R/influence.lmw.R

In lmw: Linear Model Weights

#' Regression Diagnostics for `lmw` and `lmw_est` objects
#'
#' @description
#' `influence()` produces influence measures for `lmw` objects that
#' can be used as regression diagnostics to identify influential cases. These
#' functions produce similar outputs to [lm.influence()] but also
#' include the sample influence curve (SIC) values, which combine information
#' about the hat values, residuals, and implied regression weights.
#'
#' @details
#' `influence()` computes the hat values, (weighted) residuals, and sample
#' influence curve (SIC) values for each unit, which can be used as regression
#' diagnostics to assess influence. The weighted residuals are weighted by the
#' sampling weights (if supplied), not the implied regression weights. The SIC
#' values are computed as `SIC = (N-1) * w * r / (1 - h)`, where `N`
#' is the sample size, `w` are the units' implied regression weights,
#' `r` are the (weighted) residuals, and `h` are the hat values. SIC
#' values are scaled to have a maximum of 1. Higher values indicate greater
#' relative influence.
#'
#' @param model an `lmw` or `lmw_est` object; the output of a call to
#' [lmw()] or [lmw_est()].
#' @param outcome the name of the outcome variable. Can be supplied as a string
#' containing the name of the outcome variable or as the outcome variable
#' itself. If not supplied, the outcome variable in the `formula` supplied
#' to `lmw()`, if any, will be used.
#' @param data an optional data frame containing the outcome variable named in
#' `outcome`.
#' @param \dots ignored.
#'
#' @return A list with the following components:
#' \item{hat}{a vector containing
#' the diagonal of the hat matrix.}
#' \item{wt.res}{a vector of (weighted)
#' residuals.}
#'  \item{sic}{a vector containing the scaled SIC values.}
#'
#' @note `influence.lmw()` uses non-standard evaluation to interpret its
#' `outcome` argument. For programmers who wish to use
#' `influence.lmw()` inside other functions, an effective way to pass the
#' name of an arbitrary outcome (e.g., `y` passed as a string) is to use
#' [do.call()], for example: \preformatted{fun <- function(m, y, d) {
#' do.call("influence", list(m, y, d)) } } When using `influence.lmw()`
#' inside [lapply()] or `purrr::map` to loop over outcomes, this
#' syntax must be used as well.
#'
#' @seealso [plot.lmw()] for plotting the SIC values;
#' [lm.influence()] for influence measures for `lm` objects,
#' which do not include SIC values; [hatvalues()] for hat values for
#' `lm` objects (note that `lmw_est` objects also have a
#' `hatvalues()` method).
#'
#' @examples
#'
#' data("lalonde")
#'
#' # URI regression for ATT
#' lmw.out1 <- lmw(~ treat + age + education + race + married +
#'                      nodegree + re74 + re75,
#'                 data = lalonde, estimand = "ATT",
#'                 method = "URI", treat = "treat")
#'
#' # Influence for re78 outcome
#' infl <- influence(lmw.out1, outcome = "re78")
#' str(infl)
#'
#' # Can also be used after lmw_est():
#' lmw.est1 <- lmw_est(lmw.out1, outcome = "re78")
#' all.equal(infl,
#'           influence(lmw.est1))
#'

#' @exportS3Method influence lmw
#' @name influence.lmw
influence.lmw <- function(model, outcome, data = NULL, ...) {

  data <- get_data(data, model)

  #Get model matrix
  obj <- get_X_from_formula(model$formula, data = data, treat = model$treat,
                            method = model$method, estimand = model$estimand, target = model$target,
                            s.weights = model$s.weights, target.weights = attr(model$target, "target.weights"),
                            focal = model$focal)

  outcome <- do.call("get_outcome", list(substitute(outcome), data, model$formula,
                                         obj$X))
  outcome_name <- attr(outcome, "outcome_name")

  attributes(outcome) <- NULL

  #Fit regression model; note use lm.wfit() instead of lm() because
  #we already have the model matrix (obj$X)

  if (is.null(model$s.weights)) model$s.weights <- rep(1, length(outcome))
  if (is.null(model$base.weights)) model$base.weights <- rep(1, length(outcome))
  w <- model$s.weights * model$base.weights
  pos_w <- which(w > 0)

  if (!is.null(model$fixef)) {
    for (i in seq_len(ncol(obj$X))[-1]) {
      obj$X[pos_w,i] <- demean(obj$X[pos_w,i], model$fixef[pos_w], w[pos_w])
    }
    outcome[pos_w] <- demean(outcome[pos_w], model$fixef[pos_w], w[pos_w])
  }

  fit <- lm.wfit(x = obj$X[pos_w,,drop = FALSE],
                 y = outcome[pos_w],
                 w = w[pos_w])

  n <- nrow(obj$X)

  wr <- rep(0, n)
  wr[pos_w] <- fit$residuals * w[pos_w]

  nm <- rownames(obj$X)
  if (is.null(nm)) nm <- seq_len(n)

  lmw_hat <- hat_fast(obj$X, w)

  SIC <- (n - 1) * abs(wr * model$weights/(1 - lmw_hat))
  #Note: URI formula used; same results with MRI formula when used with MRI weights

  list(hat = setNames(lmw_hat, nm),
       wt.res = setNames(wr, nm),
       sic = setNames(SIC/max(SIC), nm))
}

#' @exportS3Method influence lmw_est
#' @rdname influence.lmw
influence.lmw_est <- function(model, ...) {

  n <- sum(model$weights > 0)

  wr <- model$residuals * model$weights

  nm <- rownames(model$model.matrix)
  if (is.null(nm)) nm <- seq_len(n)

  lmw_hat <- hatvalues(model)

  SIC <- (n - 1) * abs(wr * model$lmw.weights/(1 - lmw_hat))
  #Note: URI formula used; same results with MRI formula when used with MRI weights

  list(hat = setNames(lmw_hat, nm),
       wt.res = setNames(wr, nm),
       sic = setNames(SIC/max(SIC), nm))
}