delta_method: Transform means a (co)variances using the _delta_ method

In mattansb/MSBMisc: Some functions I wrote that I find useful

Transform means a (co)variances using the delta method

Description

Transform means a (co)variances using the delta method

Usage

delta_method(..., .means, .V, return = c("means", "cov", "stddev", "cor"))

Arguments

...	Unquoted transformations. See example.
.means	A named vector of means.
.V	A covariance matrix.
return	What should be returned?

Value

A list with one of (optionally named):

• means of the transformed variables.

• cov (co) variance matrix of the the transformed variables.

• stddev standard deviations of the transformed variables (sqrt(diag(cov))).

• cor correlation matrix of the transformed variables. (cov2cor(cov))

Note

Most of this function is mostly copied from msm::deltamethod().

Examples

M <- sapply(mtcars, mean)
V <- cov(mtcars)

delta_method(
  (mpg^2) / hp,
  log_am = log1p(am),
  .means = M, .V = V,
  return = "cor"
)

# Sobel Test ----

data("mtcars")
mod.y <- lm(mpg ~ hp + cyl, mtcars[1:5, ])
mod.m <- lm(hp ~ cyl, mtcars[1:5, ])

bhat <- c(coef(mod.y), coef(mod.m))[c(2, 5)]
Vhat <- dbind(vcov(mod.y), vcov(mod.m))[c(2, 5), c(2, 5)]

res <- delta_method(
  hp * cyl,
  .means = bhat, .V = Vhat,
  return = c("means", "stddev")
)

res$means / res$stddev

# Compare:
(bhat[1] * bhat[2]) /
  sqrt(bhat[1]^2 * Vhat[2, 2] + bhat[2]^2 * Vhat[1, 1])

# Special character will give you a bad time...
m <- lm(mpg ~ factor(cyl), mtcars[1:5, ])

bhat <- coef(m)
names(bhat) <- c("cyl4", "cyl6", "cyl8")
V <- vcov(m)

delta_method(cyl4, cyl4 + cyl6, cyl4 + cyl8,
  .means = bhat,
  .V = V
)

mattansb/MSBMisc documentation built on March 22, 2023, 6:02 p.m.