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. Author manuscript; available in PMC: 2022 Feb 24.
Published in final edited form as: Proc ACM Symp User Interface Softw Tech. 2021 Oct 12;2021:1122–1143. doi: 10.1145/3472749.3474811

Table 6:

Model parameters, evaluation results, and WAIC metrics for 6 variance models (Table 1) of each task on our dataset. As shown, although there is no clear winner, the quadratic-variance model (Model #4 in Table 1) performed the best (or second-best) in three tasks, after taking into account the complexity of the model (i.e., the number of parameters).

Conditions Variance Models c d e R 2 RMSE [SD] AIC WAIC
Straight tunnel σ2 = c 0.979 [0.344, 1.627] N/A N/A 0 767.0 [655.0] 370.05 368.76
σ2 = (c · ID)2 0.054 [0.051, 0.056] N/A N/A 0.966 148.2 [178.0] 329.4 329.68
σ2 = c + d · ID −0.899 [−1.275, −0.519] 0.115 [0.095, 0.136] N/A 0.948 239.0 [138.7] 338.09 334.64
σ 2 = c + d · ID 2 0.052 [−0.126, 0.229] 0.003 [0.002, 0.003] N/A 0.968 163.3 [139.0] 332.06 330.12
σ2 = (c + d · ID)2 0.068 [−0.11,0.24] 0.051 [0.045, 0.058] N/A 0.970 185.2 [212.5] 331.57 329.82
σ2 = c + d · ID + e · ID2 −0.237 [−0.871, 0.398] 0.034 [−0.037, 0.106] 0.002 [0.0003, 0.004] 0.972 206.6 [241.9] 333.91 330.42
Narrowing tunnel σ2 = c 0.694 [0.283, 1.075] N/A N/A 0 444.3 [435.5] 358.50 358.72
c2 = (c · ID)2 0.058 [0.054, 0.061] N/A N/A 0.918 152.3 [82.5] 328.62 326.06
σ2 = c + d · ID −0.405 [−0.77, −0.067] 0.089 [0.064, 0.115] N/A 0.869 233.8 [238.3] 337.47 335.66
σ2 = c + d · ID2 0.135 [0.0008, 0.273] 0.003 [0.002, 0.003] N/A 0.946 147.6 [141.2] 326.91 323.84
σ2 = (c + d · ID)2 0.142 [−0.048, 0.315] 0.05 [0.041, 0.06] N/A 0.939 176.4 [174.5] 328.47 325.72
σ2 = c + d · ID + e · ID2 0.329 [−0.191, 0.876] −0.029 [−0.109, 0.049] 0.004 [0.001, 0.006] 0.950 196.5 [227.8] 329.39 325.14
Circular tunnel σ2 = c 1.853 [0.576, 3.215] N/A N/A 0 1517.1 [1581.3] 388.6 389
σ2 = (c · ID)2 0.085 [0.08, 0.089] N/A N/A 0.950 431.2 [543.8] 352.62 353.4
σ2 = c + d · ID −1.873 [−3.088, −0.647] 0.257 [0.177, 0.337] N/A 0.863 830.9 [933.6] 368.26 367.76
σ2 = c + d · ID2 −0.076 [−0.544, 0.424] 0.007 [0.006, 0.009] N/A 0.951 530.4 [644.6] 355.96 354.68
σ2 = (c + d · ID)2 −0.177 [−0.694, 0.185] 0.092 [0.076, 0.112] N/A 0.953 552.4 [708.5] 355.37 354.22
σ2 = c + d · ID + e · ID2 0.821 [−0.778, 2.346] −0.118 [−0.316, 0.088] 0.01 [0.005, 0.02] 0.960 613.6 [901.3] 356.92 353.8