R, Standard error (IRT) Plotting an inverse function -

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i following tutorial on creating information functions, completed tutorial looking take 1 more step , have been stalemated. tutorial following below.

http://www.gonulates.com/psychometrics/fishers-information-function-for-the-four-parameter-model-4pm/

irt.4pm.info <- function(theta,item.par,d=1.7) { # function calculates fisher information # 4 parameter model, given item parameters , ability. # # item.par should matrix 4 columns: # each row represents item, # first column represents parameters (item discrimination) # second column represents b parameters (item difficulty) # third column represents c parameters(pseudo-guessing parameter) # fourth column represents d parameters (upper asymptote) # theta can single number or vector.  return(t(sapply(theta,    fun = function (x) (      (d * item.par[,1])^2 * (item.par[,4] - item.par[,3])^2)/      ((item.par[,3] + item.par[,4] *        exp(d*item.par[,1] * (x - item.par[,2]))) *      (1 - item.par[,3] + (1-item.par[,4]) *        exp(d*item.par[,1] * (x-item.par[,2]))) *      (1 + exp(-d * item.par[,1] * (x - item.par[,2])))^2) ))) } theta.2 <- c(-1,-.5,0,1,2) itpars <- data.frame(a = c(1,  1,.75),                  b = c(0,-.5,  1),                  c = c(0,  0, .2),                  d = c(1,  1,.98)); itpars  ##         b   c    d ## 1 1.00  0.0 0.0 1.00 ## 2 1.00 -0.5 0.0 1.00 ## 3 0.75  1.0 0.2 0.98 theta.3 <- seq(-4,4,by=0.01) item.1.pars <- data.frame(a=1.2,b=-0.6,c=.1,d=1) plot(theta.3,irt.4pm.info(theta.3,item.1.pars),type="l",  main="information functon",  xlab="theta", ylab="information")

what looking plot inverse of function have right now. is, function looks bell curve , have inverse of function (upside down bell curve)

the curve looking make standard error reciprocal of information se = 1/i^.5 (i=information)


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