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

Table 6

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

Parm.	True value	Estimate	Abs. bias	APB (%)	Std. err.	t-test	value
	0.5	0.4820	0.0180	3.6006	0.0175	27.4956
	0.6	0.5733	0.0267	4.4550	0.0210	27.2643
	0.5	0.5621	0.0621	12.4248	0.0541	10.3956
	0.6	0.6657	0.0657	10.9532	0.0640	10.4023
	0.3	0.3042	0.0042	1.3913	0.0104	29.3686
	0.3	0.3058	0.0058	1.9333	0.0305	10.0157
	−0.4	−0.4098	0.0098	2.4453	0.0408	−10.0548
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.5986	0.0014	0.2263	0.0460	13.0038
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.6472	0.0472	7.8628	0.1002	6.4570
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	−1	−1.0068	0.0068	0.6844	0.0115	−87.6833
	−1	−0.9671	0.0329	3.2898	0.0161	−60.1169
	−1	−1.0078	0.0078	0.7807	0.0131	−76.7399
	−1	−0.9876	0.0124	1.2408	0.0373	−26.4477
	0.3	0.3148	0.0148	4.9407	0.0125	25.2747
	0.4	0.3509	0.0491	12.2728	0.0379	9.2709
	0.5	0.4989	0.0011	0.2154	0.0210	23.7248
	0.6	0.5913	0.0087	1.4555	0.0793	7.4595
	1.5	1.5120	0.0120	0.8026	0.0081	186.2650
	1.5	1.4793	0.0207	1.3799	0.0187	79.0895
	1.5	1.4996	0.0004	0.0299	0.0145	103.1776
	1.5	1.5160	0.0160	1.0677	0.0538	28.1597
	0.5	0.4544	0.0456	9.1144	0.0304	14.9438
	−1	−1.0425	0.0425	4.2479	0.0476	−21.8930
	−0.8	−0.8728	0.0728	9.1025	0.0445	−19.6065
	−1	−1.0116	0.0116	1.1607	0.0158	−63.9212
	−0.8	−0.8109	0.0109	1.3567	0.0127	−63.6051
	0.5	0.5382	0.0382	7.6404	0.0234	22.9612
	0.2	0.1860	0.0140	6.9835	0.0185	10.0749
	0.2	0.1878	0.0122	6.1180	0.0186	10.0900
	0.5	0.4887	0.0113	2.2598	0.0232	21.0338
	0.5	0.5099	0.0099	1.9814	0.0212	24.0589
	0.2	0.1997	0.0003	0.1510	0.0204	9.7806
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0.6	0.5923	0.0077	1.2832	0.0524	11.3058
	0.6	0.6382	0.0382	6.3702	0.0458	13.9236
	1.36	1.3895	0.0295	2.1659	0.1074	12.9430
	0.6	0.6875	0.0875	14.5838	0.0775	8.8672
	1.36	1.4629	0.1029	7.5643	0.1001	14.6142
Overall mean value			0.0259	4.2037	0.0370

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