Package 'PosiR'

Plot Simultaneous Confidence Intervals

Description

Visualizes confidence intervals returned by simultaneous_ci() using base R graphics. Estimates are shown as points with corresponding CI segments, grouped and labeled by model and coefficient name. Supports customization for log scale, character sizes, label trimming, and reference lines.

Usage

## S3 method for class 'simultaneous_ci_result'
plot(
  x,
  y = NULL,
  subset_pars = NULL,
  log.scale = FALSE,
  cex = 0.8,
  cex.labels = 0.8,
  las.labels = 1,
  pch = 16,
  col.estimate = "blue",
  col.ci = "darkgray",
  col.ref = "red",
  ref.line.pos = 0,
  lty.ref = 2,
  main = "Simultaneous Confidence Intervals",
  xlab = NULL,
  label.trim = NULL,
  ...
)

Arguments

x	An object of class simultaneous_ci_result, typically returned by simultaneous_ci().
y	Ignored.
subset_pars	Optional character vector. Coefficient names to subset the plot. Default: all.
log.scale	Logical. Plot on logarithmic scale. Intervals crossing 0 or with nonpositive bounds are excluded.
cex	Point size for estimates. Default = 0.8.
cex.labels	Label size for y-axis. Default = 0.8.
las.labels	Orientation of y-axis labels (0, 1, 2, or 3). Default = 1.
pch	Plot character for point estimates. Default = 16.
col.estimate	Color of point estimates. Default = "blue".
col.ci	Color of confidence interval lines. Default = "darkgray".
col.ref	Color of reference line(s). Default = "red".
ref.line.pos	Position(s) for vertical reference line(s). Default = 0. Set to NULL to omit.
lty.ref	Line type for reference lines. Default = 2 (dashed).
main	Plot title. Default = "Simultaneous Confidence Intervals".
xlab	X-axis label. If NULL and log.scale = TRUE, label defaults to "Log Estimate".
label.trim	Integer. Trims long coefficient labels to this width (adds "..."). Optional.
...	Additional arguments passed for future use (currently ignored).

Value

Invisibly returns a list:

• ycoords: Named vector of y-axis positions for each label

• xlim: Range of x-axis limits used

• ylim: Range of y-axis limits used

If no valid intervals are available for plotting, returns invisible(NULL).

Examples

set.seed(1)
X <- matrix(rnorm(100*2), 100, 2, dimnames = list(NULL, c("X1", "X2")))
y <- 1 + X[,1] - X[,2] + rnorm(100)
res <- simultaneous_ci(X, y, list(mod = 1:3), B = 100, add_intercept = TRUE)
plot(res)

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Compute Simultaneous Confidence Intervals via Bootstrap (Post-Selection Inference)

Description

Implements Algorithm 1 from the reference paper using bootstrap-based max-t statistics to construct valid simultaneous confidence intervals for selected regression coefficients across a user-specified universe of linear models.

Usage

simultaneous_ci(
  X,
  y,
  Q_universe,
  alpha = 0.05,
  B = 1000,
  add_intercept = TRUE,
  bootstrap_method = "pairs",
  cores = 1,
  use_pbapply = TRUE,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

X	Numeric matrix (n x p): Design matrix. Must have unique column names. Do not include an intercept if add_intercept = TRUE.
y	Numeric vector (length n): Response vector.
Q_universe	Named list of numeric vectors. Each element specifies a model as a vector of column indices (accounting for intercept if add_intercept = TRUE). Names are used to identify each model in results.
alpha	Significance level for the confidence intervals. Default is 0.05.
B	Integer. Number of bootstrap samples. Default is 1000.
add_intercept	Logical. If TRUE, adds an intercept as the first column of the design matrix. Default is TRUE.
bootstrap_method	Character. Bootstrap type. Only "pairs" is currently supported.
cores	Integer. Number of CPU cores to use for bootstrap parallelization. Default is 1.
use_pbapply	Logical. Use pbapply for progress bars if available. Default is TRUE.
seed	Optional numeric. Random seed for reproducibility. Used for parallel-safe RNG.
verbose	Logical. Whether to display status messages. Default is TRUE.
...	Reserved for future use.

Details

Supports parallel execution, internal warnings capture, and returns structured results with estimates, intervals, bootstrap diagnostics, and inference statistics.

Value

A list of class simultaneous_ci_result with elements:

• intervals: Data frame with estimates, confidence intervals, variances, and SEs

• K_alpha: Bootstrap (1 - alpha) quantile of max-t statistics

• T_star_b: Vector of bootstrap max-t statistics

• n_valid_T_star_b: Number of finite bootstrap max-t statistics

• alpha, B, bootstrap_method: Metadata

• warnings_list: Internal warnings collected during bootstrap/model fitting

• valid_bootstrap_counts: Valid bootstrap replicates per parameter

• n_bootstrap_errors: Total bootstrap fitting errors

References

Kuchibhotla, A., Kolassa, J., & Kuffner, T. (2022). Post-selection inference. Annual Review of Statistics and Its Application, 9(1), 505–527.

Examples

set.seed(123)
X <- matrix(rnorm(100 * 2), 100, 2, dimnames = list(NULL, c("X1", "X2")))
y <- X[,1] * 0.5 + rnorm(100)
Q <- list(model = 1:2)
res <- simultaneous_ci(X, y, Q, B = 100, cores = 1)
print(res$intervals)
plot(res)

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