. 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 2:

Simulation results for the situation where there are two change-points in a covariate of a linear, logistic or Poisson regression model; ${\hat{θ}}_{M}$ , estimator based on Mueggo’s method; ${\hat{θ}}_{I}$ , proposed estimator solving (4).

			${\hat{θ}}_{M}$					${\hat{θ}}_{I}$
Model	n		Bias	ASE	SD	MSE	CP	Bias	ASE	SD	MSE	CP
Linear	500	β₀	−0.007	0.092	0.095	0.009	0.943	−0.006	0.092	0.093	0.009	0.948
		β₁	−0.002	0.049	0.049	0.002	0.944	−0.002	0.049	0.048	0.002	0.947
		β₂₁	−0.001	0.115	0.117	0.014	0.944	−0.003	0.115	0.107	0.012	0.960
		β₂₂	0.002	0.124	0.125	0.016	0.953	0.004	0.124	0.116	0.013	0.963
		τ₁	−0.006	0.057	0.061	0.004	0.924	−0.006	0.057	0.056	0.003	0.938
		τ₂	0.002	0.040	0.043	0.002	0.926	0.002	0.040	0.041	0.002	0.941
	2000	β₀	−0.001	0.046	0.047	0.002	0.941	0.001	0.046	0.047	0.002	0.944
		β₁	0.000	0.024	0.025	0.001	0.944	0.000	0.024	0.024	0.001	0.942
		β₂₁	0.003	0.057	0.057	0.003	0.944	0.002	0.057	0.055	0.003	0.948
		β₂₂	−0.004	0.062	0.064	0.004	0.941	−0.003	0.062	0.062	0.004	0.944
		τ₁	0.000	0.028	0.029	0.001	0.943	0.000	0.028	0.028	0.001	0.953
		τ₂	0.000	0.020	0.020	0.000	0.946	0.000	0.020	0.020	0.000	0.954

Logistic	500	β₀	−0.162	0.462	0.625	0.417	0.910	−0.069	0.431	0.403	0.167	0.961
		β₁	−0.092	0.275	0.344	0.127	0.925	−0.046	0.262	0.250	0.064	0.967
		β₂₁	0.425	0.738	0.901	0.992	0.956	0.123	0.569	0.466	0.232	0.979
		β₂₂	−0.458	0.795	0.965	1.141	0.961	−0.163	0.633	0.526	0.303	0.985
		τ₁	0.002	0.230	0.351	0.123	0.791	−0.002	0.241	0.199	0.040	0.958
		τ₂	−0.006	0.179	0.244	0.060	0.840	0.008	0.184	0.168	0.028	0.953
	2000	β₀	−0.032	0.210	0.234	0.056	0.934	−0.023	0.209	0.204	0.042	0.963
		β₁	−0.018	0.127	0.135	0.019	0.938	−0.014	0.127	0.123	0.015	0.956
		β₂₁	0.081	0.279	0.337	0.120	0.944	0.039	0.269	0.243	0.060	0.967
		β₂₂	−0.077	0.307	0.371	0.144	0.930	−0.041	0.298	0.277	0.079	0.969
		τ₁	0.001	0.119	0.151	0.023	0.896	0.000	0.120	0.109	0.012	0.961
		τ₂	−0.005	0.092	0.110	0.012	0.904	0.001	0.093	0.092	0.008	0.947

Poisson	500	β₀	−0.005	0.057	0.059	0.003	0.938	−0.005	0.057	0.058	0.003	0.946
		β₁	−0.002	0.025	0.026	0.001	0.940	−0.002	0.025	0.025	0.001	0.944
		β₂₁	0.008	0.073	0.076	0.006	0.937	0.007	0.073	0.073	0.005	0.942
		β₂₂	−0.010	0.109	0.112	0.013	0.942	−0.008	0.109	0.107	0.011	0.950
		τ₁	0.001	0.041	0.044	0.002	0.928	0.000	0.041	0.042	0.002	0.937
		τ₂	0.001	0.024	0.026	0.001	0.924	0.001	0.024	0.025	0.001	0.933
	2000	β₀	−0.001	0.029	0.030	0.001	0.942	−0.001	0.029	0.029	0.001	0.943
		β₁	0.000	0.012	0.013	0.000	0.945	0.000	0.012	0.013	0.000	0.947
		β₂₁	0.001	0.036	0.036	0.001	0.950	0.001	0.036	0.035	0.001	0.952
		β₂₂	0.001	0.054	0.053	0.003	0.962	0.001	0.054	0.051	0.003	0.966
		τ₁	0.000	0.021	0.021	0.000	0.945	0.000	0.021	0.020	0.000	0.948
		β₂	0.000	0.012	0.012	0.000	0.950	0.000	0.012	0.012	0.000	0.949

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.