plot.AD_pvalues: Plot Empirical Cumulative Distribution Function (ECDF) of p-values

Description

This function creates several plots with the empirical cumulative distribution of the p-values obtained through simulation.

Usage

# S3 method for AD_pvalues
plot(
  x,
  which = seq_len(length(x$test_coefficients) + 1),
  caption = as.list(paste("ECDF of", c(names(x$test_coefficients), "all coefficients"))),
  ks_test = TRUE,
  signif = c(0.01, 0.05, 0.1),
  discrepancy_tol = 0.1,
  plot_uniform = TRUE,
  uniform_legend = TRUE,
  converged_only = FALSE,
  no_warnings = FALSE,
  no_messages = FALSE,
  ylab = "Empirical cumulative distribution",
  xlab = "p-value",
  ...,
  ask = prod(graphics::par("mfcol")) < length(which) && grDevices::dev.interactive()
)

Value

A vector of joint p-values for all coefficients.

Arguments

x: AD_pvalues object, usually the result of simulate_wald_pvalues()
which: A vector specifying the indices of coefficients to plot. If index is bigger than the number of coefficients it plots the joint p_value.
caption: A character vector or a list with caption for each plot. If it's a list, the list index must match the coefficient index used by which. If it's a vector, it's values are used in order.
ks_test: If TRUE inserts Kolmogorov-Smirnov p-value in the graphic.
signif: Points to verify discrepancy.
discrepancy_tol: Threshold to consider point discrepant.
plot_uniform: Logical. If TRUE, plot uniform distribution.
uniform_legend: Logical. If TRUE, a legend is added to the plot to distinguish between the p-value and U(0, 1) curves. Defaults to TRUE.
converged_only: Use p-values from converged models only.
no_warnings: If TRUE, ignore simulations that threw warnings.
no_messages: If TRUE, ignore simulations that shown messages.
ylab: The label for the y-axis. Defaults to "Empirical cumulative distribution".
xlab: The label for the x-axis. Defaults to "p-value".
...: extra arguments passed to graphics::plot
ask: Logical. If TRUE, the user is prompted before each plot. Defaults to TRUE if in an interactive session and the number of plots is greater than the available space; otherwise, FALSE.

Details

If the asymptotic approximation is valid the distribution of the p-values should be close to an uniform distribution. Discrepancies are highlighted, by default it verifies the significance on the most commonly used significance values are 0.01, 0.05 and 0.10.

The reported KS (Kolmogorov-Smirnov) test is the result of the "two-sided" stats::ks.test() function comparing the observed p-values distribution with the uniform. The test may reject the KS test due to few simulations, make sure that the lines shown in the plot are smooth before drawing any conclusions.

Examples

Run this code

model <- lm(mpg ~ wt + hp, data = mtcars)
p_values_ld <- simulate_wald_pvalues(model, n_sim = 100)
plot(p_values_ld)

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