R/heise.R

In eunscho/unirel: Compute and Compare Unidimensional Reliability Coefficients

#' Obtain Heise-Bohrnstedt's Omega (another factor analysis reliability)
#'
#' Heise-Bohrnstedt's (1970) Omega is an factor analysis (FA) reliability. 
#' This formula is different from the FA reliability we use today and yields a 
#' larger value (Cho, in press). McDonald (1999) referred to all FA reliability 
#' as omega, and capitalized omega was used to distinguish it from McDonald's 
#' omega.
#' @param data a dataframe or a matrix (unidimensional)
#' @return Heise-Bohrnstedt's Omega
#' @export heise
#' @examples heise(Graham1)
#' @references Cho, E. (in press). Neither Cronbach's alpha nor McDonald's
#' omega: A comment on Sijtsma and Pfadt. Psychometrika.
#' @references Heise, D. R., & Bohrnstedt, G. W. (1970). Validity, invalidity, 
#' and reliability. Sociological Methodology, 2, 104-129.
#' @references McDonald, R. P. (1999). Test theory: A unified treatment. 
#' Lawrence Erlbaum.
#' 
heise <- function(data) {
  matrix <- get_cov(data)
  k <- nrow(matrix)
  sum <- 0
  for (i in 1:k) {
    sum <- sum + diag(matrix)[i] * psych::fa(matrix, nfactors = k)$communality[i]
  }
  omega <- 1 - (sum(diag(matrix)) - sum) / sum(matrix)
  class(heise) <- c("heise")
  return(omega)

}