Subgroup Analysis of a Single-Index Threshold Penalty Quantile Regression Model Based on Variable Selection | Wuhan University Journal of Natural Sciences

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Table 5

Estimation results of parameters when fixing $x_{1} = A X L$

τ	Estimator	Estimate	BS-SE	95%-CI	p-value	τ	Estimator	Estimate	BS-SE	95%-CI	p-value
0.2	$β_{1}$	32.976	7.760	(17.766, 48.187)	<0.001	0.2	$β_{6}$	-0.112	0.050	(-0.212, -0.012)	0.026
0.3		27.897	3.686	(20.671, 35.123)	<0.001	0.3		-0.034	0.030	(-0.093, 0.024)	0.256
0.4		31.430	5.824	(20.014, 42.845)	<0.001	0.4		-0.060	0.036	(-0.130, 0.010)	0.096
0.5		36.214	3.805	(28.755, 43.673)	<0.001	0.5		-0.046	0.033	(-0.113, 0.019)	0.164
0.6		45.531	5.274	(35.194, 55.870)	<0.001	0.6		-0.093	0.035	(-0.163, -0.024)	0.007
0.7		50.220	4.606	(41.191, 59.249)	<0.001	0.7		-0.088	0.048	(-0.183, 0.007)	0.070
0.8		60.540	5.813	(49.145, 71.935)	<0.001	0.8		-0.125	0.047	(-0.218, -0.033)	0.007
0.2	$β_{2}$	-0.617	0.055	(-0.726, -0.509)	<0.001	0.2	$δ_{1}$	-3.781	4.058	(-11.736, 4.172)	0.351
0.3		-0.548	0.029	(-0.606, -0.491)	<0.001	0.3		-6.397	2.993	(-12.265, -0.529)	0.032
0.4		-0.568	0.066	(-0.698, -0.438)	<0.001	0.4		-5.892	5.067	(-15.824, 4.039)	0.244
0.5		-0.543	0.046	(-0.632, -0.450)	<0.001	0.5		-4.541	3.520	(-11.440, 2.358)	0.197
0.6		-0.613	0.056	(-0.723, -0.502)	<0.001	0.6		-5.031	2.871	(-10.660, 0.596)	0.079
0.7		-0.601	0.050	(-0.700, -0.502)	<0.001	0.7		-7.312	2.663	(-12.532, -2.092)	0.006
0.8		-0.657	0.056	(-0.767, -0.547)	<0.001	0.8		-10.748	2.964	(-16.558, -4.937)	<0.001
0.2	$β_{3}$	0	*	*	*	0.2	$δ_{2}$	10.080	4.811	(0.649, 19.511)	0.036
0.3		0	*	*	*	0.3		9.299	4.086	(1.290, 17.309)	0.028
0.4		0	*	*	*	0.4		12.118	5.896	(0.560, 23.675)	0.039
0.5		0	*	*	*	0.5		9.424	4.782	(0.049, 18.798)	0.048
0.6		0	*	*	*	0.6		7.773	3.709	(0.502, 15.043)	0.036
0.7		0	*	*	*	0.7		6.841	5.344	(-3.633, 17.315)	0.200
0.8		0	*	*	*	0.8		10.701	6.638	(-2.309, 23.712)	0.106
0.2	$β_{4}$	-0.136	0.096	(-0.325, 0.052)	0.157	0.2	$ψ_{0}$	-0.982	0.210	(-1.395, -0.568)	<0.001
0.3		-0.027	0.054	(-0.133, 0.078)	0.610	0.3		-0.665	0.148	(-0.956, -0.372)	<0.001
0.4		0	*	*	*	0.4		-0.885	0.113	(-1.107, -0.662)	<0.001
0.5		0	*	*	*	0.5		-1.093	0.127	(-1.342, -0.842)	<0.001
0.6		0	*	*	*	0.6		-0.869	0.116	(-1.907, -0.640)	<0.001
0.7		0	*	*	*	0.7		-0.911	0.122	(-1.151, -0.671)	<0.001
0.8		0	*	*	*	0.8		-0.848	0.147	(-1.136, -0.559)	<0.001
0.2	$β_{5}$	0	*	*	*	0.2	$ψ_{1}$	-1.217	0.200	(-1.609, -0.824)	<0.001
0.3		0	*	*	*	0.3		-1.032	0.197	(-1.418, -0.644)	<0.001
0.4		0	*	*	*	0.4		-0.824	0.252	(-1.319, -0.328)	0.001
0.5		0	*	*	*	0.5		-1.238	0.232	(-1.694, -0.781)	<0.001
0.6		0	*	*	*	0.6		-0.817	0.209	(-1.227, -0.407)	<0.001
0.7		0	*	*	*	0.7		-0.834	0.243	(-1.311, -0.357)	<0.001
0.8		0	*	*	*	0.8		-0.824	0.207	(-1.230, -0.417)	<0.001

Note： *： The previous coefficient estimates are zero， indicating that the covariate has not been selected into the model， so the later estimates， BS-SE， 95%-CI， and p-value have no estimates.

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