R/mice.impute.norm.nob.R

In mice: Multivariate Imputation by Chained Equations

#' Imputation by linear regression without parameter uncertainty
#'
#' Imputes univariate missing data using linear regression analysis without
#' accounting for the uncertainty of the model parameters.
#'
#' @aliases mice.impute.norm.nob norm.nob
#' @inheritParams mice.impute.pmm
#' @return Vector with imputed data, same type as \code{y}, and of length
#' \code{sum(wy)}
#' @details
#' This function creates imputations using the spread around the
#' fitted linear regression line of \code{y} given \code{x}, as
#' fitted on the observed data.
#'
#' This function is provided mainly to allow comparison between proper (e.g.,
#' as implemented in \code{mice.impute.norm} and improper (this function)
#' normal imputation methods.
#'
#' For large data, having many rows, differences between proper and improper
#' methods are small, and in those cases one may opt for speed by using
#' \code{mice.impute.norm.nob}.
#' @section Warning: The function does not incorporate the variability of the
#' regression weights, so it is not 'proper' in the sense of Rubin. For small
#' samples, variability of the imputed data is therefore underestimated.
#' @author Gerko Vink, Stef van Buuren, Karin Groothuis-Oudshoorn, 2018
#' @seealso \code{\link{mice}}, \code{\link{mice.impute.norm}}
#' @references Van Buuren, S., Groothuis-Oudshoorn, K. (2011). \code{mice}:
#' Multivariate Imputation by Chained Equations in \code{R}. \emph{Journal of
#' Statistical Software}, \bold{45}(3), 1-67.
#' \doi{10.18637/jss.v045.i03}
#'
#' Brand, J.P.L. (1999). Development, Implementation and Evaluation of Multiple
#' Imputation Strategies for the Statistical Analysis of Incomplete Data Sets.
#' Ph.D. Thesis, TNO Prevention and Health/Erasmus University Rotterdam.
#' @family univariate imputation functions
#' @keywords datagen
#' @export
mice.impute.norm.nob <- function(y, ry, x, wy = NULL, ...) {
  if (is.null(wy)) wy <- !ry
  x <- cbind(1, as.matrix(x))
  parm <- .norm.fix(y, ry, x, ...)
  x[wy, ] %*% parm$beta + rnorm(sum(wy)) * parm$sigma
}

.norm.fix <- function(y, ry, x, ...) {
  p <- estimice(x[ry, , drop = FALSE], y[ry], ...)
  sigma <- sqrt((sum(p$r^2)) / (sum(ry) - ncol(x) - 1))
  parm <- list(p$c, sigma)
  names(parm) <- c("beta", "sigma")
  parm
}