用R写了一下计算item characteristic curve和画item characteristic curve的代码代码,代码如下:
##R function for item characteristic curve calculations
icccal <- function(b, a, c) {
  if (missing(c)) c <- 0#对是否输入c进行判断,没有则赋值0
  if (missing(a)) a <- 1#对是否输入a进行判断,没有则赋值1
  theta <- seq(-3, 3, 1)
  L <- a * (theta - b)
  expnl <- exp(-L)
  opexpnl <- 1 + expnl
  P <- c + (1 - c) / opexpnl#三参数模型
  data.frame(theta, L, expnl, opexpnl, P)
}

#R function for plotting an item characteristic curve
icc <- function(b, a, c) {
  if (missing(c)) c <- 0 #对是否输入c进行判断,没有则赋值0
  if (missing(a)) a <- 1#对是否有输入a进行判断,没有则赋值1
  par(lab=c(7,3,3))
  theta <- seq(-3, 3, .1)
  P <- c + (1 - c) / (1 + exp(-a * (theta - b)))#三参数模型
  plot(theta, P, type="l", xlim=c(-3,3), ylim=c(0,1),
       xlab="Ability", ylab="Probability of Correct Response")
  thetai <- b
  pthetai <- c + (1 - c) / (1 + exp(-a * (thetai - b)))
  vliney <- seq(0, pthetai, .01)
  vlinex <- b + vliney * 0
  lines(vlinex, vliney, lty=2)
}



计算的结果如下：
> icccal(-1,1.7)
  theta    L        expnl   opexpnl          P
1    -3 -3.4 29.964100047 30.964100 0.03229546
2    -2 -1.7  5.473947392  6.473947 0.15446527
3    -1  0.0  1.000000000  2.000000 0.50000000
4     0  1.7  0.182683524  1.182684 0.84553473
5     1  3.4  0.033373270  1.033373 0.96770454
6     2  5.1  0.006096747  1.006097 0.99394020
7     3  6.8  0.001113775  1.001114 0.99888746

画图的结果如下：
> icc(-1,1.7)