The PoSIAdjRSquared package allows users to calculate p-values and confidence intervals for regression coefficients after they have been selected by adjusted R squared in linear models. The p-values and confidence intervals are valid after model selection with the same data. This allows the user to use all data for both model selection and inference without losing control over the type I error rate. The provided tests are more powerful than data splitting, which bases inference on less data since it discards all information used for selection.
This is a basic example which shows you how to calculate post-selection p-values and confidence intervals for some generated data. The code is similarly applicable to real data.
library(PoSIAdjRSquared)
# Generate data
Data <- datagen.norm(seed = 7, n = 100, p = 10, rho = 0, beta_vec = c(1,0.5,0,0.5,0,0,0,0,0,0))
X <- Data$X
y <- Data$y
selective_inference(y, X, intercept=FALSE, model_set = "fit_all_subset_linear_models", alpha=0.05, confidence_interval=TRUE)
# $summary
# Variable Coefficient Std_Error P_Value CI_Lower CI_Upper
# 1 1 1.2550561 0.10171810 0.000000000 1.00651134 1.4543199
# 2 2 0.3710123 0.10468937 0.322730857 -0.04019441 0.5530123
# 3 4 0.3291952 0.09248687 0.001782217 0.12471371 0.5104508
# 4 5 -0.1234033 0.10508632 0.841042743 -0.23945366 0.1111173
# 5 8 0.1358987 0.09710654 0.548071861 -0.08495766 0.3009992
# 6 10 0.1196511 0.09917412 0.997850742 -0.10880178 0.2263758Pirenne, S. and Claeskens, G. (2024). Exact post-selection inference for adjusted R squared selection. Statistics & Probability Letters, 211(110133):1-9. https://doi.org/10.1016/j.spl.2024.110133