geex
vignettes/v03_root_solvers.Rmd
v03_root_solvers.Rmd
rootFUN
By default, geex
uses the rootSolve::multiroot
function for finding roots of a set of estimating equations when
compute_roots = TRUE
in m_estimate()
. However,
a user can choose a different root find find algorithm via the
root_control
argument.
For example, consider the following estFUN
which is
Huber’s estimator for the center of symmetric distributions [@stefanski2002; example 6]. This example was
chosen because it has a single root, so that the
stats::uniroot
function can be used to find the roots.
myefun <- function(data, k = 1.5){
function(theta){
x <- data$Y1 - theta[1]
if(abs(x) <= k) x else sign(x) * k
}
}
Internally, estFUN
is used to build \(G_m = \sum_{i = 1}^m \psi(O_i, \theta)\) or
in psuedo-code f = sum(inner_estFUN(theta))
. f
is passed to the root finding function along with options in the
root_control
arguments. For example, multiroot
requires f
and start
(starting values for the
algorithm:
multiroot_results <- m_estimate(
estFUN = myefun,
data = geexex,
root_control = setup_root_control(start = 3))
The stats::uniroot
function, however, requires the
arguments f
and interval
(or
lower
and upper
)
uniroot_results <- m_estimate(
estFUN = myefun,
data = geexex,
root_control = setup_root_control(stats::uniroot, interval = c(0, 10)))
Comparing results:
## [1] 6.244845e-07
They are basically the same, but this may not be true depending
f
and the options given to the root finder.
All that is necessary for rootFUN
is a function
where:
rootFUN_object
argument in
m_estimate
. For example, both uniroot
and
multiroot
return a list where the root estimates are in the
item named “roots”. The default is
rootFUN_object = 'roots'
, so this option works for both
uniroot
and multiroot
.