app.R

library(plumber)

#* @apiTitle Effect Size Calculator API



#' Calculate a Distribution-Free Effect Size (d_reg)
#'
#' This function computes a distribution-free effect size by modeling the 
#' empirical distribution function (eCDF) of two groups via polynomial 
#' regression. The effect size is computed as the standardized
#' difference between the means of the smoothed distributions.
#'
#' The method involves:
#' 1. Fitting polynomials to each group's quantile function: x = f(z)
#' 2. Computing moments (mean, variance) of the polynomials
#' 3. Calculating d(reg) using the pooled standard deviation
#'
#' @param x1 A numeric vector of data for the first group.
#' @param x2 A numeric vector of data for the second group.
#' @param degree The degree of the polynomial to fit (default = 5).
#'        Higher degrees capture more complex distributional shapes but
#'        may overfit with small samples.
#' @param CI Confidence level for confidence interval (default = NA, no CI computed).
#'        If specified (e.g., 0.95), uses asymptotic normal approximation.
#'        WARNING: CI formula assumes Cohen's d distribution and may not be accurate for d_reg.
#' @param silent Logical; if TRUE, suppresses warnings during fitting (default = TRUE).
#'
#' @return A list (S3 class "d_reg") containing:
#'   \item{d_reg}{The distribution-free effect size (standardized mean difference).}
#'   \item{group1_mean}{Mean of the smoothed distribution for group 1.}
#'   \item{group1_variance}{Variance of the smoothed distribution for group 1.}
#'   \item{group1_sd}{Standard deviation of the smoothed distribution for group 1.}
#'   \item{group2_mean}{Mean of the smoothed distribution for group 2.}
#'   \item{group2_variance}{Variance of the smoothed distribution for group 2.}
#'   \item{group2_sd}{Standard deviation of the smoothed distribution for group 2.}
#'   \item{pooled_sd}{Pooled standard deviation.}
#'   \item{n1}{Sample size of group 1.}
#'   \item{n2}{Sample size of group 2.}
#'   \item{model1}{Fitted polynomial model for group 1.}
#'   \item{model2}{Fitted polynomial model for group 2.}
#'   \item{default_degree}{Polynomial degree used.}
#'   \item{tie_proportion_1}{Proportion of tied values in group 1.}
#'   \item{tie_proportion_2}{Proportion of tied values in group 2.}
#'   \item{n_unique_1}{Number of unique values in group 1.}
#'   \item{n_unique_2}{Number of unique values in group 2.}
#'   \item{ci_lower}{Lower bound of confidence interval (if CI specified).}
#'   \item{ci_upper}{Upper bound of confidence interval (if CI specified).}
#'   \item{ci_level}{Confidence level (if CI specified).}
#'
#' @details
#' The method is distribution-free and converges to Cohen's d under normality with 
#' increasing group size. It is robust to outliers and skewness compared to 
#' classical parametric methods.
#' 
#' Sample size requirements: At least (degree + 1) observations per group.
#' Recommended: n > 10 per group for stable polynomial fits.
#' For small samples (n < 20), consider using degree = 3 or lower.
#'
#' Confidence intervals use an asymptotic approximation based on Cohen's d 
#' distribution and may not accurately reflect the true sampling distribution 
#' of d_reg, especially in small samples or non-normal data.
#'
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' @references
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen's d.
#'
#' @examples

#' # Normal distributions

#' set.seed(123)

#' x1 <- rnorm(30, mean = 0, sd = 1)

#' x2 <- rnorm(30, mean = 0.5, sd = 1)

#' result <- d.reg(x1, x2)

#' print(result)

#' 

#' # With confidence interval

#' result_ci <- d.reg(x1, x2, CI = 0.95)

#' print(result_ci)

#' 

#' # Skewed distributions

#' x1 <- rexp(50, rate = 1)

#' x2 <- rexp(50, rate = 0.8)

#' result <- d.reg(x1, x2, degree = 4)

#' print(result)

#'

#' @export
d.reg <- function(x1, x2, degree = 5, CI = NA, silent = TRUE) {
  
  # ============================================================================
  # Input Validation
  # ============================================================================
  
  if (!is.numeric(x1) || !is.numeric(x2)) {
    stop("Both x1 and x2 must be numeric vectors.")
  }
  
