R/dem_parity.R

In kozodoi/Fairness: Algorithmic Fairness Metrics

#' @title Demographic parity
#'
#' @description
#' This function computes the Demographic parity metric
#' 
#' Formula: (TP + FP)
#'
#' @details
#' This function computes the Demographic parity metric (also known as Statistical Parity, Equal Parity,
#' Equal Acceptance Rate or Independence) as described by Calders and Verwer 2010. Demographic parity is calculated
#' based on the comparison of the absolute number of all positively classified individuals in all subgroups of the data. In the returned
#' named vector, the reference group will be assigned 1, while all other groups will be assigned values
#' according to whether their proportion of positively predicted observations are lower or higher compared to the reference group. Lower
#' proportions will be reflected in numbers lower than 1 in the returned named vector.
#'
#' @param data Data.frame that contains the necessary columns.
#' @param group Column name indicating the sensitive group (character).
#' @param base Base level of the sensitive group (character).
#' @param group_breaks If group is continuous (e.g., age): either a numeric vector of two or more unique cut points or a single number >= 2 giving the number of intervals into which group feature is to be cut.
#' @param outcome Column name indicating the binary outcome variable (character).
#' @param outcome_base Base level of the outcome variable (i.e., negative class). Default is the first level of the outcome variable.
#' @param probs Column name or vector with the predicted probabilities (numeric between 0 - 1). Either probs or preds need to be supplied.
#' @param preds Column name or vector with the predicted binary outcome (0 or 1). Either probs or preds need to be supplied.
#' @param cutoff Cutoff to generate predicted outcomes from predicted probabilities. Default set to 0.5.
#'
#' @name dem_parity
#'
#' @return
#' \item{Metric}{Absolute number of positive classifications for all groups and metrics standardized for the base group (demographic parity metric). Lower values compared to the reference group mean lower number of positively predicted observations in the selected subgroups}
#' \item{Metric_plot}{Bar plot of Demographic parity metric}
#' \item{Probability_plot}{Density plot of predicted probabilities per subgroup. Only plotted if probabilities are defined}
#'
#' @examples
#' data(compas)
#' compas$Two_yr_Recidivism_01 <- ifelse(compas$Two_yr_Recidivism == 'yes', 1, 0) 
#' dem_parity(data = compas, outcome = 'Two_yr_Recidivism_01', group = 'ethnicity',
#' probs = 'probability', cutoff = 0.4, base = 'Caucasian')
#' dem_parity(data = compas, outcome = 'Two_yr_Recidivism_01', group = 'ethnicity',
#' preds = 'predicted', cutoff = 0.5, base = 'Hispanic')
#'
#' @export


dem_parity <- function(data, outcome, group, 
                       probs = NULL, 
                       preds = NULL, 
                       outcome_base = NULL, 
                       cutoff = 0.5, 
                       base = NULL,
                       group_breaks = NULL) {

    # check if data is data.frame
    if (class(data)[1] != 'data.frame') {
        warning(paste0('Converting ', class(data)[1], ' to data.frame'))
        data <- as.data.frame(data)
    }
    
    # convert types, sync levels
    if (is.null(probs) & is.null(preds)) {
        stop({'Either probs or preds have to be supplied'})
    }
    if (is.null(probs)) {
        if (length(preds) == 1) {
            preds <- data[, preds]
        }
        preds_status <- as.factor(preds)
    } else {
        if (length(probs) == 1) {
            probs <- data[, probs]
        }
        preds_status         <- as.factor(as.numeric(probs > cutoff))
        levels(preds_status) <- levels(as.factor(data[, outcome]))
    }
    
    # check group feature and cut if needed
    if ((length(unique(data[, group])) > 10) & (is.null(group_breaks))) {
        warning('Number of unqiue group levels exceeds 10. Consider specifying `group_breaks`.')
    }
    if (!is.null(group_breaks)) {
        if (is.numeric(data[, group])) {
            data[, group] <- cut(data[, group], breaks = group_breaks)
        }else{
            warning('Attempting to bin a non-numeric group feature.')
        }
    }
    
    # convert to factor
    group_status   <- as.factor(data[, group])
    outcome_status <- as.factor(data[, outcome])
    
    # check levels matching
    if (!identical(levels(outcome_status), levels(preds_status))) {
        warn_preds   <- paste0(levels(preds_status),   collapse = ', ')
        warn_outcome <- paste0(levels(outcome_status), collapse = ', ')
        stop({paste0(c('Levels of predictions and outcome do not match. ',
                       'Please relevel predictions or outcome.\n',
                       'Outcome levels: ', warn_preds, '\n',
                       'Preds   levels: ', warn_outcome))})}
    
    # relevel preds & outcomes
    if (is.null(outcome_base)) {
        outcome_base <- levels(outcome_status)[1]
    }else{
        outcome_base <- as.character(outcome_base)
    }
    outcome_status   <- relevel(outcome_status, outcome_base)
    preds_status     <- relevel(preds_status,   outcome_base)
    outcome_positive <- levels(outcome_status)[2]
    
    # convert to numeric
    preds_status   <- as.numeric(preds_status) - 1
    outcome_status <- as.numeric(outcome_status) - 1

    # check lengths
    if (length(group_status) != length(preds_status)) {
        stop('Predictions/probabilities and group status must be of the same length')
    }

    # relevel group
    if (is.null(base)) {base <- levels(group_status)[1]}
    group_status <- relevel(group_status, base)

    # placeholders
    val         <- rep(NA, length(levels(group_status)))
    names(val)  <- levels(group_status)
    sample_size <- val

    # compute value for all groups
    for (i in levels(group_status)) {
        metric_i       <- sum(preds_status[group_status == i])
        val[i]         <- metric_i
        sample_size[i] <- length(preds_status[group_status == i])
    }
    
    # aggregate results
    res_table <- rbind(val, val/val[[1]], sample_size)
    rownames(res_table) <- c('Positively classified', 'Demographic Parity', 'Group size')

    # conversion of metrics to df
    val_df <- as.data.frame(res_table[2, ])
    colnames(val_df) <- c('val')
    val_df$groupst <- rownames(val_df)
    val_df$groupst <- as.factor(val_df$groupst)
    
    # relevel group
    if (is.null(base)) {
        val_df$groupst <- levels(val_df$groupst)[1]
    }
    val_df$groupst <- relevel(val_df$groupst, base)

    p <- ggplot(val_df, aes(x = groupst, weight = val, fill = groupst)) + geom_bar(alpha = 0.5) +
        coord_flip() + theme(legend.position = 'none') + labs(x = '', y = 'Demographic Parity')

    # plotting
    if (!is.null(probs)) {
        q <- ggplot(data, aes(x = probs, fill = group_status)) + geom_density(alpha = 0.5) +
            labs(x = 'Predicted probabilities') + guides(fill = guide_legend(title = '')) +
            theme(plot.title = element_text(hjust = 0.5)) + xlim(0, 1) + geom_vline(xintercept = cutoff,
            linetype = 'dashed')
    }

    if (is.null(probs)) {
        list(Metric = res_table, Metric_plot = p)
    } else {
        list(Metric = res_table, Metric_plot = p, Probability_plot = q)
    }

}