# est_predictiveness: Estimate a nonparametric predictiveness functional In bdwilliamson/npvi: Perform Inference on Algorithm-Agnostic Variable Importance

 est_predictiveness R Documentation

## Estimate a nonparametric predictiveness functional

### Description

Compute nonparametric estimates of the chosen measure of predictiveness.

### Usage

```est_predictiveness(
fitted_values,
y,
a = NULL,
full_y = NULL,
type = "r_squared",
C = rep(1, length(y)),
Z = NULL,
ipc_weights = rep(1, length(C)),
ipc_fit_type = "external",
ipc_eif_preds = rep(1, length(C)),
ipc_est_type = "aipw",
scale = "identity",
na.rm = FALSE,
nuisance_estimators = NULL,
...
)
```

### Arguments

 `fitted_values` fitted values from a regression function using the observed data. `y` the observed outcome. `a` the observed treatment assignment (may be within a specified fold, for cross-fitted estimates). Only used if `type = "average_value"`. `full_y` the observed outcome (from the entire dataset, for cross-fitted estimates). `type` which parameter are you estimating (defaults to `r_squared`, for R-squared-based variable importance)? `C` the indicator of coarsening (1 denotes observed, 0 denotes unobserved). `Z` either `NULL` (if no coarsening) or a matrix-like object containing the fully observed data. `ipc_weights` weights for inverse probability of coarsening (e.g., inverse weights from a two-phase sample) weighted estimation. Assumed to be already inverted (i.e., ipc_weights = 1 / [estimated probability weights]). `ipc_fit_type` if "external", then use `ipc_eif_preds`; if "SL", fit a SuperLearner to determine the correction to the efficient influence function. `ipc_eif_preds` if `ipc_fit_type = "external"`, the fitted values from a regression of the full-data EIF on the fully observed covariates/outcome; otherwise, not used. `ipc_est_type` IPC correction, either `"ipw"` (for classical inverse probability weighting) or `"aipw"` (for augmented inverse probability weighting; the default). `scale` if doing an IPC correction, then the scale that the correction should be computed on (e.g., "identity"; or "logit" to logit-transform, apply the correction, and back-transform). `na.rm` logical; should NA's be removed in computation? (defaults to `FALSE`) `nuisance_estimators` (only used if `type = "average_value"`) a list of nuisance function estimators on the observed data (may be within a specified fold, for cross-fitted estimates). Specifically: an estimator of the optimal treatment rule; an estimator of the propensity score under the estimated optimal treatment rule; and an estimator of the outcome regression when treatment is assigned according to the estimated optimal rule. `...` other arguments to SuperLearner, if `ipc_fit_type = "SL"`.

### Details

See the paper by Williamson, Gilbert, Simon, and Carone for more details on the mathematics behind this function and the definition of the parameter of interest.

### Value

A list, with: the estimated predictiveness; the estimated efficient influence function; and the predictions of the EIF based on inverse probability of censoring.

bdwilliamson/npvi documentation built on Feb. 13, 2023, 9:58 a.m.