SK package presents segment-based Kriging models, including segment-based ordinary Kriging (SOK) and segment-based regression Kriging (SRK), for spatial prediction. Segment-based Kriging models “integrate the spatial characteristics of spatial line segments and the spatial homogeneity of each single segment, consider their spatial autocorrelation and enable segment-based data to compute the best linear unbiased estimation” (Song et al. 2018). The models are proposed for the spatial predictions of segment-based traffic volumes and the burden of road pavement maintenance. The problem solving processes refer to the methods area-to-area Kriging (ATAK) (Goovaerts 2006, Goovaerts 2009) and rtop-Kriging (Skoien 2005, Skoien 2014). More details about methods and applications can refer to the articles in the reference list below.
The SK package includes a case dataset vehicles with the format of spatial polyline shapefile. The dataset vtest is a sample of vehicles. Details of datasets can be found in the manual of SK package. Users can follow the datasets and following codes to prepare data and run the segment-based Kriging models.
Load datasets:
library(SK)
data(vtest)
data(vehicles)
head(vehicles@data)[1:4,]
#> segmentID obs1pred0 length width heavy light total wpai
#> 0 1 1 14.13 12 1211.31 2658.69 3870.00 20744.33
#> 1 2 1 18.02 12 895.86 2884.14 3780.00 8997.97
#> 2 3 1 32.70 12 768.94 2867.72 3636.67 13571.85
#> 3 4 0 45.32 11 0.00 0.00 0.00 0.00
#> longitude latitude
#> 0 115.9590 -31.53769
#> 1 115.9084 -31.39701
#> 2 116.2829 -32.41138
#> 3 116.5223 -32.69080
SOK for vtest:
sok1 <- skriging(heavy ~ 1, polyline = vtest, method = "sok",
lwd = "width", obspred = "obs1pred0", boxcox = TRUE)
sok1
plot(sok1)
Note: Left figure shows both observations and predictions. Right figure shows the distributions of prediction uncertainty, where the gray lines are observation segments.
SRK for vtest:
srk1 <- skriging(heavy ~ wpai + width, polyline = vtest, method = "srk",
lwd = "width", obspred = "obs1pred0", boxcox = TRUE)
srk1
plot(srk1)
SOK for vehicles:
data(vehicles)
sok2 <- skriging(heavy ~ 1, polyline = vehicles, method = "sok",
lwd = "width", obspred = "obs1pred0", boxcox = TRUE)
sok2
plot(sok2, studyarea = wheatbelt)
SRK for vehicles:
srk2 <- skriging(heavy ~ wpai + width, polyline = vehicles, method = "srk",
lwd = "width", obspred = "obs1pred0", boxcox = TRUE)
#> Loading required namespace: rgdal
srk2
#> skriging result includes a polyline shapefile ...
#> polyline shapefile can be derived by 'yourskrigingresult$polyline' ...
#> summary of observations and predictions:
#> N Min. Median Mean Max.
#> observation 148 2.000000 1.20e+02 1.94e+02 1211.310
#> prediction 132 2.000000 1.66e+02 2.42e+02 1140.809
#> kriging stdev 132 0.127463 2.66e-01 2.76e-01 0.444
#> kriging uncertainty 132 0.000183 1.38e-03 2.53e-03 0.034
plot(srk2, studyarea = wheatbelt)
Song Y, Wang X, Wright G, Thatcher D, Wu P and Felix P (2018). “Traffic Volume Prediction With Segment-Based Regression Kriging and its Implementation in Assessing the Impact of Heavy Vehicles.” IEEE Transactions on Intelligent Transportation Systems, pp. 1-12. doi: 10.1109/TITS.2018.2805817.
Goovaerts P (2006). “Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging”. International Journal of Health Geographics, 5, pp. 52.
Goovaerts P (2009). “Combining area-based and individual-level data in the geostatistical mapping of late-stage cancer incidence”. Spatial and spatio-temporal epidemiology, 1, pp. 61-71.
Skoien JO, Merz R and Bloschl G (2005). “Top-kriging? geostatistics on stream networks”. Hydrology and Earth System Sciences Discussions, 2, pp. 2253-86.
Skoien JO, Bloschl G, Laaha G, Pebesma E, Parajka J and Viglione A (2014). “Rtop: An R package for interpolation of data with a variable spatial support, with an example from river networks”. Computers & Geosciences, 67, pp. 180-90.