  # Handle missing values
  if (any(is.na(x1)) || any(is.na(x2))) {
    if (!silent) {
      warning("Missing values detected and will be removed.")
    }
    x1 <- x1[!is.na(x1)]
    x2 <- x2[!is.na(x2)]
  }
  
  n1 <- length(x1)
  n2 <- length(x2)
  
  # Check for empty groups
  if (n1 == 0 || n2 == 0) {
    stop("Cannot compute effect size with empty groups after removing NAs.")
  }
  
  # Check sufficient sample size for polynomial degree
  if (n1 < degree + 1) {
    stop("Group 1 has insufficient data: need at least ", degree + 1, 
         " observations for degree ", degree, " polynomial (got ", n1, ").")
  }
  
  if (n2 < degree + 1) {
    stop("Group 2 has insufficient data: need at least ", degree + 1, 
         " observations for degree ", degree, " polynomial (got ", n2, ").")
  }
  
  # Validate CI parameter if provided
  if (!is.na(CI)) {
    if (!is.numeric(CI) || length(CI) != 1) {
      stop("CI must be a single numeric value or NA.")
    }
    if (CI <= 0 || CI >= 1) {
      stop("CI must be between 0 and 1 (exclusive).")
    }
  }

  model1 <- fit_polynomial(x1, degree)
  model2 <- fit_polynomial(x2, degree)
  
  # Extract tie information
  tie1 <- attr(model1, "tie_proportion")
  tie2 <- attr(model2, "tie_proportion")
  n_unique1 <- attr(model1, "n_unique")
  n_unique2 <- attr(model2, "n_unique")
  
  # Warn about substantial ties
  if (!silent && (tie1 > 0.3 || tie2 > 0.3)) {
    message(sprintf(
      "Note: Substantial ties detected (Group 1: %.1f%%, Group 2: %.1f%%).",
      tie1 * 100, tie2 * 100
    ))
    message("This suggests discrete/ordinal data. Results should be interpreted cautiously.")
    message("Consider comparing multiple effect size measures for discrete data.")
  }

  moments1 <- get_moments(model1, group_label = "Group 1")
  moments2 <- get_moments(model2, group_label = "Group 2")

  # Weighted pooled variance (population formula, not sample formula)
  weighted_pooled_variance <- (n1 * moments1$variance + n2 * moments2$variance) / (n1 + n2)
  pooled_sd <- sqrt(weighted_pooled_variance)
  mean_diff <- moments2$mean - moments1$mean
  
  # Handle edge cases
  if (pooled_sd == 0) {
    if (mean_diff == 0) {
      d_reg <- 0
    } else {
      d_reg <- sign(mean_diff) * Inf
      if (!silent) {
        warning("Pooled SD is zero but means differ. Returning Inf with appropriate sign.")
      }
    }
  } else {
    d_reg <- mean_diff / pooled_sd
  }

  result <- list(
    d_reg = d_reg,
    
    # Group 1 statistics
    group1_mean = moments1$mean,
    group1_variance = moments1$variance,
    group1_sd = sqrt(moments1$variance),
    
    # Group 2 statistics
    group2_mean = moments2$mean,
    group2_variance = moments2$variance,
    group2_sd = sqrt(moments2$variance),
    
    # Pooled statistics
    pooled_sd = pooled_sd,
    
    # Sample sizes
    n1 = n1,
    n2 = n2,
    
    # Models
    model1 = model1,
    model2 = model2,
    
    # Metadata
    default_degree = degree,
    tie_proportion_1 = tie1,
    tie_proportion_2 = tie2,
    n_unique_1 = n_unique1,
    n_unique_2 = n_unique2
  )

  if (!is.na(CI)) {
    
    # Standard error using asymptotic approximation
    # NOTE: This formula assumes Cohen's d distribution and may not be 
    # accurate for d_reg, especially in small samples or non-normal data
    se_dreg <- sqrt((n1 + n2) / (n1 * n2) + (d_reg^2) / (2 * (n1 + n2)))
    
