Visualize the Influence of Outliers

If you’re looking at linear relationships, give this code a spin. It’ll automatically flag outliers based on 1.5*IQR and show you the fit with and without the outliers. Since the output is a ggplot, you and add to it or tweak the aesthetics of the output (see example below).

Here’s the function.

scatter_w_wo_outliers <- function(temp = filter(M, Time == "Baseline"),
                                  X = "bkkca", 
                                  Y = "Ihtk.0"){
  
  # flag outliers based on 1.5xIQR from median
  X_low  <- median(temp[[X]], na.rm = T) - (1.5 * IQR(temp[[X]], na.rm = T))
  X_high <- median(temp[[X]], na.rm = T) + (1.5 * IQR(temp[[X]], na.rm = T))
  Y_low  <- median(temp[[Y]], na.rm = T) - (1.5 * IQR(temp[[Y]], na.rm = T))
  Y_high <- median(temp[[Y]], na.rm = T) + (1.5 * IQR(temp[[Y]], na.rm = T))
  
  X_pass <- (temp[[X]] > X_low) * (temp[[X]] < X_high)
  Y_pass <- (temp[[Y]] > Y_low) * (temp[[Y]] < Y_high)

  temp$flag <- ifelse((X_pass * Y_pass) == 1, T, F)
  
  
  # Duplicate so we have dataset 1, 2 (introduces duplicates)
  temp <- rbind(temp[temp$flag == T, ], mutate(temp, flag = F))
  
  formula1 <- y ~ x
  
  plt <- ggplot(temp, aes_string(X, Y, color = "flag"))+
    geom_smooth(data = temp, method = lm, se = F, fullrange = T)+
    geom_point(data = temp)+
    geom_point(data = temp, color = "black", shape = 1)+
    geom_point(data = temp[temp$flag, ])+
    ggpmisc::stat_poly_eq(aes(label =  paste(stat(eq.label), "*" with "*", 
                                             stat(rr.label), "*", "*", 
                                             stat(f.value.label), "*", and "*",
                                             stat(p.value.label), "*"."",
                                             sep = "")),
                          formula = formula1, parse = TRUE, size = 4)+
    
    scale_color_manual(values = c("darkgray", "black"))+
    theme_bw()+
    theme(legend.position = "")
  
  return(plt)
}

Here’s a reproducible example. We’re creating a Simpson’s paradox by giving the “outliers” a negative slope and the real data a positive slope. I’ve added a red line showing the true relationship.

set.seed(45645684)
df <- data.frame(x = rnorm(30, mean = 10, sd = 4),
                 noise = runif(30, min = -2, max = 2),
                 y = NA,
                 is_outlier = rbinom(30, 1, prob = 0.2))


df$y <- ifelse(df$is_outlier, 
               -5*df$x+df$noise,
               2*df$x+df$noise)

scatter_w_wo_outliers(temp = df,
                      X = "x",
                      Y = "y")+
  geom_abline(slope = 2, intercept = 0, color = "firebrick")

2020-6-4 Daniel Here’s a related utility function. For a given column it’ll return a logical vector where outliers are FALSE.

w_in_x_iqr <- function(col_in, multiplier = 1.5){
  col_in <- as.vector(col_in)
  
  X_low  <- median(col_in, na.rm = T) - (multiplier * IQR(col_in, na.rm = T))
  X_high <- median(col_in, na.rm = T) + (multiplier * IQR(col_in, na.rm = T))
  X_pass <- (col_in > X_low) * (col_in < X_high)
  
  return(as.logical(X_pass))
}

e.g.

> mutate(M, ex = w_in_x_iqr(bkkca)) %>% select(bkkca, ex) %>% arrange(bkkca) %>% tail()

#  A tibble: 6 x 2
#   bkkca ex   
#   <dbl> <lgl>
# 1 3056. TRUE 
# 2 3222. TRUE 
# 3 3255. TRUE   # Within bounds
# 4 3552. FALSE  # Outside bounds 
# 5 3817. FALSE
# 6 6740. FALSE