R/FMPMonotonicityCheck.R

In FMP: Filtered Monotonic Polynomial IRT Models

## January 27, 2016
## This function is used to determine whether the derivative of the 
## polynomial is everywhere positive. in FMP models the derivative of the polynomial
## must be positive everywhere to insure monotonicity.  
FMPMonotonicityCheck<-function(b, lower = -20, upper = 20){
  if(length(b)!=8) stop("\n\nSerious Error: b should have 8 elements\n\n")
  ## b is an 8x1 vector of FMP polynomial coefficients
  ## b0, b1, . . . b7
  DerivFMP <-  function(theta,b) {
      b[2] + 2*b[3]*theta + 3*b[4]*theta^2 + 4*b[5]*theta^3 + 5*b[6]*theta^4 +
      6*b[7]*theta^5 + 7*b[8]*theta^6
  }
  xx<-optimize(f = DerivFMP, interval = c(lower,upper), b)
  cat(paste("\nMinimum derivative of the polynomial in the interval (", lower, ",", upper,") = ", 
            xx$objective, sep=""))
  if( is.na(xx$objective) ) stop("\n\n\nSerious optimization problems occured\n\n")
  if(xx$objective < 0) cat("\nWarning: Polynomial fails the monotonicity check.\n")
  minDeriv<-xx$minimum
  invisible(minDeriv)	  
  }