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

Table 4

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

Parm.	True value	Estimate	Abs. bias	APB (%)	Std. err.	t-test	value
	0.5	0.4821	0.0179	3.5806	0.0175	27.4871
	0.6	0.5734	0.0266	4.4345	0.0210	27.2569
	0.5	0.5623	0.0623	12.4582	0.0545	10.3235
	0.6	0.6659	0.0659	10.9858	0.0645	10.3299
	0.3	0.3039	0.0039	1.2833	0.0103	29.4528
	0.3	0.3059	0.0059	1.9693	0.0306	10.0031
	−0.4	−0.4099	0.0099	2.4817	0.0408	−10.0422
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.5982	0.0018	0.3082	0.0460	13.0071
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0.6	0.6475	0.0475	7.9242	0.1007	6.4324
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	−1	−1.0068	0.0068	0.6818	0.0115	−87.6878
	−1	−0.9671	0.0329	3.2933	0.0161	−59.9248
	−1	−1.0081	0.0081	0.8070	0.0131	−76.7456
	−1	−0.9875	0.0125	1.2531	0.0373	−26.4410
	0.3	0.3147	0.0147	4.9160	0.0125	25.2686
	0.4	0.3508	0.0492	12.3020	0.0381	9.2070
	0.5	0.4996	0.0004	0.0828	0.0210	23.7820
	0.6	0.5910	0.0090	1.5023	0.0793	7.4520
	1.5	1.5120	0.0120	0.8004	0.0081	186.2783
	1.5	1.4792	0.0208	1.3835	0.0188	78.6552
	1.5	1.4999	0.0001	0.0034	0.0145	103.2049
	1.5	1.5158	0.0158	1.0553	0.0538	28.1516
	0.5	0.4547	0.0453	9.0560	0.0304	14.9540
	−1	−1.0416	0.0416	4.1616	0.0476	−21.8600
	−0.8	−0.8728	0.0728	9.1037	0.0445	−19.5951
	−1	−1.0115	0.0115	1.1490	0.0158	−63.8326
	−0.8	−0.8107	0.0107	1.3424	0.0128	−63.5246
	0.5	0.5380	0.0380	7.6064	0.0234	22.9537
	0.2	0.1858	0.0142	7.0770	0.0186	10.0106
	0.2	0.1877	0.0123	6.1475	0.0187	10.0234
	0.5	0.4891	0.0109	2.1756	0.0232	21.0530
	0.5	0.5103	0.0103	2.0632	0.0212	24.0984
	0.2	0.1997	0.0003	0.1565	0.0204	9.7718
	1	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	0	—	—	—	—	—	—
	1	—	—	—	—	—	—
	0.6	0.5956	0.0044	0.7365	0.0526	11.3276
	0.6	0.6407	0.0407	6.7772	0.0460	13.9313
	1.36	1.4008	0.0408	2.9999	0.1074	13.0425
	0.6	0.6939	0.0939	15.6422	0.0779	8.9014
	1.36	1.4723	0.1123	8.2542	0.1007	14.6142
Overall mean value			0.0266	4.2691	0.0371

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