R/Cstar.R

In PerFit: Person Fit

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# C* (Harnisch & Linn, 1981):
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Cstar <- function(matrix, 
                  NA.method="Pairwise", Save.MatImp=FALSE, 
                  IP=NULL, IRT.PModel="2PL", Ability=NULL, Ability.PModel="ML", mu=0, sigma=1)
{
  matrix      <- as.matrix(matrix)
  N           <- dim(matrix)[1]; I <- dim(matrix)[2]
  IP.NA       <- is.null(IP); Ability.NA  <- is.null(Ability)
  # Sanity check - Data matrix adequacy:
  Sanity.dma(matrix, N, I)
  # Dealing with missing values:
  res.NA <- MissingValues(matrix, NA.method, Save.MatImp, IP, IRT.PModel, Ability, Ability.PModel, mu, sigma)
  matrix <- res.NA[[1]]
  # Sanity check - Perfect response vectors:
  part.res  <- Sanity.prv(matrix, N, I)
  NC        <- part.res$NC
  all.0s    <- part.res$all.0s
  all.1s    <- part.res$all.1s
  matrix.sv <- matrix
  matrix    <- part.res$matrix.red
  # Compute PFS:
  pi          <- colMeans(matrix.sv, na.rm = TRUE)
  pi.ord      <- sort(pi, decreasing = TRUE)
  sum.firstpi <- apply(matrix, 1, function(vec)
  {
    NA.vec <- sum(vec, na.rm = TRUE)
    sum(pi.ord[!is.na(vec)][1:NA.vec])
  })  
  pi.ordrev   <- sort(pi, decreasing = FALSE)
  sum.lastpi <- apply(matrix, 1, function(vec)
  {
    NA.vec <- sum(vec, na.rm = TRUE)
    sum(pi.ordrev[!is.na(vec)][1:NA.vec])
  })
  matrix.NAs.0 <- matrix
  matrix.NAs.0[is.na(matrix.NAs.0)] <- 0
  res.red      <- as.vector((sum.firstpi - as.vector(matrix.NAs.0 %*% pi)) / (sum.firstpi - sum.lastpi))
  # Compute final PFS vector:
  res <- final.PFS(res.red, all.0s, all.1s, N)
  # Export results:
  export.res.NP(matrix.sv, N, res, "Cstar", part.res, Ncat=2, NA.method, 
                IRT.PModel, res.NA[[2]], Ability.PModel, res.NA[[3]], IP.NA, Ability.NA, res.NA[[4]])
}