Table 3:

Model parameters, evaluation results, and WAIC metrics for 6 variance models (Table 1) on Zhou and Ren’s steering law dataset. As shown, the quadratic-variance model outperformed other models in both straight and circular 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	σ2 = c	0.228 [0.1, 0.353]	N/A	N/A	0	128.54 [107.87]	246.37	245.2
	σ2 = (c · ID)2	0.017 [0.012, 0.021]	N/A	N/A	0.382	100.38 [63.56]	242.34	239.66
	σ2 = c + d · ID	0.03 [−0.1, 1.7]	0.01 [0.004, 0.016]	N/A	0.735	95.37 [67.32]	238.11	234.96
	σ2 = c + d · ID2	0.121 [0.034, 0.208]	0.0002 [0.0001, 0.0003]	N/A	0.785	83.08 [48.10]	236.20	232.72
	σ2 = (c + d · ID)2	0.23 [0.2, 0.4]	0.01 [0.009, 0.02]	N/A	0.752	98.28 [77.12]	237.43	234.38
	σ2 = c + d · ID + e · ID2	0.156 [−0.149, 0.47]	−0.0038 [−0.037, 0.027]	0.0003 [−0.0003, 0.0009]	0.788	117.10 [100.84]	240.17	235.96
Circular	σ2 = c	0.593 [0.368, 0.802]	N/A	N/A	0	225.82 [174.39]	255.92	254.12
	σ2 = (c · ID)2	0.025 [0.016, 0.032]	N/A	N/A	0	318.13 [146.48]	260.79	257.9
	σ2 = c + d · ID	0.241 [0.013, 0.445]	0.018 [0.009, 0.028]	N/A	0.808	130.88 [80.87]	244.92	241.24
	σ 2 = c + d · ID 2	0.4 [0.273, 0.522]	0.0003 [0.0002, 0.0005]	N/A	0.844	105.70 [60.04]	242.87	239.08
	σ2 = (c + d · ID)2	0.54 [0.39, 0.66]	0.01 [0.006, 0.02]	N/A	0.827	126.21 [76.33]	243.95	240.26
	σ2 = c + d · ID + e · ID2	0.393 [−0.176, 0.889]	0.0009 [−0.051, 0.058]	0.0003 [−0.0008, 0.0014]	0.844	136.62 [84.80]	247.48	243.04