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Defining variable domain functional data terms in vd_fit formulae

ffvd.Rd

Auxiliary function used to define ffvd terms within vd_fit model formulae. This term represents a functional predictor where each function is observed over a domain of varying length. The formulation is \(\frac{1}{T_i} \int _1^{T_i} X_i(t)\beta(t,T_i)dt\), where \(X_i(t)\) is a functional covariate of length \(T_i\), and \(\beta(t,T_i)\) is an unknown bivariate functional coefficient. The functional basis used to model this term is the B-spline basis.

Usage

ffvd(X, grid, nbasis = c(30, 50, 30), bdeg = c(3, 3, 3))

Arguments

X

variable domain functional covariate matrix.

grid

observation points of the variable domain functional covariate. If not provided, it will be 1:ncol(X).

nbasis

number of bspline basis to be used.

bdeg

degree of the bspline basis used.

Value

the function is interpreted in the formula of a VDPO model. list containing the following elements:

  • An item named B design matrix.

  • An item named X_hat smoothed functional covariate.

  • An item named L_Phi and B_T 1-dimensional marginal B-spline basis used for the functional coefficient.

  • An item named M matrix object indicating the observed domain of the data.

  • An item named nbasis number of basis used.

Examples

# Generate sample data
set.seed(123)
data <- data_generator_vd(beta_index = 1, use_x = FALSE, use_f = FALSE)
X <- data$X_se

# Specifying a custom grid
custom_grid <- seq(0, 1, length.out = ncol(X))
ffvd_term_custom_grid <- ffvd(X, grid = custom_grid, nbasis = c(10, 10, 10))

# Customizing the number of basis functions
ffvd_term_custom_basis <- ffvd(X, nbasis = c(10, 10, 10))

# Customizing both basis functions and degrees
ffvd_term_custom <- ffvd(X, nbasis = c(10, 10, 10), bdeg = c(3, 3, 3))