Estimate ANOVA decomposition-based variable importance.

measure_anova(
  full,
  reduced,
  y,
  full_y = NULL,
  C = rep(1, length(y)),
  Z = NULL,
  ipc_weights = rep(1, length(y)),
  ipc_fit_type = "external",
  ipc_eif_preds = rep(1, length(y)),
  ipc_est_type = "aipw",
  scale = "logit",
  na.rm = FALSE,
  nuisance_estimators = NULL,
  a = NULL,
  ...
)

Arguments

full: fitted values from a regression function of the observed outcome on the full set of covariates.
reduced: fitted values from a regression on the reduced set of observed covariates.
y: the observed outcome (may be within a specified fold, for cross-fitted estimates).
full_y: the observed outcome (not used, defaults to NULL).
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 (IPC) (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 IPC 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 NAs be removed in computation? (defaults to FALSE)
nuisance_estimators: not used; for compatibility with measure_average_value.
a: not used; for compatibility with measure_average_value.
...: other arguments to SuperLearner, if ipc_fit_type = "SL".

Value

A named list of: (1) the estimated ANOVA (based on a one-step correction) of the fitted regression functions; (2) the estimated influence function; (3) the naive ANOVA estimate; and (4) the IPC EIF predictions.