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Tolerance-Noise-Covariation (TNC) decomposition of result error

Source: R/motor-variability-ucm.R
toleranceNoiseCovariation.Rd

Decomposes the mean result error of a set of executions (Muller & Sternad 2004): how much error is removable by moving the mean to a more tolerant region, how much is due to dispersion (noise) around that region, and how much the observed inter-variable covariation already saves relative to a de-covaried (column-permuted) surrogate.

Usage

toleranceNoiseCovariation(
  execution,
  error_fn,
  optimum = NULL,
  n_surrogate = 200L
)

Arguments

execution

An N x m matrix of execution variables.

error_fn

A vectorised error function: given an N x m matrix it returns the length-N per-trial error (>= 0, 0 = perfect).

optimum

Length-m execution vector achieving (near-)zero error, used as the most tolerant target. When NULL, the dispersion (noise) reference is the cloud centroid.

n_surrogate

Number of column-permutation surrogates for the covariation estimate (default 200).

Value

a tnc_result list: tolerance, noise, covariation (error components; covariation > 0 = the observed covariation reduces error), e_data (mean data error), e_optimum.

References

Muller H, Sternad D (2004) J Exp Psychol Hum Percept Perform 30:212-233; Cohen RG, Sternad D (2009) Exp Brain Res 193:69-83.

See also

uncontrolledManifold()

Examples

set.seed(3)
# redundant reaching task: result = x1 + x2, target 20, error squared
x1 <- rnorm(300, 12, 3); x2 <- 20 - x1 + rnorm(300, 0, 0.6)   # covary to hit 20
err <- function(M) (M[, 1] + M[, 2] - 20)^2
toleranceNoiseCovariation(cbind(x1, x2), err, optimum = c(10, 10))$covariation
#> [1] 17.5002