fmriAR

Fast AR and ARMA prewhitening for fMRI GLM workflows. Estimate a noise model from residuals, apply the same filter to the design matrix and the data, then fit a standard linear model on the whitened series.

The C++ core (RcppArmadillo) keeps large-scale whitening fast. Estimation is run-aware and censor-aware: lag products never cross a run boundary or a scrubbed frame.

Installation

install.packages("fmriAR")

Development version:

# install.packages("remotes")
# remotes::install_github("bbuchsbaum/fmriAR")
install.packages("fmriAR", repos = c('https://bbuchsbaum.r-universe.dev', 'https://cloud.r-project.org'))

Documentation: https://bbuchsbaum.github.io/fmriAR/

Typical workflow

1. Fit an initial OLS model and take residuals.
2. Estimate an AR/ARMA plan with fit_noise().
3. Whiten both X and Y with whiten_apply() (or do both steps with whiten()).
4. Fit the linear model on the whitened matrices.
5. Optionally compute sandwich standard errors and residual autocorrelation.

library(fmriAR)

# X: design (n x p), Y: data (n x voxels), runs: one label per timepoint
resid <- Y - X %*% qr.solve(X, Y)

plan <- fit_noise(
  resid,
  runs = runs,
  method = "ar",
  p = "auto",
  pooling = "global",
  design = X            # optional: undo residual-projection bias
)

xyw <- whiten_apply(plan, X, Y, runs = runs)
fit <- lm.fit(xyw$X, xyw$Y)
se  <- sandwich_from_whitened_resid(xyw$X, xyw$Y, beta = fit$coefficients)
ac  <- acorr_diagnostics(xyw$Y - xyw$X %*% fit$coefficients, runs = runs)

With censoring, the scrubbed rows stay in the whitened output and are listed in xyw$censor; drop them before fitting, e.g. lm.fit(xyw$X[-xyw$censor, ], xyw$Y[-xyw$censor, ]).

One-step shortcut (fits the plan from Y and X internally):

xyw <- whiten(X, Y, runs = runs, method = "ar", p = "auto")

What the package does

• AR and ARMA plans. method = "ar" fits Yule–Walker on autocovariances pooled over voxels and selects the order by BIC (p = "auto"), counting pooled voxels at their effective number. method = "arma" uses Hannan–Rissanen (1982) pooled over voxels, with p/q = "auto" for BIC order selection.
• Exact whitening at run starts. Every run and post-censoring segment is whitened with the exact stationary start of the fitted AR/ARMA model, so the result equals exact GLS within each segment (exact_first = "ar1", the default).
• Pooling. "global" (one filter), "run" (one per run), or "parcel" (one per parcel, estimated from its voxels, with optional multiscale shrinkage via parcel_sets).
• Censoring. Pass motion-scrubbed frames as indices or a logical mask; they are dropped from estimation and treated as segment breaks when whitening. whiten_apply() reuses the plan's censor set for data of the same length.
• Residual-bias correction. Autocovariance from GLM residuals is biased low (E[ehat ehat'] = M Sigma M). Pass design = X to fit_noise() or noise_acvf() to undo that bias (method = "ar", any pooling, with or without censoring). Cache the map with acvf_bias_matrix() when many datasets share a design.
• Standard errors. sandwich_from_whitened_resid() gives iid, HC0, or Newey–West HAC (type = "hac", within runs) standard errors, and handles rank-deficient designs.
• Noise scale on the plan. An fmriAR_plan now stores gamma (voxel-scale autocovariance) and sigma2 (innovation variance) per pooling unit, not just the AR/MA coefficients.
• Autocovariance without a model. noise_acvf() returns the same run- and censor-aware covariances fit_noise() uses internally, plus pair counts so you can see how much data backs each lag.
• AFNI-style restricted AR. afni_restricted_plan() builds a plan from AFNI root parameters (Cox, 2012) for pipeline comparison, including AFNI's additive white-noise ratio vrt.

See vignette("fmriAR-introduction") and ?fit_noise for parcel pooling, ARMA, and AFNI examples.

Options

• options(fmriAR.max_threads = n) — cap the OpenMP threads used for whitening. OpenMP is used automatically when the compiler supports it; results are identical for any thread count.
• options(fmriAR.use_cpp_hr = TRUE) — use the C++ single-series Hannan–Rissanen estimator (default) in the internal hr_arma() helper. Set FALSE to fall back to the R implementation. fit_noise() uses the pooled estimator regardless.

Validation

tools/validation/accuracy_benchmark.R (in the source repository) runs seeded accuracy, calibration, and timing scenarios through the exported API, so any two installed versions can be compared directly:

Rscript tools/validation/accuracy_benchmark.R <lib_path_or_-> results.rds

References

• Hannan, E. J., & Rissanen, J. (1982). Recursive estimation of mixed autoregressive-moving average order. Biometrika, 69(1), 81–94. https://doi.org/10.1093/biomet/69.1.81
• Cox, R. W. (2012). AFNI: What, where, how? NeuroImage, 62(2), 743–747. https://doi.org/10.1016/j.neuroimage.2011.08.056