PoSIAdjRSquared (version 0.1.0)

selective_inference: Selective inference

Description

This function conducts selective inference for selected models by adjusted R squared. Selective p-values (and optionally, selective confidence intervals) are calculated.

Usage

selective_inference(y, X, intercept, model_set, alpha, confidence_interval, size)

Value

selected_model

The indices of the selected columns of X.

coefficients

The estimated coefficients in the selected model.

standard_errors

The standard errors of the coefficients in the selected model.

p_values

The selective p-values for tests whether the selected coefficients are 0 with two-sided alternatives.

confidence_intervals

The selective confidence intervals for the coefficients in the selected model.

summary

A summary table.

Arguments

y

Response vector of type "matrix" and dimension nx1

X

The full model design matrix

intercept

Logical value: TRUE if the selected model contains an intercept, FALSE if not

model_set

Can take values "fit_all_subset_linear_models" and "fit_specified_size_subset_linear_models". For selection out of all possible subset of the full model, choose option "fit_all_subset_linear_models". For selection from models of a specified size, choose option "fit_specified_size_subset_linear_models".

alpha

The significance level: number between 0 and 1. For example, for 95% confidence intervals, choose alpha=0.05.

confidence_interval

Logical value: TRUE if selective confidence intervals should be calculated, FALSE if not

size

Integer for specified size of selected model (number of coefficients). Use if model_set is "fit_specified_size_subset_linear_models".

Author

Sarah Pirenne and Gerda Claeskens.

References

Pirenne, S. and Claeskens, G. (2024). Exact Post-Selection Inference for Adjusted R Squared.

Examples

  # Generate example 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 0.2263758