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Computes the leverage (hat values) for a RAL estimator. Used internally for HC3 standard errors.

Usage

# S3 method for class 'ral'
hatvalues(model, fit_idx = 1, ...)

Arguments

model

An object inheriting from class ral.

fit_idx

Integer index of the fit to extract leverage values for. Defaults to 1.

...

Currently unused.

Value

A numeric vector of leverage values.

Details

The leverage for observation \(i\) is

$$h_i(\theta) = -\mathrm{tr}\!\left( \frac{1}{n} \frac{\partial \phi_i(\theta)} {\partial \theta} \right).$$

The sample analog replaces \(\phi_i(\theta)\) with its estimate \(\hat\phi_i\): \(\hat{h}_i = h_i(\hat\theta).\)

The derivative \(\partial \hat\phi_i / \partial \theta\) is stored in the dinf_dtheta slot. For the specific form of this derivative in the DML context, see ddml-intro. For the leverage of linear combinations, see lincom.