R/alpha_functions.R

In jbullock35/Bullock: Tools for table-making and miscellaneous helper utilities

#' Compute Cronbach's alpha
#' 
#' \code{alpha_cronbach()} takes a covariance matrix of data, \code{S}, 
#' that has been created from a matrix in which each column represents a 
#' variable. It returns Cronbach's alpha for the battery. It is not 
#' exported, but it is called by \linkInt{reliability}.
#' 
#' @author Joseph F. Lucke
#' 
#' @param S Covariance matrix generated by \code{var()}.
#' 
#' @return 
#' The return value is a number (double): the estimated value of Cronbach's 
#' alpha.
alpha_cronbach <- function(S) {
  d <- dim(S)[1]
  (d/(d - 1)) * (1 - sum(diag(S))/sum(S))
}


#' Compute and report Cronbach's alpha
#' 
#' Given a matrix \code{x} in which every column represents a variable,
#' this function reports (a) the estimated reliability (Cronbach's alpha) 
#' for the battery of \code{n} variables, and (b) the estimated reliability 
#' for each possible combination of \code{n - 1} variables. If \code{x} 
#' contains missing values, listwise deletion will be done via 
#' \code{na.omit(x)} so that alpha can be calculated.
#' 
#' @author Peter Ellis
#' @author John G. Bullock
#' 
#' 
#' @param x Matrix of numbers
#' @param ... additional arguments passed to \code{var()}
#' 
#' @return The function prints output to the screen and invisibly returns a list with five elements:
#' * \code{nrowBeforeListwiseDeletion} is the number of rows of \code{x}.
#' * \code{nrowAfterListwiseDeletion} is the number of rows of \code{x} after listwise deletion.
#' * \code{alpha} is Cronbach's alpha for \code{x} after listwise deletion.
#' * \code{alphaSmall} is a vector of \code{ncol(x)} numbers. It shows what Cronbach's alpha is when we remove one variable at a time from \code{na.omit(x)}.
#' * \code{alphaSmallAfterListwiseDeletion} is a vector of \code{ncol(x)} numbers. It shows what Cronbach's alpha is when we remove one variable at a time from \code{x} and then use listwise deletion on the new matrix.
#' @md 
#' 
#' @examples 
#' data(iris)
#' reliability(iris[, 1:4])
#' 
#' @importFrom stats na.omit
#' @export 
reliability <- function(x, ...) {
  xSmall   <- na.omit(x)
  j        <- dim(xSmall)[2]
  out      <- numeric(j)
  outSmall <- numeric(j)
  
  alpha <- alpha_cronbach(var(xSmall, ...))
  
  for (i in 1:j){
    out[i] <- alpha_cronbach(var(xSmall[ , -i], ...))
    
    xSmallListwise <- na.omit(x[, -i])
    outSmall[i]    <- alpha_cronbach(var(xSmallListwise, ...))
  }

  cat("nrow before listwise deletion:", nrow(x), "\n")
  cat("nrow after listwise deletion: ", nrow(xSmall), "\n")
  cat("Cronbach's alpha:", alpha, "\n")
  cat("Cronbach's alpha if one var. deleted, with this matrix:                        ", out, "\n")
  cat("Cronbach's alpha if one var. deleted, with listwise deletion on the new matrix:", outSmall, "\n")
  
  reliabilityList <- list(
    nrowBeforeListwiseDeletion = nrow(x),
    nrowAfterListwiseDeletion  = nrow(xSmall),
    alpha = alpha,
    alphaSmall = out,
    alphaSmallAfterListwiseDeletion = outSmall
  )
  
}