R/alpha.R

In eunscho/reliacoef: Compute and Compare Unidimensional and Multidimensional Reliability Coefficients

#' Obtain coefficient alpha
#'
#' Alpha, also referred to as Cronbach's alpha or tau-equivalent reliability,
#' is the most commonly used reliability coefficient.
#'
#' History: Kuder and Richardson (1937) first developed this formula, but they
#'  did name it. At the time, it was referred to as Kuder-Richardson Formula 20.
#'  Cronbach (1951) argued that this name was strange and insisted on calling it
#'   coefficient alpha, which is now widely used.
#'
#' Interpretations: Alpha can be derived with an ANOVA approach to reliability
#' (Hoyt 1941).Alpha is lambda3, one of the six lower bound of reliability
#' (Guttman 1945). Alpha is the average of lambda4 values obtained over all
#' possible split-halves (Cronbach 1951). Alpha equals  reliability
#'  if the x meets the condition of being essentially tau-equivalent (Novick
#'  & Lewis, 1967). Alpha is mu0, the first in Ten Berge and
#'  Socan's (1978) series of reliability coefficients.
#'
#'  Accuracy: Alpha is found to be inferior in several studies examining the
#'  accuracy of the reliability coefficients (Cho and Kim 2015). Alpha can
#'  produce negative reliability estimates and is sensitive to the violation of
#'  the assumption of essential tau-equivalence (Cho in press).
#'
#' @param x a dataframe or a matrix (unidimensional)
#' @param print If TRUE, the result is printed to the screen.
#' @return coefficient alpha reliability estimate
#' @export alpha
#' @examples alpha(Graham1)
#' @references Cho, E. (in press). Neither Cronbach's alpha nor McDonald's
#' omega: A comment on Sijtsma and Pfadt. Psychometrika.
#' @references Cho, E., & Kim, S. (2015). Cronbach's coefficient alpha: Well
#' known but poorly understood. Organizational Research Methods, 18(2), 207-230.
#' @references Cronbach, L. J. (1951). Coefficient alpha and the internal
#' structure of tests. Psychometrika, 16(3), 297-334
#' @references Guttman, L. (1945). A basis for analyzing test-retest reliability.
#'  Psychometrika, 10(4), 255-282.
#' @references Hoyt, C. (1941). Test reliability estimated by analysis of
#' variance. Psychometrika, 6(3), 153-160.
#' @references Kuder, G. F., & Richardson, M. W. (1937). The theory of the
#' estimation of test reliability. Psychometrika, 2(3), 151-160.
#' @references Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the
#' reliability of composite measurements. Psychometrika, 32(1), 1-13.
#' @references Ten Berge, J. M. F., & Zegers, F. E. (1978). A series of lower
#' bounds to the reliability of a test. Psychometrika, 43(4), 575-579.
#' @seealso [mu0()] alpha equals mu0
#' @seealso [psych::alpha()] for a related function of the package psych
#' @seealso [Lamdbda4::lambda3()] for a related function of the package Lambda4
#' @seealso [MBESS::ci.reliability()] for a related function of the package MBESS
#'
alpha <- function(x, print = TRUE) {
  m <- get_cov(x)
  n <- nrow(m)/(nrow(m) - 1)
  off <- m
  diag(off) <- 0
  out <- n * sum(off)/sum(m)
  if (print) {
    cat("coefficient alpha (tau-equivalent reliability, mu0)               ", out,
        "\n")
  }
  invisible(out)
}