    # Degrees of freedom
    df <- n1 + n2 - 2
    
    # Critical value from t-distribution
    alpha <- 1 - CI
    t_crit <- qt(1 - alpha / 2, df)
    
    # Confidence interval bounds
    ci_lower <- d_reg - t_crit * se_dreg
    ci_upper <- d_reg + t_crit * se_dreg
    
    # Add to result
    result$ci_lower <- ci_lower
    result$ci_upper <- ci_upper
    result$ci_level <- CI
    result$ci_se <- se_dreg
    result$ci_df <- df
  }

  class(result) <- "d_reg"
  return(result)
}


#' Fit a Polynomial to eCDF
#'
#' This helper function fits a polynomial regression model to represent the
#' distribution. It models the relationship between
#' z-scores and observed raw scores.
#'
#' @param x A numeric vector of observations.
#' @param poly_degree The degree of the polynomial to fit.
#' @param check_monotonicity Logical; should monotonicity be enforced by 
#'   reducing polynomial degree if needed? (default = FALSE for speed)
#' @param min_degree Minimum polynomial degree to try (default = 1, representing
#'   a linear fit to a normal distribution).
#'
#' @return An lm model object representing x = f(z), where z ~ N(0,1).
#'   Additional attributes:
#'   \describe{
#'     \item{sample_size}{Original sample size}
#'     \item{n_unique}{Number of unique values (for tie detection)}
#'     \item{tie_proportion}{Proportion of tied observations}
#'     \item{poly_degree}{Actual polynomial degree used (may be reduced)}
#'     \item{monotonic}{Logical; is the fitted function monotonic?}
#'     \item{degree_reduced}{Logical; was degree reduced from requested?}
#'   }
#'
#' @details
#' The function uses average ranks (midrank method) to handle tied observations,
#' which is the standard approach in rank-based statistics. Plotting positions 
#' (rank - 0.5)/n avoid infinite z-scores at boundaries.
#'
#' When substantial ties are present (>10% of observations), the function may
#' automatically reduce the polynomial degree to avoid overfitting to a small
#' number of unique values.
#'
#' If check_monotonicity=TRUE, the function iteratively reduces the polynomial
#' degree until a monotonic fit is achieved or min_degree is reached.
#'
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' Licensed under the MIT License
#'
#' Citation:
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen’s d.
#'
#' @export
fit_polynomial <- function(x, poly_degree, 
                                  check_monotonicity = TRUE,
                                  min_degree = 1) {
  
  # Step 1: Input validation and tie detection
  n <- length(x)
  
  if (n < 3) {
    stop("Need at least 3 observations to fit a polynomial.")
  }
  
  # Count unique values to detect ties
  n_unique <- length(unique(x))
  tie_proportion <- 1 - (n_unique / n)
  
  # Step 2: Adjust polynomial degree based on unique values
  # Can't fit more parameters than unique data points
  max_possible_degree <- n_unique - 1
  
  if (poly_degree > max_possible_degree) {
    warning(sprintf(
      "Requested polynomial degree (%d) exceeds number of unique values (%d). ",
      poly_degree, n_unique,
      "Reducing to degree %d."
    ), max_possible_degree)
    poly_degree <- max_possible_degree
  }
  
  # Additional reduction for substantial ties
  if (tie_proportion > 0.3 && poly_degree > 3) {
    # With >30% ties, be more conservative
    recommended_degree <- min(poly_degree, max(3, floor(n_unique / 2)))
    if (recommended_degree < poly_degree) {
      warning(sprintf(
        "High proportion of ties (%.1f%%). Reducing polynomial degree from %d to %d for stability.",
        tie_proportion * 100, poly_degree, recommended_degree
      ))
      poly_degree <- recommended_degree
    }
  }
  
  # Ensure we stay above minimum
  if (poly_degree < min_degree) {
    stop(sprintf(
      "Insufficient unique values (%d) to fit minimum polynomial degree (%d). ",
      n_unique, min_degree,
      "Need at least %d unique observations."
    ), min_degree + 1)
  }
  
  # Step 3: Compute ranks and z-scores (handles ties via midrank)
  # Average ranks handle ties by assigning mean rank to tied observations
  avg_ranks <- rank(x, ties.method = "average")
  
