CepReg (version 0.1.3)

boot_effect: Bootstrap Confidence Intervals for Functional Effect Curves

Description

Computes bias-corrected percentile bootstrap confidence intervals for the intercept and covariate effect functions in cepstral-based regression models.

Usage

boot_effect(
  logspect,
  res,
  alpha_effect,
  beta_effect,
  X,
  nbase,
  frq1,
  frq2,
  nrank,
  ind,
  level,
  nboot,
  method = "rrr_get",
  verb = FALSE
)

Value

A list with:

alpha_ci

Matrix with lower and upper CI for intercept effect.

beta_ci

Array or matrix of lower and upper CI for covariate effects.

Arguments

logspect

Matrix of estimated log-spectra.

res

Matrix of residuals from cepstral regression.

alpha_effect

Vector of estimated intercept effect function.

beta_effect

Matrix of estimated covariate effect functions.

X

Covariate matrix.

nbase

Number of cepstral basis functions.

frq1

Frequency grid used for cepstral modeling.

frq2

Frequency grid used for reconstructing spectra.

nrank

Rank for reduced-rank regression.

ind

A vector of indices indicating which covariates to compute effect confidence intervals for.

level

Confidence level.

nboot

Number of bootstrap iterations.

method

Regression method: "rrr", "ols", or "env".

verb

Logical; if TRUE, prints bootstrap iteration number.

Examples

set.seed(123)
N <- 10
len <- 12
nbase <- 2
nrank <- 1
nboot <- 10
level <- 0.95
p <- 2
ind <- 1:p

Y <- matrix(rnorm(N * nbase), nrow = N, ncol = nbase)
X <- matrix(rnorm(N * p), nrow = N, ncol = p)
frq <- seq(1, nbase) / len

rrr_out <- rrr_get(X, Y, frq, nbase, nrank)

res_matrix <- rrr_out$res
if (ncol(res_matrix) != length(frq)) {
  res_matrix <- matrix(
  res_matrix[, 1:length(frq)],
  nrow = N,
  ncol = length(frq))}

eff <- effect_get(rrr_out$alph, rrr_out$bet, frq, nbase, ind)
alpha_eff <- eff$alpha_effect
beta_eff <- eff$beta_effect

logspect <- matrix(rnorm(N * length(frq)), nrow = N, ncol = length(frq))

boot_ci <- boot_effect(
  logspect = logspect,
  res = res_matrix,
  alpha_effect = alpha_eff,
  beta_effect = beta_eff,
  X = X,
  nbase = nbase,
  frq1 = frq,
  frq2 = frq,
  nrank = nrank,
  ind = ind,
  level = level,
  nboot = nboot,
  method = "rrr_get",
  verb = TRUE
)

plot(frq, beta_eff[, 1], type = "l", col = "blue", lwd = 2,
     ylab = "Effect", xlab = "Frequency",
     main = paste("Effect Function and", level*100, "% CI for Covariate", ind[1]))
lines(frq, boot_ci[[ind[1]]][, 1], col = "red", lty = 2)
lines(frq, boot_ci[[ind[1]]][, 2], col = "red", lty = 2)
legend("topright", legend = c("Effect", "Bootstrap CI"), col = c("blue", "red"),
       lty = c(1, 2), lwd = c(2, 1))