cnvrtItemParam function

cnvrtItemParam

takes an item in one model's parameterisation and returns it in another parameterisation.

cnvrtItemParam(item, from = "muraki", to = "conquest", D = 1)

Arguments

• 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")

• from: a string, either "muraki" or "conquest" (default) (see 10.1177/0146621697211001). Describing the parameterisation of item

• to: a string, either "muraki" or "conquest" (default) (see 10.1177/0146621697211001). Describing the output parameterisation of the returned item parameter matrix Note that "muraki" assumes the scaling constant D = 1.7 (to give the normal ogive metric)

• 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

an m x 4 matrix of item parameters. The same dimensions as the input, item

Examples

myTheta <- 0
myDelta <- 1.5
a <- 1.5
m <- 3
itemParamX <- seq(0, m-1, 1)
itemParamD <- rep(myDelta, m)
itemParamT <- c(0, -0.5, 0.5)
itemParamA <- rep(a, m)
itemParam <- cbind(itemParamX, itemParamD, itemParamT, itemParamA)
colnames(itemParam)<- c("x", "d", "t", "a")
myItem <- cnvrtItemParam(itemParam, from = "conquest", to = "muraki")