simplep function

simplep

returns response probabilities for each response category of an item at a given value of theta.

simplep(theta, item, model = "conquest", D = 1)

Arguments

• theta: a scalar value of theta.

• item: an item design matrix that is of size response categories (m) by four:

  • column one is category values, usually from 0 to m. Sometimes referred to as 'x', and in this case, this value times the discrimination is the category score.
  • column two is the delta dot parameter repeated m times (the average difficulty of the item)
  • column three is the tau (step) parameter where for the first response category (x = 0) tau = 0, and for m >= 2, entries are deviations from delta dot. In the dichotomous case, all items in this column are zero.
  • column four is the discrimination parameter ("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 k x 1 matrix of response probabilities evaluated at theta.

Examples

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