Windowpane Tests for Correlation Analysis — windowpane

This function performs bootstrapped correlation analysis for multiple predictors against a response variable. It applies the Simes method for global significance testing and calculates individual correlations, p-values, and bootstrap statistics.

Usage

windowpane_tests(
  data,
  response_var,
  corr_type = "spearman",
  R = 1000,
  global_alpha = 0.05,
  individual_alpha = 0.005
)

Arguments

data: A data frame containing the predictors and the response variable.
response_var: A string representing the name of the response variable in the data frame.
corr_type: A string specifying the correlation method to use; options are "spearman" (default), "pearson", or "kendall".
R: An integer indicating the number of bootstrap replications. Default is 1000.
global_alpha: A numeric value representing the global alpha level for the Simes correction. Default is 0.05.
individual_alpha: A numeric value for the individual alpha threshold for testing individual predictors. Default is 0.005.

Value

A list containing the following elements:

results: A data frame with columns: variable, correlation, p_value, mean_corr, sd_corr, median_corr, rank, simes_threshold, significant_simes, and individual_significant.
summary_table: A data frame summarizing the global p-value (Pg) and maximum correlation.
global_significant: A logical value indicating whether the global test is significant.

Details

The function calculates correlations between the response variable and each predictor in the data frame, using bootstrapping to generate mean, standard deviation, and median estimates of the correlation. The Simes correction is applied to control for multiple testing, providing a global p-value (Pg). The function also returns the maximum observed correlation.

Examples

# Example usage
data <- data.frame(x1 = rnorm(100), x2 = rnorm(100), y = rnorm(100))
result <- windowpane_tests(data, "y", corr_type = "spearman", R = 500)
result$results
#>   variable correlation    p_value  mean_corr   sd_corr median_corr rank m
#> 1       x2   0.1766337 0.07875094  0.1653792 0.1026392   0.1685394    1 2
#> 2       x1  -0.1663486 0.09810340 -0.1719860 0.1031982  -0.1724914    2 2
#>   simes_threshold significant_simes individual_significant
#> 1           0.025             FALSE                  FALSE
#> 2           0.050             FALSE                  FALSE
result$summary_table
#>                Metric     Value
#> 1 Global P-value (Pg) 0.0981034
#> 2     Max Correlation 0.1766337