vim: Nonparametric Intrinsic Variable Importance Estimates and...
In bdwilliamson/nova: Perform Inference on Algorithm-Agnostic Variable Importance

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vim	R Documentation

Nonparametric Intrinsic Variable Importance Estimates and Inference

Description

Compute estimates of and confidence intervals for nonparametric intrinsic variable importance based on the population-level contrast between the oracle predictiveness using the feature(s) of interest versus not.

Usage

vim(
  Y = NULL,
  X = NULL,
  f1 = NULL,
  f2 = NULL,
  indx = 1,
  type = "r_squared",
  run_regression = TRUE,
  SL.library = c("SL.glmnet", "SL.xgboost", "SL.mean"),
  alpha = 0.05,
  delta = 0,
  scale = "identity",
  na.rm = FALSE,
  sample_splitting = TRUE,
  sample_splitting_folds = NULL,
  final_point_estimate = "split",
  stratified = FALSE,
  C = rep(1, length(Y)),
  Z = NULL,
  ipc_scale = "identity",
  ipc_weights = rep(1, length(Y)),
  ipc_est_type = "aipw",
  scale_est = TRUE,
  nuisance_estimators_full = NULL,
  nuisance_estimators_reduced = NULL,
  exposure_name = NULL,
  bootstrap = FALSE,
  b = 1000,
  boot_interval_type = "perc",
  clustered = FALSE,
  cluster_id = rep(NA, length(Y)),
  ...
)

Arguments

`Y`	the outcome.
`X`	the covariates. If `type = "average_value"`, then the exposure variable should be part of `X`, with its name provided in `exposure_name`.
`f1`	the fitted values from a flexible estimation technique regressing Y on X. A vector of the same length as `Y`; if sample-splitting is desired, then the value of `f1` at each position should be the result of predicting from a model trained without that observation.
`f2`	the fitted values from a flexible estimation technique regressing either (a) `f1` or (b) Y on X withholding the columns in `indx`. A vector of the same length as `Y`; if sample-splitting is desired, then the value of `f2` at each position should be the result of predicting from a model trained without that observation.
`indx`	the indices of the covariate(s) to calculate variable importance for; defaults to 1.
`type`	the type of importance to compute; defaults to `r_squared`, but other supported options are `auc`, `accuracy`, `deviance`, and `anova`.
`run_regression`	if outcome Y and covariates X are passed to `vimp_accuracy`, and `run_regression` is `TRUE`, then Super Learner will be used; otherwise, variable importance will be computed using the inputted fitted values.
`SL.library`	a character vector of learners to pass to `SuperLearner`, if `f1` and `f2` are Y and X, respectively. Defaults to `SL.glmnet`, `SL.xgboost`, and `SL.mean`.
`alpha`	the level to compute the confidence interval at. Defaults to 0.05, corresponding to a 95% confidence interval.
`delta`	the value of the `\delta`-null (i.e., testing if importance < `\delta`); defaults to 0.
`scale`	should CIs be computed on original ("identity") or another scale? (options are "log" and "logit")
`na.rm`	should we remove NAs in the outcome and fitted values in computation? (defaults to `FALSE`)
`sample_splitting`	should we use sample-splitting to estimate the full and reduced predictiveness? Defaults to `TRUE`, since inferences made using `sample_splitting = FALSE` will be invalid for variables with truly zero importance.
`sample_splitting_folds`	the folds used for sample-splitting; these identify the observations that should be used to evaluate predictiveness based on the full and reduced sets of covariates, respectively. Only used if `run_regression = FALSE`.
`final_point_estimate`	if sample splitting is used, should the final point estimates be based on only the sample-split folds used for inference (`"split"`, the default), or should they instead be based on the full dataset (`"full"`) or the average across the point estimates from each sample split (`"average"`)? All three options result in valid point estimates – sample-splitting is only required for valid inference.
`stratified`	if run_regression = TRUE, then should the generated folds be stratified based on the outcome (helps to ensure class balance across cross-validation folds)
`C`	the indicator of coarsening (1 denotes observed, 0 denotes unobserved).
`Z`	either (i) NULL (the default, in which case the argument `C` above must be all ones), or (ii) a character vector specifying the variable(s) among Y and X that are thought to play a role in the coarsening mechanism. To specify the outcome, use `"Y"`; to specify covariates, use a character number corresponding to the desired position in X (e.g., `"1"`).
`ipc_scale`	what scale should the inverse probability weight correction be applied on (if any)? Defaults to "identity". (other options are "log" and "logit")
`ipc_weights`	weights for the computed influence curve (i.e., inverse probability weights for coarsened-at-random settings). Assumed to be already inverted (i.e., ipc_weights = 1 / [estimated probability weights]).
`ipc_est_type`	the type of procedure used for coarsened-at-random settings; options are "ipw" (for inverse probability weighting) or "aipw" (for augmented inverse probability weighting). Only used if `C` is not all equal to 1.
`scale_est`	should the point estimate be scaled to be greater than or equal to 0? Defaults to `TRUE`.
`nuisance_estimators_full`	(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.
`nuisance_estimators_reduced`	(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.
`exposure_name`	(only used if `type = "average_value"`) the name of the exposure of interest; binary, with 1 indicating presence of the exposure and 0 indicating absence of the exposure.
`bootstrap`	should bootstrap-based standard error estimates be computed? Defaults to `FALSE` (and currently may only be used if `sample_splitting = FALSE`).
`b`	the number of bootstrap replicates (only used if `bootstrap = TRUE` and `sample_splitting = FALSE`); defaults to 1000.
`boot_interval_type`	the type of bootstrap interval (one of `"norm"`, `"basic"`, `"stud"`, `"perc"`, or `"bca"`, as in `boot{boot.ci}`) if requested. Defaults to `"perc"`.
`clustered`	should the bootstrap resamples be performed on clusters rather than individual observations? Defaults to `FALSE`.
`cluster_id`	vector of the same length as `Y` giving the cluster IDs used for the clustered bootstrap, if `clustered` is `TRUE`.
`...`	other arguments to the estimation tool, see "See also".

