Estimate the cross-entropy

Compute nonparametric estimate of cross-entropy.

measure_cross_entropy(
  fitted_values,
  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 = "identity",
  na.rm = FALSE,
  nuisance_estimators = NULL,
  a = NULL,
  ...
)

Arguments

fitted_values

fitted values from a regression function using the observed data (may be within a specified fold, for cross-fitted estimates).

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 cross-entropy of the fitted regression function; (2) the estimated influence function; and (3) the IPC EIF predictions.