R/measure_anova.R

In vimp: Perform Inference on Algorithm-Agnostic Variable Importance

#' Estimate ANOVA decomposition-based variable importance.
#'
#' @param full fitted values from a regression function of the observed outcome
#'   on the full set of covariates.
#' @param reduced fitted values from a regression on the reduced set of observed
#'   covariates.
#' @param y the observed outcome.
#' @param full_y the observed outcome (not used, defaults to \code{NULL}).
#' @param C the indicator of coarsening (1 denotes observed, 0 denotes
#'   unobserved).
#' @param Z either \code{NULL} (if no coarsening) or a matrix-like object
#'   containing the fully observed data.
#' @param 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]).
#' @param ipc_fit_type if "external", then use \code{ipc_eif_preds}; if "SL",
#'   fit a SuperLearner to determine the correction to the efficient influence
#'   function.
#' @param ipc_eif_preds if \code{ipc_fit_type = "external"}, the fitted values
#'   from a regression of the full-data EIF on the fully observed covariates
#'   /outcome; otherwise, not used.
#' @param ipc_est_type IPC correction, either \code{"ipw"} (for classical
#'   inverse probability weighting) or \code{"aipw"} (for augmented inverse
#'   probability weighting; the default).
#' @param 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)
#' @param na.rm logical; should \code{NA}s be removed in computation?
#'   (defaults to \code{FALSE})
#' @param ... other arguments to SuperLearner, if \code{ipc_fit_type = "SL"}.
#'
#' @return 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.
#' @importFrom SuperLearner predict.SuperLearner SuperLearner
#' @export
measure_anova <- function(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 = "identity",
                          na.rm = FALSE, ...) {
    if (is.null(full_y)) {
        obs_mn_y <- mean(y, na.rm = na.rm)
    } else {
        obs_mn_y <- mean(full_y, na.rm = na.rm)
    }
    # add on if they aren't equal length
    if (length(full) < length(reduced)) {
        full <- c(full, rep(NA, length(reduced) - length(full)))
    }
    if (length(reduced) < length(full)) {
        reduced <- c(reduced, rep(NA, length(reduced) - length(full)))
    }
    # compute the EIF: if there is coarsening, do a correction
    if (!all(ipc_weights == 1)) {
        # observed full-data EIF
        obs_num <- mean(((full - reduced) ^ 2), na.rm = na.rm)
        obs_var <- measure_mse(
            fitted_values = rep(obs_mn_y, length(y)), y, na.rm = na.rm
        )
        obs_eif_num <- (2 * (y - full) * (full - reduced) +
                            (full - reduced) ^ 2 - obs_num)[C == 1]
        obs_grad <- obs_eif_num / obs_var$point_est -
            obs_num / (obs_var$point_est ^ 2) * obs_var$eif
        # if IPC EIF preds aren't entered, estimate the regression
        if (ipc_fit_type != "external") {
            ipc_eif_mod <- SuperLearner::SuperLearner(
                Y = obs_grad, X = subset(Z, C == 1, drop = FALSE),
                method = "method.CC_LS", ...
            )
            ipc_eif_preds <- SuperLearner::predict.SuperLearner(
                ipc_eif_mod, newdata = Z, onlySL = TRUE
            )$pred
        }
        weighted_obs_grad <- rep(0, length(C))
        weighted_obs_grad[C == 1] <- obs_grad * ipc_weights
        grad <- weighted_obs_grad - (C * ipc_weights - 1) * ipc_eif_preds
        num <- mean((1 * ipc_weights[C == 1]) * ((full - reduced) ^ 2),
                    na.rm = na.rm)
        denom <- mean((1 * ipc_weights[C == 1]) *
                          (y - mean(y, na.rm = na.rm)) ^ 2, na.rm = na.rm)
        obs_est <- num / denom
        if (ipc_est_type == "ipw") {
            est <- scale_est(obs_est, rep(0, length(grad)), scale = scale)
        } else {
            est <- scale_est(obs_est, grad, scale = scale)
        }
    } else {
        num <- mean((full - reduced) ^ 2, na.rm = na.rm)
        var <- measure_mse(fitted_values = rep(obs_mn_y, length(y)), y, 
                           na.rm = na.rm)
        num_eif <- 2 * (y - full) * (full - reduced) +
            (full - reduced) ^ 2 - num
        grad <- num_eif / var$point_est - num / (var$point_est ^ 2) * var$eif
        est <- num / var$point_est + mean(grad)
    }
    return(list(point_est = est, eif = grad, naive = num / var$point_est,
                ipc_eif_preds = ipc_eif_preds))
}