**Fig. 1. **The top left panel indicates the underlying function for Example 1. The true location of the knot was set to 0.4, 0.7. The solid line is a function when k = 1 (z = (1, 0)) and the dashed line is a function when k = 2 (z = (0, 1)). The top right panel demonstrates the true underlying function for Example 2. The true locations of the knots are 0.2, 0.45, and 0.75. The bottom left panel indicates the underlying function for Example 3. In the top right and bottom left panels, the lines represent the same category as the top left panel. The bottom right panel presents the underlying function for Example 4. The solid line is a function of k = 1 (z = (1, 0, 0, 0)), the dashed line is k = 2 (z = (0, 1, 0, 0)), the dotted line is k = 3 (z = (0, 0, 1, 0)), and the dotdash line is k = 4 (z = (0, 0, 0, 1)).

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