STAT 305 Homework 2
Please submit an R source package file, robust_0.1.tar.gz. We’ll grade it by running
install.packages(pkgs=”robust_0.1.tar.gz”, repos=NULL, type=”source”)
require(“robust”)
example(lad)
lad
area
print.lad
coef.lad
predict.lad
and by running other tests on your code, and by reading your code.
1 Least absolute deviations regression: a lad() function
Your package will have a function lad(x, y) which takes as arguments vectors x and y and returns
an object having the (new) class “lad” and consisting of a list with these components:
coefficients, a named numeric vector of length 2 containing the coefficients (β 0, β 1) of a
linear model and having the names “(Intercept)” and “x”
fitted.values, a vector of the {y i}
residuals, a vector of the {ei = yi y i}
(The name “lad” stands for “least absolute deviations.” lad() will be a function somewhat like
lm(), which uses the usual “least squared deviations” regression.)
To find (β 0, β 1), use optim() with its (default) Nelder-Mead algorithm to minimize the sum of
absolute deviations (SAD) of data yi from predictions y i. That is, minimize
SAD(β0, β1) = SAD(β0, β1; ~x, ~y) =
n∑
i=1
|yi β0 β1xi|
over (β0, β1). Use the least squares estimates from lm() as initial values.
Test your function by running
area = read.csv(“http://www.stat.wisc.edu/~jgillett/305/2/farmLandArea.csv”
lad(x=area$land, y=area$farm)
Make your function code general–we may test it on several data sets, so don’t write any dependence
on “farmLandArea.csv” in lad().
2 Write an R package
Create a package robust containing:
the function lad(), described above
the data frame area (which should have no persisting dependence on “farmLandArea.csv”)
the method print.lad(x, …), which writes the named coefficients vector to the console
the method coef.lad(object, …), which takes a lad object object and returns its vector
of coefficients. (This will allow abline(reg) to work, where reg is a regression model object
returned by lad(), making it easy to add a lad regression line to a scatterplot. See abline
if you want more understanding of its reg parameter.)
the method predict.lad(object, new.x, …), which takes a lad object object and a
vector new.x and returns a vector containing lad’s predictions at the x values in new.x.
Each of these items should be documented so that R’s help via works for them. Document the
… parameter in each of the methods via
@param … further arguments passed to or from other methods
(This “…” parameter is necessary to pass check() without warnings, and to make our new
methods behave correctly in object oriented programming situations we didn’t discuss.)
After installing your package, when we run example(lad), it must
call your lad() function for the farmland dataset
use print() to print β 0 and β 1
make a scatterplot with the lm() line, the lad() line in a different color, and a legend
use predict() to find y for x values corresponding to the 0, 1/4, 1/2, 3/4, and 1 quantiles of
the data; add these five predictions as solid green points to the graph
Cautions: lad() should not produce a graph. Do not call print.lad(), coef.lad(), or predict.lad()
directly: use print(), abline(), and predict() on your lad object.
3 Optional (for extra credit in the form of candy)
Include test code in your package. I recommend http://r-pkgs.had.co.nz/tests.html.
Write a function base.function.most.methods() that returns a list with components base.function,
the base R generic function having the most methods, and n, the number of its methods. Hint:
See base for how to list base functions, methods for how to list the methods of a generic
function, and try for how to prevent errors produced by calling methods() on non-generic
functions from terminating your function.
