Development of Integrated Choice and Latent Variable (ICLV) Models Using Matrix-Based Analytic Approximation and Automatic Differentiation Methods on TensorFlow Platform
Table 3
Simulation results for the three-alternative ICLV model.
Parm.
True value
Parameter estimates
Standard error estimates
Mean est.
Abs. bias
APB (%)
ASE
FSSD
R. eff
0.5
0.5300
0.0300
5.9924
0.0961
0.0807
1.1908
0.6
0.6411
0.0411
6.8506
0.1177
0.1003
1.1730
0.5
0.5022
0.0022
0.4432
0.2037
0.1493
1.3648
0.6
0.6017
0.0017
0.2775
0.2451
0.1845
1.3288
0.3
0.3125
0.0125
4.1630
0.0408
0.0466
0.8740
0.3
0.3027
0.0027
0.9119
0.1336
0.1118
1.1950
−0.4
−0.4061
0.0061
1.5186
0.1773
0.1455
1.2182
1
—
—
—
—
—
—
0
—
—
—
—
—
—
0.6
0.6855
0.0855
14.2485
0.2567
0.2516
1.0206
0
—
—
—
—
—
—
1
—
—
—
—
—
—
0
—
—
—
—
—
—
0.6
0.6230
0.0230
3.8411
0.4800
0.3951
1.2149
1
—
—
—
—
—
—
0
—
—
—
—
—
—
1
—
—
—
—
—
—
−1
−1.0013
0.0013
0.1312
0.0366
0.0334
1.0974
−1
−1.0244
0.0244
2.4418
0.0680
0.0638
1.0664
−1
−1.0031
0.0031
0.3117
0.0441
0.0453
0.9720
−1
−1.0665
0.0665
6.6513
0.1629
0.1609
1.0124
0.3
0.2880
0.0120
3.9911
0.0508
0.0441
1.1524
0.4
0.4459
0.0459
11.4847
0.1550
0.1355
1.1441
0.5
0.4924
0.0076
1.5296
0.0754
0.0832
0.9064
0.6
0.7157
0.1157
19.2758
0.3046
0.2619
1.1633
1.5
1.4971
0.0030
0.1967
0.0275
0.0265
1.0375
1.5
1.5354
0.0354
2.3578
0.0873
0.0823
1.0601
1.5
1.4949
0.0051
0.3431
0.0504
0.0549
0.9191
1.5
1.6141
0.1141
7.6054
0.2346
0.2114
1.1101
0.5
0.4863
0.0137
2.7409
0.0954
0.0888
1.0741
−1
−0.9972
0.0028
0.2784
0.1360
0.1530
0.8893
−1
−0.9980
0.0020
0.1971
0.0419
0.0434
0.9667
−0.8
−0.7978
0.0022
0.2772
0.0338
0.0343
0.9852
0.5
0.4807
0.0193
3.8694
0.0885
0.0811
1.0907
0.2
0.2129
0.0129
6.4477
0.0661
0.0517
1.2771
0.5
0.4929
0.0071
1.4146
0.0718
0.0723
0.9929
0.2
0.2112
0.0112
5.6136
0.0622
0.0543
1.1441
1
—
—
—
—
—
—
0
—
—
—
—
—
—
0
—
—
—
—
—
—
1
—
—
—
—
—
—
0.6
0.6065
0.0065
1.0794
0.1374
0.1196
1.1483
1.36
1.3753
0.0153
1.1286
0.2742
0.2571
1.0668
Overall mean value
0.0236
3.7940
0.1308
0.1169
1.1190
Note: “--” indicates that the corresponding parameter is fixed at the true value.