# Geographic_Data_Example

#### Zhuoran (Angela) Yu

#### 2025-11-12

Due to runtime constraints, the code chunks in this vignette are not executed during the build process. Users may run these examples locally or refer to the package website for the full outputs.

The following example is for displaying the confidence region for the increase of the mean summer temperature (June–August) in North America between the 20th and 21st centuries according to the specific climate model analyzed in Sommerfeld et al. (2018).

`SCoRES::SCB_gls_geospatial()` function uses multiplier bootstrap algorithm to construct the SCB for a specified linear combination of coefficients across a geographical area. The argument `sp_list` specifies a list containing the spatial coordinates and the observations on each spot. `data_fit` specifies a data frame containing the design matrix used to fit the spatial generalized least squares model (notice that the intercept should also be included inside the data frame), while `w` defines the weights for the linear combination of coefficients on which the simultaneous confidence bands (SCB) are constructed. Use the `correlation` argument to specify the correlation structure for model fitting. If the observations are grouped, a grouping factor can be specified using the `group` argument, and a covariance array `V` may also be provided to supply a known covariance matrix for each spot. `mask` is an optional logical matrix indicating spatial locations to include in the SCB, with excluded areas (e.g., water) set to 0 or NA.

    library(patchwork)
    library(nlme)
    library(SCoRES)
    library(ggplot2)

    # Load data
    data(climate_data)
    start_time <- Sys.time()

    # construct confidence region for the increase of the mean temperature (June-August) in North America between the 20th and 21st centuries
    temp = SCB_gls_geospatial(sp_list = climate_data$Z,
                           level = 2,
                           data_fit = climate_data$X,
                           w = c(1,0,0,0),
                           correlation = climate_data$correlation,
                           mask = climate_data$mask,
                           alpha = 0.1)

    end_time <- Sys.time()
    time_taken <- end_time - start_time
    print(time_taken)

Heat maps show the estimate of the mean temperature difference. The first row displays the contours of the outer confidence regions, the estimated inverse regions, and the inner confidence regions, for various levels. The three plots in the second row display the simultaneous confidence regions (SCRs) for the inverse regions, where the estimated mean difference is greater or equal to the individual levels of 1.5, 2.0, or 2.5 respectively. In the second row, the blue line is the contour of the outer confidence region, the green line is the contour of the estimated inverse region and the red line is the contour of the inner confidence region.

    par(mfrow = c(2, 3), mar = c(3, 3, 2, 1))
    p2 = plot_cs(list(scb_up = temp$scb_up, scb_low = temp$scb_low), levels = c(1.5, 2,2.5,3), x = temp$x, y = temp$y, mu_hat = temp$mu_hat, xlab = "Longitude", ylab = "Latitude", level_label = T, min.size = 40, palette = "Spectral", color_level_label = "black")
    p1 = plot_cs(list(scb_up = temp$scb_up, scb_low = temp$scb_low), levels = c(1.5,2,2.5), x = temp$x, y = temp$y, mu_hat = temp$mu_hat, xlab = "Longitude", ylab = "Latitude",together = F)
    p = p2/p1
    p

Sommerfeld, M., Sain, S., & Schwartzman, A. (2018). Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate. Journal of the American Statistical Association, 113(523), 1327–1340. https://doi.org/10.1080/01621459.2017.1341838