# Bootstrap Confidence Intervals for Functional Effect Curves Computes bias-corrected percentile bootstrap confidence intervals for the intercept and covariate effect functions in cepstral-based regression models. ```r boot_effect( logspect, res, alpha_effect, beta_effect, X, nbase, frq1, frq2, nrank, ind, level, nboot, method = "rrr", verb = FALSE ) ``` ## 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. ## Returns 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. ## Examples ```r 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(Y, X, 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", 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)) ```

boot_effect function