Development of Integrated Choice and Latent Variable (ICLV) Models Using Matrix-Based Analytic Approximation and Automatic Differentiation Methods on TensorFlow Platform

Table 5

Simulation results for the four-alternative ICLV model with the BME method.

Parm.	True value	Estimate	Abs. bias	APB (%)	Std. err.	t-test	value
	0.5	0.4821	0.0179	3.5760	0.0175	27.4890
	0.6	0.5734	0.0266	4.4307	0.0210	27.2577
	0.5	0.5622	0.0622	12.4302	0.0540	10.4099
	0.6	0.6658	0.0658	10.9583	0.0639	10.4166
	0.3	0.3044	0.0044	1.4537	0.0103	29.4308
	0.3	0.3060	0.0060	2.0160	0.0306	9.9954
	−0.4	−0.4101	0.0101	2.5280	0.0409	−10.0344
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.5990	0.0010	0.1662	0.0461	12.9991
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.6477	0.0477	7.9500	0.1004	6.4540
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	−1	−1.0068	0.0068	0.6816	0.0115	−87.6890
	−1	−0.9671	0.0329	3.2903	0.0161	−60.1612
	−1	−1.0076	0.0076	0.7647	0.0131	−76.8664
	−1	−0.9873	0.0127	1.2682	0.0373	−26.4510
	0.3	0.3147	0.0147	4.9110	0.0125	25.2700
	0.4	0.3509	0.0491	12.2775	0.0378	9.2838
	0.5	0.4985	0.0015	0.2924	0.0210	23.7831
	0.6	0.5906	0.0094	1.5625	0.0793	7.4485
	1.5	1.5120	0.0120	0.8000	0.0081	186.2896
	1.5	1.4793	0.0207	1.3804	0.0187	79.1925
	1.5	1.4993	0.0007	0.0456	0.0145	103.4676
	1.5	1.5156	0.0156	1.0393	0.0538	28.1629
	0.5	0.4546	0.0454	9.0790	0.0304	14.9559
	−1	−1.0417	0.0417	4.1748	0.0476	−21.8780
	−0.8	−0.8719	0.0719	8.9935	0.0445	−19.5883
	−1	−1.0112	0.0112	1.1215	0.0158	−63.9360
	−0.8	−0.8106	0.0105	1.3187	0.0127	−63.6256
	0.5	0.5379	0.0379	7.5720	0.0234	22.9583
	0.2	0.1859	0.0141	7.0455	0.0184	10.0864
	0.2	0.1877	0.0123	6.1600	0.0186	10.1024
	0.5	0.4882	0.0118	2.3654	0.0232	21.0692
	0.5	0.5094	0.0094	1.8768	0.0211	24.1120
	0.2	0.1995	0.0005	0.2665	0.0204	9.7651
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0.6	0.5952	0.0048	0.7927	0.0525	11.3353
	0.6	0.6377	0.0377	6.2887	0.0457	13.9456
	1.36	1.4002	0.0402	2.9534	0.1073	13.0519
	0.6	0.6930	0.0930	15.4950	0.0776	8.9351
	1.36	1.4628	0.1028	7.5551	0.1001	14.6143
Overall mean value			0.0262	4.2400	0.0370

Note: “—” indicates that the corresponding parameter is fixed at the true value.