Delta method using numerical derivatives
(via numerical_deriv) for the provided function.
Convenient when target transformation function is
easier to automate programmatically
instead of using explicit formula or math expressions. Can
also be useful for checking analytic results.
Arguments
- fn
a function specifying the type of transformation to make for each new parameter of interest. Must be of the form
fn(par, ...), or more simplyfn(par), and return a numeric vector with one element- par
numerical vector passed to
fn(par)(typically vector of MLEs)- acov
numeric matrix for the ACOV of the MLEs
- ...
additional arguments passed to fn
Examples
# Slightly modified example from ?msm::deltamethod
# Multiple linear regression, E(y) = alpha + beta1 x + beta2 g
x <- 1:100
g <- rep(0:1, each=50)
y <- rnorm(100, 4*x, 5)
toy.lm <- lm(y ~ x + g)
estmean <- coef(toy.lm)
estvar <- vcov(toy.lm)
# Estimate of (1 / (b0 + b1)) and (1 / (b0 + b1 + b2))
1 / (estmean[1] + estmean[2])
#> (Intercept)
#> 0.4537866
1 / (estmean[1] + estmean[2] + estmean[3])
#> (Intercept)
#> 0.8571418
## Approximate standard error (uncomment to check)
# msm::deltamethod (~ 1 / (x1 + x2), estmean, estvar)
# msm::deltamethod (~ 1 / (x1 + x2 + x3), estmean, estvar)
# with DeltaMethod
fn <- function(par) 1 / sum(par[1:2])
fn2 <- function(par) 1 / sum(par[1:3])
DeltaMethod(fn, estmean, estvar)$se
#> [1] 0.235754
DeltaMethod(fn2, estmean, estvar)$se
#> [1] 2.037618
# index argument for easier flexibility
fn <- function(par, index) 1 / sum(par[index])
DeltaMethod(fn, estmean, estvar, index=1:2)$se
#> [1] 0.235754
DeltaMethod(fn, estmean, estvar, index=1:3)$se
#> [1] 2.037618