R/helper_output_print.R

In jrosen48/konfound: Quantify the Robustness of Causal Inferences

# Function to output printed text

#' Output printed text with formatting
#'
#' This function outputs printed text for various indices such as RIR 
#' (Robustness of Inference to Replacement) 
#' and IT (Impact Threshold for a Confounding Variable) with specific formatting
#'  like bold, underline, and italic
#' using functions from the crayon package. It handles different scenarios based
#'  on the effect difference, 
#' beta threshold, and other parameters, providing formatted 
#' output for each case.
#'
#' @param eff_diff The difference in the effect size being evaluated.
#' @param beta_threshhold The threshold value of beta, used for 
#' statistical significance determination.
#' @param bias The percentage of the estimate that could be due to bias (optional).
#' @param sustain The percentage of the estimate necessary to sustain an inference (optional).
#' @param nu The hypothesized effect size used in replacement analysis.
#' @param recase The number of cases that need to be replaced to change the inference.
#' @param obs_r The observed correlation coefficient in the data.
#' @param critical_r The critical correlation coefficient for statistical significance.
#' @param r_con The correlation coefficient of an omitted variable with both the outcome and the predictor.
#' @param itcv The impact threshold for a confounding variable.
#' @param alpha The level of statistical significance.
#' @param index A character string indicating the index for which the output is generated ('RIR' or 'IT').
#' @importFrom crayon bold underline italic
output_print <- function(eff_diff, 
                         beta_threshhold, 
                         bias = NULL, 
                         sustain = NULL, 
                         nu, 
                         recase, 
                         obs_r, 
                         critical_r, 
                         r_con, 
                         itcv, 
                         alpha, 
                         index) {
 if (index == "RIR") { 
  cat(crayon::bold("Robustness of Inference to Replacement (RIR):\n"))
  if (abs(eff_diff) > abs(beta_threshhold)) {
    cat("To invalidate an inference, ", round(bias, 3), 
        "% of the estimate would have to be due to bias. ")
    cat("\n")
    cat("This is based on a threshold of ", round(beta_threshhold, 3), 
        " for statistical significance (alpha = ", alpha, ").\n", 
        sep = "")
    cat("\n")
    cat("To invalidate an inference, ", round(recase, 3), 
        " observations would have to be replaced with cases")
    cat("\n")
    cat("for which the effect is ", nu,
        " (RIR = ", round(recase, 3), ").\n", sep = "")
    cat("\n")
    }
    else if (abs(eff_diff) < abs(beta_threshhold)) {
      cat("To sustain an inference, ", round(sustain, 3), 
          "% of the estimate would have to be due to bias. ")
      cat("\n")
      cat("This is based on a threshold of ", round(beta_threshhold, 3), 
          " for statistical significance (alpha = ", alpha, ").\n", 
          sep = "")
      cat("\n")
      cat("To sustain an inference, ", round(recase, 3), 
          " of the cases with ", nu, 
          " effect would have to be replaced with cases at the 
          threshold of inference",
          " (RIR = ", round(recase, 3), ").\n", sep = "")
    }
    else if (eff_diff == beta_threshhold) {
      warning("The coefficient is exactly equal to the threshold.\n")
    }
    cat("See Frank et al. (2013) for a description of the method.")
    cat("\n")
    cat("\n")
    cat(crayon::underline("Citation:"), 
        "Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).")
    cat("\n")
    cat("What would it take to change an inference?")
    cat("\n")
    cat("Using Rubin's causal model to interpret the 
        robustness of causal inferences.")
    cat("\n")
    cat(crayon::italic("Education, Evaluation and 
                       Policy Analysis, 35"), "437-460.")
    cat("\n")
  } 
