Moving-window linear regression over raster matrices

Fits, for every cell, a linear regression of the response on one or more predictors over a square moving window, and returns full-resolution intercept and slope grids. The fit uses summed-area tables, so the cost does not grow with the window size. Cells are excluded from a window where the response or any predictor is non-finite; a cell is returned as NA when its window holds fewer valid cells than the model needs or a predictor has no spread.

Usage

window_regression(y, x, radius, min_cells = 0L, min_variance = 1e-08)

Arguments

y

Numeric matrix, the response on the coarse grid.

x

Numeric matrix, or a list of numeric matrices, the predictor(s) on the same grid as y.

radius

Integer window radius in cells; the window is a square of side 2 * radius + 1.

min_cells

Integer, additional valid cells required in a window beyond the k + 1 model terms (k predictors plus the intercept). Default 0.

min_variance

Numeric, the minimum within-window variance a predictor must have for the cell to be fit. Default 1e-8.

Value

A list with intercept (a numeric matrix) and slope (a list of numeric matrices, one per predictor), each the same size as y.

Details

This is the matrix engine behind topocast(); it works on plain numeric matrices and does not depend on terra.

See also

topocast() for the terra workflow.

Examples

set.seed(1)
elevation <- matrix(runif(100, 0, 1000), 10, 10)
climate <- 50 + 0.01 * elevation
fit <- window_regression(climate, elevation, radius = 3)
str(fit)