tscsRegression {TSCS} | R Documentation |
The First Step of TSCS for 2D Rectangular Grid System - Regression
Description
To implement TSCS spatial interpolation for a spatial domain that is a 2D rectangular grid system,
the first step is obtaining regression coefficient matrix, which can be done
by function tscsRegression
. It is the prerequisite of TSCS interpolation process
because the 'matrix' derived from historical spatio-temporal data is the initial value of
the second step - estimating missing observations.
Usage
tscsRegression(data, h, v, alpha = 0.05)
Arguments
data |
data frame; should contain these variables in order: X coordinate, Y coordinate and observations
as time goes on. That is to say, each row should include X and Y coordinate first, and then a time series.
This is the historical spatio-temporal data that you intend to analyze as the basis for
interpolation later on in |
h |
numeric; side length of the unit grid in X coordinate direction. |
v |
numeric; side length of the unit grid in Y coordinate direction. |
alpha |
numeric; specify the significance level for ADF test, to test if the time series of a group of spatial locations are cointegrated. (default: 0.05) |
Details
The second step of TSCS spatial interpolation should be carried out by function
tscsEstimate
, where you have to input the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict.For 3D rectangular grid system, the procedure of TSCS stays the same. Please see
tscsRegression3D
andtscsEstimate3D
.Attentions: (1) Since TSCS is only capable of interpolation but not extrapolation, it is necessary to highlight the difference between interior spatial locations and system boundary. Function
plot_dif
can help. (2) NA value in historical spatio-temporal datadata
is not allowed. Please handle them beforehand (such as filling these NA values through spatio-temporal kriging).
Value
A list of 2 is returned, including:
coef_matrix
data frame; regression coefficient matrix to be used as input parameter of function
tscsEstimate
in the second step of TSCS interpolation.percentage
numeric; percentage of cointegrated relationships, a measurement of the degree it satisfies the assumption of cointegrated system. It is highly affected by parameter
alpha
, the significance level you have set. Explicitly, smalleralpha
results in smallerpercentage
.
See Also
tscsEstimate
, tscsRegression3D
, plot_dif
Examples
## Not run:
## TSCS spatial interpolation procedure:
basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression
basis$percentage # see the percentage of cointegrated relationships
est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation
str(est)
## comparison of estimates and true values:
plot_compare(est = est$estimate[,3], true = true) # graphic comparison
index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std
index
## data visualization:
plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations
plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data
plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data
## End(Not run)