  if (index == "IT") { 
    cat(crayon::bold("Impact Threshold for a Confounding Variable:\n"))
    if (abs(obs_r) > abs(critical_r) & obs_r > 0) {
      cat("The minimum impact of an omitted variable to invalidate an 
          inference for a null hypothesis of 0 effect is based on
          a correlation of ", r_con)
      cat("\n")
      cat(" with the outcome and at ", r_con,
          " with the predictor of interest 
          (conditioning on observed covariates) based on a threshold of ")
      cat("\n")
      cat(round(critical_r, 3), " for statistical 
          significance (alpha = ", alpha, ").\n",sep = "")
      cat("\n")
      cat("Correspondingly the impact of an omitted variable
          (as defined in Frank 2000) must be ") 
      cat("\n")
      cat(r_con, " X ", r_con, " = ", round(r_con^2, 3), 
          " to invalidate an inference for a null hypothesis of 0 effect.
          \n", sep = "")
    } else if (abs(obs_r) > abs(critical_r) & obs_r < 0) {
      cat("The minimum (in absolute value) impact of an omitted 
          variable to invalidate an inference for a null hypothesis of 0 
          effect is based on a correlation of ", -r_con)
      cat("\n")
      cat(" with the outcome and at ", r_con,
          " with the predictor of interest (conditioning on observed
          covariates; signs are interchangable) based on a threshold of ")
      cat("\n")
      cat(round(critical_r, 3), " for statistical significance 
          (alpha = ", alpha, ").\n",
          sep = "")
      cat("\n")
      cat("Correspondingly the impact of an omitted variable 
          (as defined in Frank 2000) must be ") 
      cat("\n")
      cat(-r_con, " X ", r_con, " = ", -round(r_con^2, 3), 
          " to invalidate an inference for a null hypothesis
          of 0 effect.\n", sep = "")
    } else if (abs(obs_r) < abs(critical_r) & obs_r > 0) {
      cat("The maximum impact (in absolute value) of an omitted variable 
          to sustain an inference for a null hypothesis of 0 effect is 
          based on a correlation of ", -r_con)
      cat("\n")
      cat(" with the outcome and at ", r_con,
          " with the predictor of interest (conditioning on observed 
          covariates; signs are interchangable) based on a threshold of ", 
          round(beta_threshhold, 3))
      cat("\n")
      cat(" for statistical significance (alpha = ", alpha, ").\n",
          sep = "")
      cat("\n")
      cat("Correspondingly the impact of an omitted variable 
          (as defined in Frank 2000) must be ")
      cat("\n")
      cat(-r_con, " X ", r_con, " = ", -round(r_con^2, 3), 
          " to sustain an inference for a null hypothesis of 0 effect.\n", 
          sep = "")
    } else if (abs(obs_r) < abs(critical_r) & obs_r < 0) {
      cat("The maximum impact of an omitted variable to sustain an 
          inference for a null hypothesis of 0 effect is based on a 
          correlation of ", r_con)
      cat("\n")
      cat(" with the outcome and at ", r_con,
          " with the predictor of interest (conditioning on observed 
          covariates) based on a threshold of ", round(beta_threshhold, 3))
      cat("\n")
      cat(" for statistical significance (alpha = ", alpha, ").\n",
          sep = "")
      cat("\n")
      cat("Correspondingly the impact of an omitted variable 
          (as defined in Frank 2000) must be ")
      cat("\n")
      cat(r_con, " X ", r_con, " = ", round(r_con^2, 3), 
          " to sustain an inference for a null hypothesis of 0 effect.\n", 
          sep = "")
    } else if (obs_r == critical_r) {
      warning("The correlation is exactly equal to the threshold.\n")
    }
    cat("See Frank (2000) for a description of the method.")
    cat("\n")
    cat("\n")
    cat(crayon::underline("Citation:"))
    cat("\n")
    cat("Frank, K. (2000). Impact of a confounding variable on the")
    cat("\n")
    cat("inference of a regression coefficient.", 
        crayon::italic("Sociological Methods and Research, 29"), 
        "(2), 147-194")
    cat("\n")
  }
    
}