal data; ${\hat{θ}}_{L}$ , proposed estimator solving (6).

		${\hat{θ}}_{L}$ (ρ = 0.3)					${\hat{θ}}_{L}$ (ρ = 0.7)
Model		Bias	ASE	SD	MSE	CP	Bias	ASE	SD	MSE	CP
Linear	β₀	0.001	0.016	0.016	0.000	0.951	0.001	0.022	0.022	0.000	0.951
	β₁	0.000	0.008	0.008	0.000	0.952	0.000	0.005	0.005	0.000	0.955
	β₂	0.006	0.088	0.088	0.008	0.942	0.004	0.058	0.058	0.003	0.939
	τ	0.001	0.027	0.028	0.001	0.941	0.000	0.018	0.018	0.000	0.944

Logistic	β₀	−0.003	0.096	0.095	0.009	0.955	0.002	0.128	0.128	0.016	0.950
	β₁	−0.005	0.059	0.060	0.004	0.945	−0.010	0.069	0.073	0.005	0.935
	β₂	0.079	0.400	0.383	0.153	0.961	0.070	0.361	0.335	0.117	0.964
	τ	0.004	0.125	0.125	0.016	0.933	0.001	0.113	0.116	0.013	0.925

Poisson	β₀	−0.002	0.027	0.027	0.001	0.944	−0.002	0.032	0.032	0.001	0.944
	β₁	−0.001	0.009	0.009	0.000	0.943	−0.001	0.010	0.010	0.000	0.957
	β₂	0.023	0.224	0.220	0.049	0.939	0.019	0.173	0.168	0.029	0.954
	τ	0.002	0.074	0.074	0.005	0.938	0.003	0.058	0.058	0.003	0.946

Note: SD denotes the sample standard deviation of the estimates; ASE is the average of the estimated standard errors; MSE is mean square error; CP represents the coverage probabilities of the 95% confidence intervals.