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Scalar-on-function regression (functional coefficient)

Source: R/stats-functional-regression.R
scalarOnFunctionRegression.Rd

Predicts a scalar outcome from a predictor CURVE (e.g. a clinical score from a joint-moment waveform). The curve is reduced to functional principal components, the outcome is regressed on the scores, and the coefficients are mapped back to a coefficient function beta(t): where along the curve the predictor matters.

Usage

scalarOnFunctionRegression(y, curves, npc = NULL, ve = 0.95)

Arguments

y

Length-N numeric outcome.

curves

N x P matrix of predictor curves.

npc

Number of functional principal components (default: enough to explain ve variance).

ve

Variance-explained target for choosing npc when npc is NULL (default 0.95).

Value

a sofr_result: beta (length-P coefficient function), intercept, fitted, r_squared, npc, scores, pve (proportion variance explained by the retained PCs).

References

Reiss PT, Ogden RT (2007) scalar-on-function regression; Ramsay & Silverman (2005).

See also

functionalRegression()

Examples

set.seed(2)
P <- 80; t <- seq(0, 1, length.out = P)
X <- matrix(rnorm(50 * P), 50, P) + outer(rnorm(50), sin(2 * pi * t))
beta_true <- dnorm(t, 0.3, 0.05)
y <- as.numeric(scale(X %*% beta_true)) + rnorm(50, 0, 0.3)
m <- scalarOnFunctionRegression(y, X, npc = 5)
m$r_squared
#> [1] 0.8919058