weighted_median_line function

Robust Simple Linear Regression Based on Medians

Robust simple linear regression based on medians: two methods are available: "slopes" and "product".

weighted_median_line(x, y = NULL, w, type = "slopes", na.rm = FALSE)

Arguments

• x: [numeric vector] explanatory variable.

• y: [numeric vector] response variable (default: NULL).

• w: [numeric vector] weights (same length as x).

• type: [character] "slopes" or "products"

  (default: "slopes").

• na.rm: [logical] indicating whether NA values should be removed before the computation proceeds (default: FALSE).

Details

• Overview.: Robust simple linear regression based on medians

• Type.: Two methods/ types are available. Let $m(x,w)$

   denote the weighted median of variable `x` with weights `w`:
   
   - **`type = "slopes"`:**: The slope is computed as 
  

   - **`type = "products"`:**: The slope is computed as 

Returns

A vector with two components: intercept and slope

See Also

Overview (of all implemented functions)

line, weighted_line and weighted_median_ratio

Examples

x <- c(1, 2, 4, 5)
y <- c(3, 2, 7, 4)
weighted_line(y ~ x, w = rep(1, length(x)))
weighted_median_line(y ~ x, w = rep(1, length(x)))
m <- weighted_median_line(y ~ x, w = rep(1, length(x)), type = "prod")
m
coef(m)
fitted(m)
residuals(m)

# cars data
head(cars)
with(cars, weighted_median_line(dist ~ speed, w = rep(1, length(dist))))
with(cars, weighted_median_line(dist ~ speed, w = rep(1, length(dist)),
type = "prod"))

# weighted
w <- c(rep(1,20), rep(2,20), rep(5, 10))
with(cars, weighted_median_line(dist ~ speed, w = w))
with(cars, weighted_median_line(dist ~ speed, w = w, type = "prod"))

# outlier in y
cars$dist[49] <- 360
with(cars, weighted_median_line(dist ~ speed, w = w))
with(cars, weighted_median_line(dist ~ speed, w = w, type = "prod"))

# outlier in x
data(cars)
cars$speed[49] <- 72
with(cars, weighted_median_line(dist ~ speed, w = w))
with(cars, weighted_median_line(dist ~ speed, w = w, type = "prod"))