Construct Simultaneous Confidence Bands for Regression Coefficients

This function fits either a linear or logistic regression model and computes simultaneous confidence bands (SCBs) for the model coefficients using a non-parametric bootstrap procedure.

Usage

SCB_regression_coef(
  df_fit,
  model,
  n_boot = 5000,
  alpha = 0.05,
  type = "linear"
)

Arguments

df_fit

A data frame containing the design matrix and response variable used to fit the model.

model

A character string specifying the regression formula (e.g., "y ~ x1 + x2").

n_boot

Integer. Number of bootstrap samples to use for constructing the SCBs. Default is 5000.

alpha

Numeric. Significance level for the confidence bands (e.g., 0.05 for 95% SCBs). Default is 0.05.

type

A character string specifying the model type. Either "linear" (default) or "logistic".

Value

A data frame with the following columns:

scb_low

Lower bound of the simultaneous confidence band. The first row corresponds to the intercept, and subsequent rows correspond to regression coefficients.

Mean

Estimated values. The first element is the intercept estimate, and the remaining are coefficient estimates.

scb_up

Upper bound of the simultaneous confidence band. The first row corresponds to the intercept, and subsequent rows correspond to regression coefficients.

References

Ren, J., Telschow, F. J. E., & Schwartzman, A. (2024). Inverse set estimation and inversion of simultaneous confidence intervals. Journal of the Royal Statistical Society: Series C (Applied Statistics), 73(4), 1082–1109. doi:10.1093/jrsssc/qlae027

Examples

library(MASS)
set.seed(262)
M <- 5
rho <- 0.4
n <- 100
beta <- rnorm(M, mean = 0, sd = 1)
Sigma <- outer(1:M, 1:M, function(i, j) rho^abs(i - j))
X <- MASS::mvrnorm(n = n, mu = rep(0, M), Sigma = Sigma)
epsilon <- rnorm(n, mean = 0, sd = 1)
y <- X %*% beta + epsilon
df <- as.data.frame(X)
names(df) <- paste0("x", 1:M)
df$y <- as.vector(y)
model <- "y ~ ."
results <- SCB_regression_coef(df, model, n_boot = 100)