R/Pi.R

In integIRTy: Integrating Multiple Modalities of High Throughput Assays Using Item Response Theory

Pi <-function(th,it,D=1) {
  a<-it[,1]
  b<-it[,2]
  c<-it[,3]
  d<-it[,4]
  e<-exp(D*a*(th-b))
  Pi<-c+(d-c)*e/(1+e)
  Pi[Pi==0]<-1e-10
  Pi[Pi==1]<-1-1e-10
  dPi<-D*a*e*(d-c)/(1+e)^2
  d2Pi<-D^2*a^2*e*(1-e)*(d-c)/(1+e)^3
  d3Pi<-D^3*a^3*e*(d-c)*(e^2-4*e+1)/(1+e)^4
  res<-list(Pi=Pi,dPi=dPi,d2Pi=d2Pi,d3Pi=d3Pi)
  return(res)
}