Details

We define the population variable importance measure (VIM) for the group of features (or single feature) s with respect to the predictiveness measure V by

\psi_{0,s} := V(f_0, P_0) - V(f_{0,s}, P_0),

where f_0 is the population predictiveness maximizing function, f_{0,s} is the population predictiveness maximizing function that is only allowed to access the features with index not in s, and P_0 is the true data-generating distribution. VIM estimates are obtained by obtaining estimators f_n and f_{n,s} of f_0 and f_{0,s}, respectively; obtaining an estimator P_n of P_0; and finally, setting \psi_{n,s} := V(f_n, P_n) - V(f_{n,s}, P_n).

In the interest of transparency, we return most of the calculations within the vim object. This results in a list including:

s: the column(s) to calculate variable importance for
SL.library: the library of learners passed to SuperLearner
type: the type of risk-based variable importance measured
full_fit: the fitted values of the chosen method fit to the full data
red_fit: the fitted values of the chosen method fit to the reduced data
est: the estimated variable importance
naive: the naive estimator of variable importance (only used if type = "anova")
eif: the estimated efficient influence function
eif_full: the estimated efficient influence function for the full regression
eif_reduced: the estimated efficient influence function for the reduced regression
se: the standard error for the estimated variable importance
ci: the (1-\alpha) \times 100% confidence interval for the variable importance estimate
test: a decision to either reject (TRUE) or not reject (FALSE) the null hypothesis, based on a conservative test
p_value: a p-value based on the same test as test
full_mod: the object returned by the estimation procedure for the full data regression (if applicable)
red_mod: the object returned by the estimation procedure for the reduced data regression (if applicable)
alpha: the level, for confidence interval calculation
sample_splitting_folds: the folds used for sample-splitting (used for hypothesis testing)
y: the outcome
ipc_weights: the weights
cluster_id: the cluster IDs
mat: a tibble with the estimate, SE, CI, hypothesis testing decision, and p-value

Value

An object of classes vim and the type of risk-based measure. See Details for more information.

Examples

# generate the data
# generate X
p <- 2
n <- 100
x <- data.frame(replicate(p, stats::runif(n, -1, 1)))

# apply the function to the x's
f <- function(x) 0.5 + 0.3*x[1] + 0.2*x[2]
smooth <- apply(x, 1, function(z) f(z))

# generate Y ~ Bernoulli (smooth)
y <- matrix(rbinom(n, size = 1, prob = smooth))

# set up a library for SuperLearner; note simple library for speed
library("SuperLearner")
learners <- c("SL.glm")

# using Y and X; use class-balanced folds
est_1 <- vim(y, x, indx = 2, type = "accuracy",
           alpha = 0.05, run_regression = TRUE,
           SL.library = learners, cvControl = list(V = 2),
           stratified = TRUE)

# using pre-computed fitted values
set.seed(4747)
V <- 2
full_fit <- SuperLearner::CV.SuperLearner(Y = y, X = x,
                                          SL.library = learners,
                                          cvControl = list(V = 2),
                                          innerCvControl = list(list(V = V)))
full_fitted <- SuperLearner::predict.SuperLearner(full_fit)$pred
# fit the data with only X1
reduced_fit <- SuperLearner::CV.SuperLearner(Y = full_fitted,
                                             X = x[, -2, drop = FALSE],
                                             SL.library = learners,
                                             cvControl = list(V = 2, validRows = full_fit$folds),
                                             innerCvControl = list(list(V = V)))
reduced_fitted <- SuperLearner::predict.SuperLearner(reduced_fit)$pred

est_2 <- vim(Y = y, f1 = full_fitted, f2 = reduced_fitted,
            indx = 2, run_regression = FALSE, alpha = 0.05,
            stratified = TRUE, type = "accuracy",
            sample_splitting_folds = get_cv_sl_folds(full_fit$folds))

bdwilliamson/nova documentation built on Feb. 1, 2024, 10:04 p.m.