Function-on-scalar regression (coefficient curves)

Models a set of response CURVES as a linear function of one or more scalar predictors, giving a coefficient curve for each predictor (how the waveform changes per unit predictor) with pointwise inference and a domain-wide permutation test.

Usage

functionalRegression(curves, predictor, n_perm = 1000L, seed = NULL)

Arguments

curves

An N x P matrix: N observations (curves), P domain points (e.g. % gait cycle).

predictor

A length-N vector, N x q matrix, or data frame of scalar predictors. An intercept is added automatically.

n_perm

Permutations for the curve-wide (family-wise) p-value per coefficient (default 1000); set 0 to skip.

seed

Optional integer seed for the permutation test (reproducibility).

Value

a fosr_result: coefficients (k x P, incl. intercept), se, tval, p_pointwise (k x P), p_global (length k, family-wise), the fitted curves and terms.

References

Ramsay JO, Silverman BW (2005) Functional Data Analysis; Reiss PT, et al. (2010) function-on-scalar regression.

See also

scalarOnFunctionRegression(), spmRegression()

Examples

set.seed(1)
P <- 101; t <- seq(0, 1, length.out = P)
speed <- runif(40, 0.8, 1.6)
curves <- outer(speed, rep(1, P)) * matrix(sin(2 * pi * t), 40, P, byrow = TRUE) +
  matrix(rnorm(40 * P, 0, 0.05), 40, P)
fit <- functionalRegression(curves, speed, n_perm = 200)
fit$p_global                       # speed coefficient curve is significant
#> (Intercept)          x1 
#>          NA 0.004975124