  # Convert ranks to plotting positions
  p <- (avg_ranks - 0.5) / n
  
  # Transform to standard normal quantiles
  z <- qnorm(p)
  
  # Step 4: Fit polynomial, with optional monotonicity enforcement
  check_range <- range(z)
  
  current_degree <- poly_degree
  degree_reduced <- FALSE
  monotonic <- FALSE
  
  if (check_monotonicity) {
    while (current_degree >= min_degree) {
      
      model <- lm(x ~ poly(z, current_degree, raw = TRUE))
      check <- check_monotonicity(model, z_range = check_range)
      
      if (check$is_monotonic) {
        monotonic <- TRUE
        break
      }
      
      # Reduce degree and try again
      current_degree <- current_degree - 1
      degree_reduced <- TRUE
    }
    
    # Emergency fallback
    if (current_degree < min_degree) {
      current_degree <- min_degree
      # Fit linear even if non-monotonic (rare/impossible for degree 1 unless negative correlation)
      model <- lm(x ~ poly(z, current_degree, raw = TRUE))
      check <- check_monotonicity(model, z_range = check_range)
      monotonic <- check$is_monotonic
    }
    
  } else {
    model <- lm(x ~ poly(z, current_degree, raw = TRUE))
    check <- check_monotonicity(model, z_range = check_range)
    monotonic <- check$is_monotonic
  }
  
  # Metadata
  attr(model, "sample_size") <- n
  attr(model, "n_unique") <- n_unique              # ADD THIS
  attr(model, "tie_proportion") <- tie_proportion  # ADD THIS
  attr(model, "poly_degree") <- current_degree
  attr(model, "monotonic") <- monotonic
  attr(model, "min_derivative") <- check$min_derivative

  return(model)
}



#' Check Monotonicity of Fitted Quantile Function
#'
#' Analytically checks if a polynomial quantile function is monotonic 
#' within the observed range of the data.
#'
#' @param model An lm model object fitted with poly(..., raw=TRUE).
#' @param z_range A numeric vector of length 2 defining the range [min, max]
#'   over which to check monotonicity. If NULL, checks reasonable defaults 
#'   based on N (-4 to 4).
#' @param strictly_positive Logical; if TRUE, derivative must be > 0 (strict).
#'   If FALSE, derivative can be >= 0 (allows flat regions).
#'
#' @return A list containing:
#'   \item{is_monotonic}{Logical; TRUE if monotonic in range.}
#'   \item{min_derivative}{The lowest slope found in the range.}
#'   \item{location_min}{The z-value where the minimum slope occurs.}
#'
#'
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' Licensed under the MIT License
#'
#' Citation:
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen’s d.
#'   
#' @export
check_monotonicity <- function(model, z_range = c(-4, 4), 
                                        strictly_positive = FALSE) {
  
  # Input handling
  if (!inherits(model, "lm")) stop("model must be an lm object")
  if (length(z_range) != 2 || z_range[1] >= z_range[2]) {
    stop("z_range must be a vector [min, max] with min < max")
  }
  
  # Extract polynomial coefficients
  coeffs <- coef(model)
  
  # Handle NAs (rare cases where regression had failed)
  if (any(is.na(coeffs))) return(list(
    is_monotonic = FALSE, 
    min_derivative = -Inf,
    location_min = NA
  ))
  
  degree <- length(coeffs) - 1
  
  # Special cases for low-degree polynomials
  if (degree == 0) {
    # CASE: Constant (Degree 0)
    return(list(
      is_monotonic = TRUE,
      min_derivative = 0,
      location_min = 0
    ))
  } else if (degree == 1) {
    # CASE: Linear (Degree 1)
    # f(z) = b0 + b1*z -> f'(z) = b1
    slope <- coeffs[2]
    return(list(
      is_monotonic = if(strictly_positive) slope > 0 else slope >= 0,
      min_derivative = slope,
      location_min = 0
    ))
  }
  
  # 1. Calculate coefficients of First Derivative f'(z)
  # f(z)  = c0 + c1*z + c2*z^2 + c3*z^3 ...
  # f'(z) = c1 + 2*c2*z + 3*c3*z^2 ...
  deriv1_coeffs <- numeric(degree) # Degree drops by 1
  for (i in 1:degree) {
    # Coeff index i+1 corresponds to power z^i in original model
    deriv1_coeffs[i] <- coeffs[i + 1] * i 
  }
  
