area_between_icc  R Documentation 
This function calculates the area between two item characteristic curves (ICC) for unidimensional dichotomous IRT models.
There are two types of area calculation methods. The first one is
type = "exact"
where the exact area from negative infinity to
positive infinity between the two ICC curves will be calculated.
This method implements the approach in Raju's 1988 paper. This
method works for 'Rasch', '1PL', '2PL', '3PL' models but when the
pseudoguessing parameters of the items differ for '3PL' model, the
area will be infinity. In such cases it is advisable to use
type = "closed"
.
The area can only be calculated for 'Rasch', '1PL', '2PL', '3PL' or '4PL' models.
area_between_icc(
...,
type = c("closed", "exact"),
theta_range = c(5, 5),
signed_area = FALSE
)
... 
An 
type 
A string representing the method that will be used to calculate the area between two ICC curves. Available values are:
The default method is 
theta_range 
A numeric vector of length two with the first element
smaller than the second element. The values define the boundaries in which
the area between two ICC's will be calculated. The default value is

signed_area 
A logical value for whether the signed or unsigned area
between two curves will be calculated. When 
A matrix where the values in cells are the areas between items. The rows represent the first item and the columns represents the second item and the area of second item is subtracted from the first item when "signed" area is desired. For example, the value corresponding to the cell where row is for "Item_4" and column is for "Item_2", the value in the cell is the area of "Item_4  Item_2".
Emre Gonulates
Kim, S.H., & Cohen, A. S. (1991). A comparison of two area measures for detecting differential item functioning. Applied Psychological Measurement, 15(3), 269–278.
Raju, N. S. (1988). The area between two item characteristic curves. Psychometrika, 53(4), 495–502.
# Closed area example:
ip < generate_ip(model = c("3PL", "3PL", "3PL"))
# plot(ip) # See the ICCs
area_between_icc(ip, type = "closed")
area_between_icc(ip, type = "closed", signed_area = TRUE)
# The result is infinite because 'c' parameters are not equal
area_between_icc(ip, type = "exact")
# Exact area example:
ip < generate_ip(model = c("2PL", "2PL", "2PL"))
area_between_icc(ip, type = "exact")
area_between_icc(ip, type = "exact", signed_area = TRUE)
# The 'closed' area is very close to the 'exact' area with a wide theta range
area_between_icc(ip, type = "closed", theta_range = c(10, 10))
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