R/kaiser.R

In eunscho/unirel: Compute and Compare Unidimensional Reliability Coefficients

#' Obtain Kaiser-Caffrey's alpha (principal component analysis reliability)
#'
#' Kaiser-Caffrey's (1965) alpha is the principal component analysis (PCA) 
#' reliability. They presented this formula in the context of factor analysis, 
#' but Bentler (1968) showed that it was in fact PCA reliability. Armor (1974), 
#' citing Bentler (1968), referred to this formula as theta, and some studies 
#' refer to it as Armor's theta. Kaiser and Caffrey (1965) labeled this formula 
#' alpha, and people may have mistaken it for coefficient alpha. See Vehkalahti 
#' (2000) and Cho(in press) for further explanation of this formula.
#' @param data a dataframe or a matrix (unidimensional)
#' @return Kaiser-Caffrey's alpha
#' @export kaiser
#' @examples kaiser(Graham1)
#' @references Armor, D. J. (1974). Theta reliability and factor scaling. 
#' In H. L. Costner (Ed.), Sociological methodology (pp. 17-50). Jossey-Bass.
#' @references Bentler, P. M. (1968). Alpha-maximized factor analysis (alphamax)
#' : Its relation to alpha and canonical factor analysis. Psychometrika, 33(3), 
#' 335-345. 
#' @references Cho, E. (in press). Neither Cronbach's alpha nor McDonald's
#' omega: A comment on Sijtsma and Pfadt. Psychometrika.
#' @references Kaiser, H. F., & Caffrey, J. (1965). Alpha factor analysis. 
#' Psychometrika, 30(1), 1-14. 
#' @references Vehkalahti, K. (2000). Reliability of measurement scales: 
#' Tarkkonen's general method supersedes Cronbach's alpha. University of 
#' Helsinki.
#' 
kaiser <- function(data) {
  matrix <- get_cov(data)
  k <- nrow(matrix)
  first_eigen <- eigen(stats::cov2cor(matrix))$values[1]
  kaiser <- k / (k - 1) * (1 - 1 / first_eigen)
  class(kaiser) <- c("kaiser")
  return(kaiser)
}