Estimated mean surface with data points using predictors in set 1. The fit seems to be more normal, there is no flunk of data centers at somewhere on the surface.

## Starting surface estimation for 900 points at 2026-04-07 10:09:37.130254...
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Estimated mean surface without data points using predictors in set 1. Rotate to the plane of (Drought Score, Time), at higher single index value cross section, we can see that the estimated mean drought score are relatively low in the middle of Time, which is the summer and relatively high in the head and tail of Time, which are spring and winter. This results resembles our observation of drought for raw data. However, at lower single index value cross section, the effect of Time seems to be small, since the estimated mean curve is quite wiggle on the cross section. This is an interesting observation that the value of single index value will change the temporal effect of mixed predictors. Rotate to the plane of (Drought Score, Single Index), we can observe that lower and higher single index value will cause the higher estimated mean drought score. The next step is to find out how each selected predictors in set 1 contribute to the single index. I’ll keep studying this in this week, also check if I can split the original bivariate link function into an additive model.

## Starting surface estimation for 900 points at 2026-04-07 10:09:39.564374...
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History index functions of functional predictors considered in set 1.

Coefficients of scalar predictors

##   Predictor   Coefficient
## 1 elevation -0.0471533052
## 2       lon  0.1959440962
## 3  GRS_LAND  0.0005981943