robsurvey (version 0.1.0)

weighted_median_line: Robust simple linear regression based on medians

Description

For type medslopes the median individual ratios response/explanatory is used as estimator of the slope. For version ratiomeds the ratio of the median crossproduct to the median of squares of the explanatory variable is used as the estimator of the slope. Survey weights may be used. Missing values are neglected.

Usage

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

Arguments

x

a numeric vector (explanatory variable)

y

a numeric vector (response variable)

w

a numeric vector of weights

type

either "slopes" (default) or "products"

na.rm

a logical value indicating whether rows with NA values should be stripped before the computation proceeds

Value

a vector with two components: intercept and slope

Details

Uses weighted_median(). The median of slopes (type="slopes") uses \(b1=M((y-M(y,w))/(x-M(x,w)), w)\). The median of crossproducts by median of squares (type="products") uses \(b1=M((y-M(y,w))(x-M(x,w)), w )/ M((x-M(x,w )^2), w )\), where \(M(x, w)\) is shorthand for the function weighted_median(x, w). The function allows weights and missing values.

See Also

line, weighted_line, weighted_median_ratio

Examples

# NOT RUN {
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)))
weighted_median_line(y~x, w=rep(1, length(x)), type="prod")

data(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"))
# }