mirt (version 1.42)

areainfo: Function to calculate the area under a selection of information curves

Description

Compute the area of a test or item information function over a definite integral range.

Usage

areainfo(
  x,
  theta_lim,
  which.items = 1:extract.mirt(x, "nitems"),
  group = NULL,
  ...
)

Value

a data.frame with the lower and upper integration range, the information area within the range (Info), the information area over the range -10 to 10 (Total.Info), proportion of total information given the integration range (Info.Proportion), and the number of items included (nitems)

Arguments

x

an object of class 'SingleGroupClass', or an object of class 'MultipleGroupClass' if a suitable group input were supplied

theta_lim

range of integration to be computed

which.items

an integer vector indicating which items to include in the expected information function. Default uses all possible items

group

group argument to pass to extract.group function. Required when the input object is a multiple-group model

...

additional arguments passed to integrate

Author

Phil Chalmers

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. tools:::Rd_expr_doi("10.18637/jss.v048.i06")

Examples

dat <- expand.table(LSAT7)
mod <- mirt(dat, 1)

areainfo(mod, c(-2,0), which.items = 1) #item 1
if (FALSE) {
areainfo(mod, c(-2,0), which.items = 1:3) #items 1 to 3
areainfo(mod, c(-2,0)) # all items (total test information)

# plot the area
area <- areainfo(mod, c(-2,0))
Theta <- matrix(seq(-3,3, length.out=1000))
info <- testinfo(mod, Theta)
plot(info ~ Theta, type = 'l')

pick <- Theta >= -2 & Theta <=0
polygon(c(-2, Theta[pick], 0), c(0, info[pick], 0), col='lightblue')
text(x = 2, y = 0.5, labels = paste("Total Information:", round(area$TotalInfo, 3),
           "\n\nInformation in (-2, 0):", round(area$Info, 3),
           paste("(", round(100 * area$Proportion, 2), "%)", sep = "")), cex = 1.2)

}