# Building fMRI Regressors

#### Bradley R. Buchsbaum

#### 2025-09-11

## Introduction: What is a Regressor?

In fMRI analysis, a regressor (or predictor) represents the expected BOLD signal timecourse associated with a specific experimental condition or event type. It’s typically created by convolving a series of event onsets (often represented as delta functions or “sticks”) with a hemodynamic response function (HRF).

`fmrihrf` provides the `regressor()` function to easily create these objects from event timings and an HRF. While these regressor objects are often constructed automatically by modeling functions in other packages, this vignette explores how to create and manipulate them directly, offering finer control over the model components.

## Basic Regressor from Event Onsets

Suppose we have a simple event-related fMRI design with stimuli presented every 12 seconds. We want to model these events using the SPM canonical HRF (`HRF_SPMG1`). The events are brief, so we model them with a duration of 0 seconds (instantaneous).

    # Define event onsets
    onsets <- seq(0, 10 * 12, by = 12)

    # Create the regressor object
    # Uses HRF_SPMG1 by default if no hrf is specified
    # Duration is 0 by default
    reg1 <- regressor(onsets = onsets, hrf = HRF_SPMG1)

    # Print the regressor object to see its properties (uses new print.Reg method)
    print(reg1)

    # Access components using helper functions
    head(onsets(reg1))
    #> [1]  0 12 24 36 48 60
    nbasis(reg1)
    #> [1] 1

## Evaluating and Plotting a Regressor

A `regressor` object stores the event information but doesn’t automatically compute the timecourse. To get the predicted BOLD signal at specific time points (e.g., corresponding to scan acquisition times), we use the `evaluate()` function.

    # Define a time grid corresponding to scan times (e.g., TR=2s)
    TR <- 2
    scan_times <- seq(0, 140, by = TR)

    # Evaluate the regressor at scan times
    predicted_bold <- evaluate(reg1, scan_times)

    # Plot the predicted timecourse using ggplot2
    plot_df <- data.frame(Time = scan_times, Response = predicted_bold)
    ggplot(plot_df, aes(x = Time, y = Response)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg1), linetype = "dashed", color = "red", alpha = 0.7) +
      labs(title = "Predicted BOLD Response (SPM HRF)",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()

## Varying Event Durations

Sometimes events have different durations. The `duration` argument in `regressor()` can take a vector matching the length of `onsets`.

    # Example onsets and durations
    onsets_var_dur <- seq(0, 5 * 12, length.out = 6)
    durations_var <- 1:length(onsets_var_dur) # Durations increase from 1s to 6s

    # Create regressor with varying durations
    reg_var_dur <- regressor(onsets_var_dur, HRF_SPMG1, duration = durations_var)
    print(reg_var_dur)

    # Evaluate and plot
    scan_times_dur <- seq(0, max(onsets_var_dur) + 30, by = TR)
    pred_var_dur <- evaluate(reg_var_dur, scan_times_dur)

    plot_df_dur <- data.frame(Time = scan_times_dur, Response = pred_var_dur)
    ggplot(plot_df_dur, aes(x = Time, y = Response)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_var_dur), linetype = "dashed", color = "red", alpha = 0.7) +
      labs(title = "Regressor with Varying Event Durations",
           subtitle = "Duration increases over time",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()

### Duration and Summation

By default (`summate=TRUE`), the predicted response accumulates if events overlap or have extended duration. Setting `summate=FALSE` models saturation, where the response width increases with duration, but the peak amplitude doesn’t necessarily.

    # Create regressor with varying durations, summate=FALSE
    reg_var_dur_nosum <- regressor(onsets_var_dur, HRF_SPMG1,
                                   duration = durations_var, summate = FALSE)

    # Evaluate and plot
    pred_var_dur_nosum <- evaluate(reg_var_dur_nosum, scan_times_dur)

    plot_df_dur_nosum <- data.frame(Time = scan_times_dur, Response = pred_var_dur_nosum)
    ggplot(plot_df_dur_nosum, aes(x = Time, y = Response)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_var_dur_nosum), linetype = "dashed", color = "red", alpha = 0.7) +
      labs(title = "Regressor with Varying Durations (summate=FALSE)",
           subtitle = "Models saturation, peak height may not increase with duration",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()

## Varying Event Amplitudes (Parametric Modulation)

We can model variations in event intensity or some associated parameter by providing an `amplitude` vector. This creates a parametric regressor where the height of the HRF for each event is scaled by the corresponding amplitude value.

