Suggest Kernel Bandwidth for Density Estimation

Estimates a reasonable kernel bandwidth (sigma) for fixation density maps using a 2D variant of Silverman's rule of thumb, adapted for eye-tracking data. The estimate accounts for spatial spread of fixations and sample size.

Usage

suggest_sigma(x, y = NULL, xbounds = NULL, ybounds = NULL)

Arguments

x

A fixation_group object, or a numeric vector of x-coordinates.

y

A numeric vector of y-coordinates (only used when x is not a fixation_group).

xbounds

Optional numeric vector of length 2 for the x-axis display bounds. Used to scale the estimate relative to display size.

ybounds

Optional numeric vector of length 2 for the y-axis display bounds. Used to scale the estimate relative to display size.

Value

A single numeric value representing the suggested sigma (kernel standard deviation in coordinate units).

Details

The function uses a 2D Silverman rule: \(\sigma = n^{-1/6} \cdot \sqrt{(IQR_x^2 + IQR_y^2)/2} / 1.349\). When display bounds are provided, the result is clamped to between 1% and 15% of the mean display dimension to avoid extreme values.

Examples

fg <- fixation_group(x = runif(30, 0, 1280), y = runif(30, 0, 1024),
                     onset = cumsum(rep(200, 30)), duration = rep(200, 30))
suggest_sigma(fg, xbounds = c(0, 1280), ybounds = c(0, 1024))
#> [1] 172.8