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Delta method for variance of transformed parameters

Source: R/sandwich.R
delta_method.Rd

Computes the variance-covariance matrix for a transformation of parameters using the Delta Method: $$Var[g(\theta)] \approx G \Sigma G^T$$ where \(G\) is the Jacobian of \(g\) and \(\Sigma\) is the covariance matrix of \(\theta\).

Usage

delta_method(
  object,
  transform,
  covariance = NULL,
  deriv_method = "capprox",
  dx = 1e-09,
  ...
)

Arguments

object

A fitted MEstimator object, or a numeric vector of parameter estimates.

transform

Function that takes theta and returns a numeric vector.

covariance

Numeric covariance matrix (only used when object is a numeric vector).

deriv_method

Character string for the derivative method used to build the Jacobian of transform. One of "capprox" (central difference), "fapprox" (forward difference), "bapprox" (backward difference), or "exact" (forward-mode automatic differentiation). Default "capprox".

dx

Numeric step size for the finite-difference methods; ignored when deriv_method = "exact". Default 1e-9. Must be a single positive finite number, which is checked whichever deriv_method is in force. The step is absolute and is floored at the floating-point resolution of each estimate, so a large parameter magnitude cannot silently reduce it to nothing; see approx_differentiation().

...

Not used. Must be empty, so a name that is not one of the documented arguments is an error rather than silently ignored. Exact names matter here because deriv_method selects how the Jacobian is built, and a dropped misspelling would leave the default in place and return a different variance with nothing to signal the substitution.

Value

A covariance matrix for transform(theta).

Examples

fit <- m_estimate(vs ~ mpg, data = mtcars, .ee = ee_regression,
                  model = "logistic")

# Variance of the odds ratio for mpg, exponentiating the log-odds coefficient
delta_method(fit, transform = function(theta) exp(theta[2]))
#>            [,1]
#> [1,] 0.06420381

# The same variance from the estimates and covariance alone
delta_method(coef(fit), transform = function(theta) exp(theta[2]),
             covariance = vcov(fit))
#>            [,1]
#> [1,] 0.06420381