    # Example onsets and amplitudes (e.g., representing task difficulty)
    onsets_amp <- seq(0, 10 * 12, length.out = 11)
    amplitudes_raw <- 1:length(onsets_amp)

    # It's common practice to center the modulator
    amplitudes_scaled <- scale(amplitudes_raw, center = TRUE, scale = FALSE)

    # Create the parametric regressor
    reg_amp <- regressor(onsets_amp, HRF_SPMG1, amplitude = amplitudes_scaled)
    print(reg_amp)

    # Evaluate and plot
    scan_times_amp <- seq(0, max(onsets_amp) + 30, by = TR)
    pred_amp <- evaluate(reg_amp, scan_times_amp)

    plot_df_amp <- data.frame(Time = scan_times_amp, Response = pred_amp)
    ggplot(plot_df_amp, aes(x = Time, y = Response)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_amp), linetype = "dashed", color = "red", alpha = 0.7) +
      # Add points showing amplitude (scaled for visibility)
      geom_point(data = data.frame(Time = onsets(reg_amp), Amplitude = amplitudes(reg_amp)),
                 aes(x = Time, y = Amplitude * 0.2), color = "blue", size = 2) +
      labs(title = "Parametric Regressor with Varying Amplitude",
           subtitle = "Amplitude (centered) increases over time",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()

## Combining Duration and Amplitude Modulation

You can provide both `duration` and `amplitude` vectors to model events that vary in both aspects.

    set.seed(123)
    onsets_comb <- seq(0, 10 * 12, length.out = 11)
    amps_comb <- scale(1:length(onsets_comb), center = TRUE, scale = FALSE)
    durs_comb <- sample(1:5, length(onsets_comb), replace = TRUE)

    reg_comb <- regressor(onsets_comb, HRF_SPMG1,
                          amplitude = amps_comb, duration = durs_comb)
    print(reg_comb)

    # Evaluate and plot
    scan_times_comb <- seq(0, max(onsets_comb) + 30, by = TR)
    pred_comb <- evaluate(reg_comb, scan_times_comb)

    plot_df_comb <- data.frame(Time = scan_times_comb, Response = pred_comb)
    ggplot(plot_df_comb, aes(x = Time, y = Response)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_comb), linetype = "dashed", color = "red", alpha = 0.7) +
      labs(title = "Regressor with Varying Duration and Amplitude",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()

## Regressors with HRF Basis Sets

If you use an HRF object with multiple basis functions (e.g., `HRF_SPMG3`, `HRF_BSPLINE`), the `regressor` object will represent multiple timecourses, one for each basis function. `evaluate()` will return a matrix.

    # Use a B-spline basis set
    onsets_basis <- seq(0, 10 * 12, length.out = 11)
    hrf_basis <- HRF_BSPLINE # Uses N=5 basis functions by default

    reg_basis <- regressor(onsets_basis, hrf_basis)
    print(reg_basis)
    nbasis(reg_basis) # Should be 5
    #> [1] 5

    # Evaluate - this returns a matrix
    scan_times_basis <- seq(0, max(onsets_basis) + 30, by = TR)
    pred_basis_matrix <- evaluate(reg_basis, scan_times_basis)
    dim(pred_basis_matrix) # rows = time points, cols = basis functions
    #> [1] 76  5

    # Or plot manually with ggplot
    colnames(pred_basis_matrix) <- paste0("Basis_", 1:ncol(pred_basis_matrix))
    plot_df_basis <- as.data.frame(pred_basis_matrix) %>%
      mutate(Time = scan_times_basis) %>%
      pivot_longer(-Time, names_to = "Basis", values_to = "Response")

    ggplot(plot_df_basis, aes(x = Time, y = Response, color = Basis)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_basis), linetype = "dashed", color = "red", alpha = 0.3) +
      labs(title = "Regressor using B-Spline Basis Set (N=5)",
           x = "Time (seconds)",
           y = "Predicted Response",
           color = "Basis Function") +
      theme_minimal()

## Shifting Regressors

You can temporally shift all onsets within a regressor using the `shift()` method.

    # Original regressor
    reg_orig <- regressor(onsets = c(10, 30, 50), hrf = HRF_SPMG1)

    # Shifted regressor (delay by 5 seconds)
    reg_shifted <- shift(reg_orig, shift_amount = 5)

    onsets(reg_orig)
    #> [1] 10 30 50
    onsets(reg_shifted) # Onsets are now 15, 35, 55
    #> [1] 15 35 55

    # Plot both
    scan_times_shift <- seq(0, 80, by = TR)
    pred_orig <- evaluate(reg_orig, scan_times_shift)
    pred_shifted <- evaluate(reg_shifted, scan_times_shift)

    plot_df_shift <- data.frame(
      Time = scan_times_shift,
      Original = pred_orig,
      Shifted_p5s = pred_shifted
    ) %>%
      pivot_longer(-Time, names_to = "Regressor", values_to = "Response")

    ggplot(plot_df_shift, aes(x = Time, y = Response, color = Regressor)) +
      geom_line(linewidth = 1) +
      geom_vline(xintercept = onsets(reg_orig), linetype = "dashed", color = "red", alpha = 0.5) +
      geom_vline(xintercept = onsets(reg_shifted), linetype = "dashed", color = "blue", alpha = 0.5) +
      labs(title = "Shifting a Regressor",
           subtitle = "Original (red lines) vs. Shifted +5s (blue lines)",
           x = "Time (seconds)",
           y = "Predicted Response") +
      theme_minimal()