README.md
In PosiR: 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).

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"))

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.

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.