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Weighted HRF (No Hemodynamic Delay)

Source: R/hrf-functions.R
hrf_weighted.Rd

Creates a flexible weighted HRF starting at t=0 with user-specified weights. Unlike traditional HRFs, this has no built-in hemodynamic delay - it directly maps weights to time points, allowing for arbitrary temporal response shapes.

Usage

hrf_weighted(
  weights,
  width = NULL,
  times = NULL,
  method = c("constant", "linear"),
  normalize = FALSE
)

Arguments

weights

Numeric vector of weights. Required.

width

Total duration of the window in seconds. If provided without times, [0, width) is divided into length(weights) equal bins (constant method), or the weights are placed at evenly spaced points from 0 to width (linear method).

times

Numeric vector of time points (in seconds, relative to t=0) where weights are specified. Must be strictly increasing and start at 0 for consistency with other HRFs. If provided, width is ignored.

method

Interpolation method between time points:

"constant"

Step function (default): each weight applies to one time bin. With times, weight i covers [times[i], times[i + 1]) and the last weight covers a bin as wide as the one before it. Every weight is used.

"linear"

Linear interpolation between points. Good for smooth weight transitions.

normalize

Logical; if TRUE, weights are scaled so all of them sum to 1 (for method = "constant") or the curve integrates to 1 (for method = "linear"). This fixes the scale of the weight profile; see Details for what the regression coefficient estimates. Default is FALSE.

Value

An HRF object that can be used with regressor() and other fmrihrf functions.

Details

This is useful for summarising the signal in chosen post-stimulus windows with a chosen temporal profile. In a least-squares GLM, an isolated event's coefficient is the amplitude of the weight profile \(w(t)\) that best matches the data, \(\sum_t w(t) y(t) / \sum_t w(t)^2\). This equals the mean signal in the window only when all non-zero weights are 1 (a boxcar); in general it is not a weighted mean. Normalizing rescales the coefficient but does not change this.

There are two ways to specify the temporal structure:

  1. width + weights: the window [0, width) is divided into length(weights) equal bins (constant method) or the weights are placed at evenly spaced points from 0 to width (linear method)

  2. times + weights: explicit time points for each weight (relative to t=0)

For delayed windows (not starting at t=0), use lag_hrf to shift the weighted HRF in time.

Note on durations

The temporal structure (width or times) is fixed when the HRF is created. The duration parameter in regressor() does not modify the weighted HRF's structure—it controls how long the neural input is sustained (which then gets convolved with this HRF). For trial-varying weighted HRFs, use a list of HRFs:


hrf_early <- hrf_weighted(width = 6, weights = c(1, 1, 0, 0), normalize = TRUE)
hrf_late <- hrf_weighted(width = 6, weights = c(0, 0, 1, 1), normalize = TRUE)
reg <- regressor(onsets = c(0, 20), hrf = list(hrf_early, hrf_late))

See also

hrf_boxcar for simple uniform boxcars, lag_hrf to shift the window in time, empirical_hrf for HRFs from measured data

Other hrf_functions: hrf_basis_lwu(), hrf_boxcar(), hrf_bspline(), hrf_gamma(), hrf_gaussian(), hrf_inv_logit(), hrf_lwu(), hrf_mexhat(), hrf_sine(), hrf_spmg1(), hrf_time()

Examples

# Simple: 6 s window split into 4 bins of 1.5 s (starting at 0, 1.5, 3, 4.5 s)
hrf1 <- hrf_weighted(width = 6, weights = c(0.2, 0.5, 0.8, 0.3))
t <- seq(-1, 10, by = 0.1)
plot(t, evaluate(hrf1, t), type = "s", main = "Weighted HRF (width + weights)")


# Explicit times for precise control
hrf2 <- hrf_weighted(
  times = c(0, 1, 3, 5, 6),
  weights = c(0.1, 0.5, 0.8, 0.5, 0.1),
  method = "linear"
)
plot(t, evaluate(hrf2, t), type = "l", main = "Smooth Weighted HRF")


# Normalized weights: all four bin weights sum to 1
hrf3 <- hrf_weighted(
  width = 8,
  weights = c(1, 2, 2, 1),
  normalize = TRUE
)

# Trial-varying weighted HRFs
hrf_early <- hrf_weighted(width = 6, weights = c(1, 1, 0, 0), normalize = TRUE)
hrf_late <- hrf_weighted(width = 6, weights = c(0, 0, 1, 1), normalize = TRUE)
reg <- regressor(onsets = c(0, 20), hrf = list(hrf_early, hrf_late))

# For delayed windows, use lag_hrf
hrf_delayed <- lag_hrf(hrf_weighted(width = 5, weights = c(1, 2, 1)), lag = 10)