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

Table 2

MVNCD evaluation results for the different analytic approximation methods.

Dim	Measure	ME		BME		TVBS
		Gauss	TF	Gauss	TF	Gauss	TF
K = 4	MAE	0.00226	0.00226	0.00152	0.00152	0.00117	0.00117
	MAPE	0.59	0.59	0.40	0.40	0.26	0.26
	%MAE > 0.005	15.2	15.2	9.8	9.8	5.8	5.8
	%MAPE > 2	18.0	18.0	12.8	12.8	8.4	8.4
	Time (s)	0.052	0.010	0.033	0.004	0.039	0.007
K = 5	MAE	0.00171	0.00171	0.00142	0.00142	0.00108	0.00108
	MAPE	0.54	0.54	0.44	0.44	0.33	0.33
	%MAE > 0.005	9.2	9.2	7.0	7.0	4.8	4.8
	%MAPE > 2	18.8	18.8	15.4	15.4	13.0	13.0
	Time (s)	0.077	0.016	0.060	0.007	0.065	0.011
K = 7	MAE	0.00120	0.00120	0.00104	0.00104	0.00093	0.00093
	MAPE	0.45	0.45	0.38	0.38	0.33	0.33
	%MAE > 0.005	5.9	5.9	4.7	4.7	3.6	3.6
	%MAPE > 2	21.5	21.5	20.2	20.2	18.3	18.3
	Time (s)	0.141	0.031	0.097	0.014	0.105	0.021
K = 10	MAE	0.00064	0.00064	0.00057	0.00057	0.00054	0.00054
	MAPE	0.32	0.32	0.29	0.29	0.29	0.29
	%MAE > 0.005	1.6	1.6	1.2	1.2	1.1	1.1
	%MAPE > 2	25.0	25.0	23.1	23.1	22.6	22.6
	Time (s)	0.258	0.061	0.156	0.023	0.182	0.033
K = 15	MAE	0.00041	0.00041	0.00040	0.00040	0.00037	0.00037
	MAPE	0.29	0.29	0.28	0.28	0.25	0.25
	%MAE > 0.005	0.2	0.2	0.2	0.2	0.1	0.1
	%MAPE > 2	34.1	34.1	32.6	32.6	32.0	32.0
	Time (s)	0.558	0.146	0.317	0.058	0.352	0.076