Using MAE as the error function for a linear model - r

Question

I'd like to perform linear regression, however instead of using RMSE as my error function, I'd like to use MAE (Mean Absolute Error).
Is there a package that would allow me to do this?

Answer 1

You may use caret and Metrics packages.
library(caret)
data("mtcars")
maeSummary <- function (data,
lev = NULL,
model = NULL) {
require(Metrics)
out <- mae(data$obs, data$pred)
names(out) <- "MAE"
out
}
mControl <- trainControl(summaryFunction = maeSummary)
set.seed(123)
lm_model <- train(mpg ~ wt,
data = mtcars,
method = "lm",
metric = "MAE",
maximize = FALSE,
trControl = mControl)
> lm_model$metric
[1] "MAE"

Answer 2

Probably late to the party, but here is a solution using CVXR package for optimisation.
library(CVXR)
# defining variables to be tuned during optimisation
coefficient <- Variable(1)
intercept <- Variable(1)
# defining the objective i.e. minimizing the sum af absolute differences (MAE)
objective <- Minimize(sum(abs(mtcars$disp - (mtcars$hp * coefficient) - intercept)))
# optimisation
problem <- Problem(objective)
result <- solve(problem)
# result
result$status
mae_coefficient <- result$getValue(coefficient)
mae_intercept <- result$getValue(intercept)
lm_coeff_intrc <- lm(formula = disp ~ hp, data = mtcars)$coefficients
library(tidyverse)
ggplot(mtcars, aes(hp, disp)) +
geom_point() +
geom_abline(
slope = lm_coeff_intrc["hp"],
intercept = lm_coeff_intrc["(Intercept)"],
color = "red"
) +
geom_abline(
slope = mae_coefficient,
intercept = mae_intercept,
color = "blue"
)
df <- mtcars %>%
select(disp, hp) %>%
rownames_to_column() %>%
mutate(
mae = disp - hp * mae_coefficient - mae_intercept,
lm = disp - hp * lm_coeff_intrc["hp"] - lm_coeff_intrc["(Intercept)"]
)
df %>%
select(mae, lm) %>%
pivot_longer(cols = 1:2) %>%
group_by(name) %>%
summarise(
mae = sum(abs(value))
)