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PosiR provides tools for post-selection inference (PoSI) in linearregression models. Post-Selection Inference addresses the challenge ofperforming valid statistical inference after model selection, ensuringthat confidence intervals maintain their nominal coverage probability(e.g., 95%) even when the model is chosen based on the data. The packageimplements simultaneous confidence intervals using bootstrap-based max-tstatistics, following Algorithm 1 from Kuchibhotla, Kolassa, and Kuffner(2022).

You can install the development version ofPosiR from GitHub:

# Install devtools if not already installedif (!requireNamespace("devtools",quietly=TRUE)) {  install.packages("devtools")}# Install PosiRdevtools::install()# Optional dependencies for vignette and examplesinstall.packages(c("dplyr","pbapply"))

This example demonstrates how to usesimultaneous_ci() to computesimultaneous confidence intervals for regression coefficients across aset of models:

library(PosiR)# Simulate dataset.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, X2model2=1:3# Model with X1, X2, X3)# Compute simultaneous confidence intervalsresult<- simultaneous_ci(X,y,Q,B=500,verbose=FALSE)# View resultsprint(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 intervalsplot(result,main="Simultaneous Confidence Intervals",las.labels=1)

##Interpretation

The outputresult$intervals provides the coefficient estimates andsimultaneous 95% confidence intervals for each model inQ. Forexample:

The(Intercept) andX1 intervals inmodel1 should contain theirtrue values (1 and 0.5, respectively).

The intervals are wider than naive intervals to account for modelselection uncertainty, ensuring valid coverage across all models inQ.

Vignette: Runvignette(“Vignette”).

Source Paper: Kuchibhotla, A., Kolassa, J., & Kuffner, T. (2022).Post-selection inference. Annual Review of Statistics and ItsApplication, 9(1), 505–527. DOI:10.1146/annurev-statistics-100421-044639.