simplef function

simplef

returns expected score at a given value of theta.

simplef(theta, item, model, D)

Arguments

• theta: a scalar value of theta.

• item: an item design matrix that is of size response categories (k) by three. The three columns are:

  • column one is scoring values, usually from 0 to k.
  • column two is the delta dot parameter repeated k times (the average difficulty of the item)
  • column three is the tau (step) parameter where for k = 1, tau = 0, and for k >= 2, subsequent entries are deviations from delta dot.
  • column four is the discrimination paramter ("a")

• model: a string, either "muraki" or "conquest" (default) (see 10.1177/0146621697211001). This tells downstream functions what parameterisation has been used for the model and helps with plotting and other outputs.

• D: a number, giving the scaling constant. Default is 1 (logistic metric). Other common values are D = 1.7 (to give the normal ogive metric)

Returns

a double - the expected score at theta.

Examples

myTheta <- 0
myDelta <- 1.5
k <- 3
a <- 1
itemParamX <- seq(0, k-1, 1)
itemParamD <- rep(myDelta, k)
itemParamT <- c(0, -0.5, 0.5)
itemParamA <- rep(a, k)
itemParam <- cbind(itemParamX, itemParamD, itemParamT, itemParamA)
colnames(itemParam)<- c("x", "d", "t", "a")
myExpect <- simplef(myTheta, itemParam)