R/calc_info_trace.R

In susanne-frick/MFCblockInfo: compute block information for multidimensional forced-choice questionnaires

#' Trace of information matrix
#'
#' calculates the traits (= sum of diagonal elements) of the information matrix
#'
#' @param infos block information as returned from calc.info.block()
#' @param avg logical, average result across persons? defaults to FALSE
#' @param prior prior covariance matrix for the traits, defaults to NULL
#'
#' @return matrix of traces of information matrices, rows=persons, columns=blocks
#' @export
#'
#' @details This is the criterion of A-optimality used in computerized adaptive testing (CAT).
#' It can be used to summarize information for a block in one number, weighting all precision for all traits equally.
#' It is inversely proportional to standard errors.
#'
calc.info.trace <- function(infos, avg=F, prior = NULL) {
  if(isFALSE(is.null(prior))) {
    # invert 
    iprior <- solve(prior)
    iprior <- array(rep(iprior, each = dim(infos[[1]])[1]), dim = dim(infos[[1]]))
    infos <- lapply(infos, function(ip, p) ip + p, p = iprior)
  }
  info.trace <- do.call(rbind, lapply(infos, function(ip) apply(ip, 1, function(i) sum(diag(i)))))
  if(avg==TRUE) {
    return(colSums(info.trace))
  } else {
    return(info.trace)
  }
}