Post-Selection Inference via Simultaneous Confidence Intervals.
PosiR provides tools for post-selection inference (PoSI) in linear regression models. Post-Selection Inference addresses the challenge of performing valid statistical inference after model selection, ensuring that confidence intervals maintain their nominal coverage probability (e.g., 95%) even when the model is chosen based on the data. The package implements simultaneous confidence intervals using bootstrap-based max-t statistics, following Algorithm 1 from Kuchibhotla, Kolassa, and Kuffner (2022).
Installation
You can install the development version of PosiR from GitHub:
# Install devtools if not already installed
if (!requireNamespace("devtools", quietly = TRUE)) {
install.packages("devtools")
}
# Install PosiR
devtools::install()
# Optional dependencies for vignette and examples
install.packages(c("dplyr", "pbapply"))
Example: Simultaneous Confidence Intervals
This example demonstrates how to use simultaneous_ci() to compute simultaneous confidence intervals for regression coefficients across a set of models:
library(PosiR)
# Simulate data
set.seed(123)
X <- matrix(rnorm(100 * 3), 100, 3)
colnames(X) <- c("X1", "X2", "X3")
y <- 1 + X[, "X1"] * 0.5 + rnorm(100) # True intercept = 1, X1 coefficient = 0.5
# Define model universe (column indices of X)
Q <- list(
model1 = 1:2, # Model with X1, X2
model2 = 1:3 # Model with X1, X2, X3
)
# Compute simultaneous confidence intervals
result <- simultaneous_ci(X, y, Q, B = 500, verbose = FALSE)
# View results
print(result$intervals)
#> model_id coefficient_name estimate lower upper psi_hat_nqj
#> 1 model1 (Intercept) 0.96831201 0.7198033 1.2168207 1.084196
#> 2 model1 X1 0.44983825 0.2037940 0.6958825 1.062799
#> 3 model2 (Intercept) 0.97292290 0.7230406 1.2228052 1.096215
#> 4 model2 X1 0.45219170 0.2012421 0.7031413 1.105600
#> 5 model2 X2 0.04485171 -0.1971332 0.2868366 1.028019
#> se_nqj
#> 1 0.1041248
#> 2 0.1030922
#> 3 0.1047003
#> 4 0.1051475
#> 5 0.1013913
# Plot the intervals
plot(result, main = "Simultaneous Confidence Intervals", las.labels = 1)
## Interpretation
The output result$intervals provides the coefficient estimates and simultaneous 95% confidence intervals for each model in Q. For example:
The (Intercept) and X1 intervals in model1 should contain their true values (1 and 0.5, respectively).
The intervals are wider than naive intervals to account for model selection uncertainty, ensuring valid coverage across all models in Q.
Learn More
Vignette: Run vignette(“Vignette”).
Source Paper: Kuchibhotla, A., Kolassa, J., & Kuffner, T. (2022). Post-selection inference. Annual Review of Statistics and Its Application, 9(1), 505–527. DOI: 10.1146/annurev-statistics-100421-044639.