  # Define function to evaluate slope at specific z values
  eval_deriv <- function(z, coefs) {
    # Horner's method
    val <- coefs[length(coefs)]
    if (length(coefs) > 1) {
      for (i in (length(coefs)-1):1) {
        val <- val * z + coefs[i]
      }
    }
    return(val)
  }
  
  # 2. Find Critical Points of the Derivative
  # To find where slope is minimized, we look for roots of f''(z)
  
  # Coefficients of f''(z)
  degree_d1 <- degree - 1
  if (degree_d1 >= 1) {
    deriv2_coeffs <- numeric(degree_d1)
    for (i in 1:degree_d1) {
      deriv2_coeffs[i] <- deriv1_coeffs[i + 1] * i
    }
    
    # Find roots (complex) of f''(z)
    roots_complex <- polyroot(deriv2_coeffs)
    
    # Filter for real roots within the z_range
    # Keep if imaginary part is negligible
    real_indices <- abs(Im(roots_complex)) < 1e-9
    roots_real <- Re(roots_complex)[real_indices]
    
    # Filter roots strictly inside our check range
    critical_z <- roots_real[roots_real >= z_range[1] & roots_real <= z_range[2]]
    
  } else {
    # If derivative is constant (should be handled by degree=1 check above)
    critical_z <- numeric(0)
  }
  
  # 3. Check Constraints (Boundaries + Critical Points)
  # The minimum slope MUST occur either at endpoints or at a local extremum
  
  check_points <- unique(c(z_range[1], z_range[2], critical_z))
  slopes <- sapply(check_points, eval_deriv, coefs = deriv1_coeffs)
  
  min_slope <- min(slopes)
  loc_min <- check_points[which.min(slopes)]
  
  threshold <- if(strictly_positive) 1e-9 else -1e-9
  
  return(list(
    is_monotonic = min_slope >= threshold,
    min_derivative = min_slope,
    location_min = loc_min
  ))
}



#' Calculate Moments from a Fitted Polynomial Function
#'
#' This function computes the mean and variance of the distribution represented 
#' by a polynomial function using Iserlis (1918) theorem.
#'
#' @param model An lm model object from \code{\link{fit_quantile_function}()}.
#'   The model should represent the relationship x = f(z) where z are standard 
#'   normal quantiles and x are the observed values.
#' @param group_label Optional character string label for warning messages 
#'   (default = "Unknown"). Used to identify which group produced warnings in 
#'   multi-group comparisons.
#'
#' @return A list with elements:
#'   \item{mean}{The expected value E[X] where X = f(Z), Z ~ N(0,1).}
#'   \item{variance}{The variance Var(X) = E[X²] - (E[X])².}
#'
#'
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' Licensed under the MIT License
#'
#' Citation:
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen’s d.
#'
#' @seealso 
#' \code{\link{fit_polynomial}} for fitting the polynomial model.
#' \code{\link{d.reg}} for the main effect size calculation.
#' 
#' @examples

#' # Generate sample data

#' set.seed(123)

#' x <- rnorm(50, mean = 100, sd = 15)

#' 

#' # Fit quantile function

#' n <- length(x)

#' avg_ranks <- rank(x, ties.method = "average")

#' p <- (avg_ranks - 0.5) / n

#' z <- qnorm(p)

#' model <- lm(x ~ poly(z, 5, raw = TRUE))

#' 

#' # Compute moments 

#' moments <- get_moments(model, group_label = "Test Group")

#' 

#' cat("Mean:", moments$mean, "\n")

#' cat("Variance:", moments$variance, "\n")

#' cat("SD:", sqrt(moments$variance), "\n")

#' 

#' # Compare with sample statistics

#' cat("\nSample mean:", mean(x), "\n")

#' cat("Sample variance:", var(x), "\n")

#' 

#' 

#'

#' @export
get_moments <- function(model, group_label = "Unknown") {
  
  # Extract coefficients and determine polynomial degree
  coeffs <- coef(model)
  k <- length(coeffs) - 1  # polynomial degree
  
  # Pre-compute standard normal raw moments: E[Z^j]
  # For j even: E[Z^j] = (j-1)!! = (j-1) × (j-3) × ... × 3 × 1
  # For j odd:  E[Z^j] = 0 (due to symmetry)
  
  compute_moment <- function(j) {
    if (j == 0) return(1)           # E[Z^0] = 1 (total probability)
    if (j %% 2 == 1) return(0)      # Odd moments vanish
    
