Since it is hard to check the goodness of fit when combining all 6 years of results(2000/01/01-2005/12/31), we fit the model year by year and render its fitting result. I think our model has the best fitting result on data in 2004.

We can see that at the same time value, as single index value decreases, the drought score increases. Our mean surface successfully capture this pattern.

It shows at larger single index value(about 0.5), the mean of drought score has higher value at two intervals, week 15 - 23 and week 39 - 43, which corresponds to mid April to early June and late September to late October. We can go down to the “Pointwise mean of drought score in 2000-2006” and observe the same pattern in the plot of 2004. We can see there are several peaks for some states from mid April to early June and from late September to late October.

The interpretation for scalar predictors, as altitude increases, longitude decreases(moving from east to west in US corn belt) and less land of grass will lead to higher risk of drought.

I think we have to use less bases for the approximation of history index functions, since it is too wiggling now.

Estimated mean surface, corresponding history index functions and coefficients of scalar predictors.

Set 1: 2000

##   Predictor   Coefficient
## 1 elevation  0.2868516361
## 2       lon  0.0738312619
## 3  GRS_LAND -0.0000962171

Set 2: 2001

##   Predictor  Coefficient
## 1 elevation  0.199522022
## 2       lon -0.169974094
## 3  GRS_LAND -0.002952514

Set 3: 2002

##   Predictor  Coefficient
## 1 elevation  0.608184869
## 2       lon  0.066809342
## 3  GRS_LAND -0.004627402

Set 4: 2003

##   Predictor  Coefficient
## 1 elevation  0.536794832
## 2       lon -0.128850462
## 3  GRS_LAND -0.008610599

Set 5: 2004

##   Predictor Coefficient
## 1 elevation  0.79465759
## 2       lon -0.12735971
## 3  GRS_LAND -0.01756763

Set 6: 2005

##   Predictor  Coefficient
## 1 elevation  0.346599091
## 2       lon  0.089131058
## 3  GRS_LAND -0.001246104

Pointwise mean of drought score in 2000-2006, divided by state