DeltaMethod: Numerical derivative version of delta method

In mirt: Multidimensional Item Response Theory

Numerical derivative version of delta method

Description

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.

Usage

DeltaMethod(fn, par, acov, ...)

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 simply fn(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

Value

returns a list of the transformed parameters, ACOV, and SEs

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])
1 / (estmean[1] + estmean[2] + estmean[3])

## 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)$se
DeltaMethod(fn2, estmean, estvar)$se

# index argument for easier flexibility
fn <- function(par, index) 1 / sum(par[index])
DeltaMethod(fn, estmean, estvar, index=1:2)$se
DeltaMethod(fn, estmean, estvar, index=1:3)$se

mirt documentation built on April 3, 2025, 11:59 p.m.