    # Even moments: double factorial
    # E[Z^2] = 1, E[Z^4] = 3, E[Z^6] = 15, E[Z^8] = 105, ...
    result <- 1
    for (i in seq(j - 1, 1, by = -2)) {
      result <- result * i
    }
    return(result)
  }
  
  # We need moments up to degree 2k for computing E[X^2]
  max_moment <- 2 * k
  moments_z <- sapply(0:max_moment, compute_moment)
  
  # Compute mean: μ = E[X] = E[f(Z)] = Σ β_j E[Z^j]
  # Only even-powered terms contribute due to symmetry
  
  mu <- 0
  for (j in 0:k) {
    mu <- mu + coeffs[j + 1] * moments_z[j + 1]
  }
  
  # Compute variance: σ² = E[X²] - μ²
  # First calculate E[X²] = E[(Σ β_i Z^i)²] = Σ_i Σ_j β_i β_j E[Z^(i+j)]
  
  E_X2 <- 0
  for (i in 0:k) {
    for (j in 0:k) {
      power <- i + j
      if (power <= max_moment) {
        E_X2 <- E_X2 + coeffs[i + 1] * coeffs[j + 1] * moments_z[power + 1]
      }
    }
  }
  
  variance <- E_X2 - mu^2
  
  # Handle numerical edge cases
  if (variance < 0) {
    if (abs(variance) < 1e-10) {
      # Likely just numerical noise - round to zero
      variance <- 0
    } else {
      # Substantial negative variance indicates a real problem
      warning(
        "Variance for ", group_label, " is negative (", 
        format(variance, scientific = TRUE, digits = 3), 
        "). This indicates numerical instability in the polynomial fit. ",
        "Consider reducing the polynomial degree or checking for data issues.",
        call. = FALSE
      )
      # Set to zero to avoid downstream errors, but flag it
      variance <- 0
    }
  }
  
  return(list(
    mean = mu, 
    variance = variance
  ))
}




#' Print Method for d_reg Objects
#'
#' @param x An object of class "d_reg"
#' @param ... Additional arguments (not used)
#' 
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' Licensed under the MIT License
#'
#' Citation:
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen’s d.
#'   
#' @export
print.d_reg <- function(x, ...) {
  cat("\nDistribution-Free Effect Size (d_reg)\n")
  cat("===================================\n\n")
  cat("Effect size d_reg:", round(x$d_reg, 4), "\n")
  
  # Display CI if available
  if (!is.null(x$ci_lower)) {
    cat(sprintf("%d%% CI: [%.4f, %.4f]\n", 
                round(x$ci_level * 100), 
                x$ci_lower, 
                x$ci_upper), "\n")
  }
  
  cat("\nGroup 1: n =", x$n1, ", mean =", round(x$group1_mean, 4), 
      ", SD =", round(x$group1_sd, 4), "\n")
  cat("Group 2: n =", x$n2, ", mean =", round(x$group2_mean, 4), 
      ", SD =", round(x$group2_sd, 4), "\n")
  cat("Pooled SD:", round(x$pooled_sd, 4), "\n")
  cat("Polynomial degree:", x$default_degree, "\n")
  invisible(x)
}

#' Summary Method for d_reg Objects
#'
#' Provides detailed summary statistics and diagnostic information.
#'
#' @param object An object of class "d_reg"
#'
#' @author Wolfgang Lenhard and Alexandra Lenhard
#' Licensed under the MIT License
#'
#' Citation:
#'   Lenhard, W. & Lenhard, A. (submitted). Distribution-Free Effect Size Estimation: 
#'   A Robust Alternative to Cohen’s d.
#'   
#' @export
summary.d_reg <- function(object, ...) {
  
  cat("\n")
  cat("=======================================================\n")
  cat("  Distribution-Free Effect Size Analysis (d_reg)\n")
  cat("=======================================================\n\n")
  
  cat("Effect Size:\n")
  cat("  d_reg =", round(object$d_reg, 4), "\n")
  
