Scalar-on-Shape Regression

Fits a scalar-on-shape regression model where the response depends on the shape of the functional predictor, with phase variation removed via elastic alignment (Fisher-Rao framework).

Usage

scalar.on.shape(
  fdataobj,
  y,
  nbasis = 11,
  lambda = 0.001,
  index.method = c("identity", "polynomial", "nadaraya.watson"),
  index.param = 2,
  g.degree = 2,
  dp.lambda = 0,
  max.iter.outer = 10,
  max.iter.inner = 15,
  tol = 1e-04
)

Arguments

fdataobj

An object of class 'fdata'.

y

Scalar response vector (length n).

nbasis

Number of Fourier basis functions for beta (default 11).

lambda

Roughness penalty weight (default 1e-3).

index.method

Index function method: "identity" (default), "polynomial", or "nadaraya.watson".

index.param

Parameter for the index method: polynomial degree (integer) or Nadaraya-Watson bandwidth (numeric). Default 2.

g.degree

Polynomial degree for the amplitude link g (default 2).

dp.lambda

Dynamic programming alignment penalty (default 0).

max.iter.outer

Maximum outer iterations (default 10).

max.iter.inner

Maximum inner iterations (default 15).

tol

Convergence tolerance (default 1e-4).

Value

An object of class 'scalar.on.shape' (a list) with components:

beta

Estimated shape index function (length m).

beta.coefficients

Fourier coefficients for beta.

gammas

Warping functions (n x m matrix).

shape.scores

Shape scores (length n).

h.coefficients

Index link function coefficients.

g.coefficients

Amplitude link function coefficients.

fitted.values

Fitted response values.

residuals

Residuals.

sse

Residual sum of squares.

r.squared

Coefficient of determination.

n.iter.outer

Number of outer iterations.

n.iter.inner

Number of inner iterations.

index.method

Index method used.

index.param

Index method parameter.

fdataobj

Training fdata object.

y

Training response.

Examples

# \donttest{
fd <- fdata(matrix(rnorm(500), 50, 10), argvals = seq(0, 1, length.out = 10))
y <- rnorm(50)
fit <- scalar.on.shape(fd, y, nbasis = 5)
# }