  # Interpretation
  abs_d <- abs(object$d_reg)
  interpretation <- if (abs_d < 0.2) {
    "negligible"
  } else if (abs_d < 0.5) {
    "small"
  } else if (abs_d < 0.8) {
    "medium"
  } else {
    "large"
  }
  cat("  Interpretation:", interpretation, "\n\n")
  
  cat("Group 1:\n")
  cat("  Sample size:      ", object$n1, "\n")
  cat("  Mean (smoothed):  ", round(object$group1_mean, 4), "\n")
  cat("  SD (smoothed):    ", round(object$group1_sd, 4), "\n")
  cat("  Variance:         ", round(object$group1_variance, 4), "\n\n")
  
  cat("Group 2:\n")
  cat("  Sample size:      ", object$n2, "\n")
  cat("  Mean (smoothed):  ", round(object$group2_mean, 4), "\n")
  cat("  SD (smoothed):    ", round(object$group2_sd, 4), "\n")
  cat("  Variance:         ", round(object$group2_variance, 4), "\n\n")
  
  cat("Pooled Statistics:\n")
  cat("  Pooled SD:        ", round(object$pooled_sd, 4), "\n")
  cat("  Mean difference:  ", round(object$group2_mean - object$group1_mean, 4), "\n\n")
  
  cat("Model Details:\n")
  cat("  Polynomial degree:", object$default_degree, "\n")
  cat("  Model 1 R²:       ", round(summary(object$model1)$r.squared, 4), "\n")
  cat("  Model 2 R²:       ", round(summary(object$model2)$r.squared, 4), "\n\n")
  
  if(!is.null(object$ci_lower) && !is.null(object$ci_upper)) {
    cat(sprintf("Confidence Interval (%.1f%%): [%.4f, %.4f]\n\n", 
                object$ci_level * 100, 
                round(object$ci_lower, 4), 
                round(object$ci_upper, 4)))
  }
  cat("=======================================================\n\n")
  
  invisible(object)
}



# API endpoint
#* Calculate effect size from two groups
#* @param group1 Comma-separated numeric values for group 1
#* @param group2 Comma-separated numeric values for group 2
#* @param ci Confidence interval level (default 0.95)
#* @post /calculate
#* @get /calculate
function(group1 = NULL, group2 = NULL, degree = 4, ci = 0.95) {
  
  tryCatch({
    
    # Check if parameters are missing
    if (is.null(group1) || is.null(group2) || group1 == "" || group2 == "") {
      return(list(
        success = FALSE,
        error = "Missing required parameters: group1 and group2"
      ))
    }
    
    # Parse input
    x1 <- as.numeric(unlist(strsplit(as.character(group1), ",")))
    x2 <- as.numeric(unlist(strsplit(as.character(group2), ",")))
    ci_level <- as.numeric(ci)
	degree <- as.numeric(degree)
    
    # Remove any NA values from parsing
    x1 <- x1[!is.na(x1)]
    x2 <- x2[!is.na(x2)]
    
    if (length(x1) == 0 || length(x2) == 0) {
      return(list(
        success = FALSE,
        error = "Invalid input: Could not parse numeric values from input strings"
      ))
    }
    
    # Calculate effect size with CI
    result <- d.reg(x1, x2, degree, CI = ci_level, silent = TRUE)
    
    # Return clean result
    return(list(
      success = TRUE,
      d_reg = result$d_reg,
      ci_lower = result$ci_lower,
      ci_upper = result$ci_upper,
      ci_level = result$ci_level,
      group1 = list(
        n = result$n1,
        mean = result$group1_mean,
        sd = result$group1_sd,
		mean_classic = mean(x1),
		sd_classic = sd(x1)
      ),
      group2 = list(
        n = result$n2,
        mean = result$group2_mean,
        sd = result$group2_sd,
		mean_classic = mean(x2),
		sd_classic = sd(x2)
      ),
      pooled_sd = result$pooled_sd,
      degree = result$default_degree
    ))
    
  }, error = function(e) {
    return(list(
      success = FALSE,
      error = as.character(e$message)
    ))
  })
}

#* Health check endpoint
#* @get /
function() {
  return(list(
    status = "running",
    message = "Effect Size Calculator API is ready",
    endpoints = list(
      calculate = "/calculate?group1=1,2,3&group2=4,5,6"
    )
  ))
}