difR (version 4.1)

trItemDiff: Transformed Item Difficulties Perpendicular Distances

Description

Computes the perpendicular distances for DIF detection with Transformed Item Difficulties (TID) approach.

Usage

trItemDiff(prop, anchor=1:nrow(prop))

Arguments

prop

numeric: a matrix with one row per subject and two columns: the first column with proportions of success in the reference group, the second column with proportions of success in the focal group.

anchor

a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See Details.

Value

• A list with four arguments:
• prop
  the value of the prop argument.
• delta
  the matrix of Delta scores, in the same format as prop.
• pars
  a vector of length two with the intercept and slope parameters of the major axis of Delta points.
• dist
  a numeric vector of perpendicular distances.

Details

This command basically computes the perpendicular distances from each Delta point to the major axis (Angoff, 1982; Angoff and Ford, 1973). It forms the basic command of difTID and is specifically designed for this call. The data are passed through the prop argument, a matrix with one row per item and two columns. The first column holds the proportions of success (correct responses) for each item in the reference group, and the second column provides the same information but for the focal group. Missing values are not allowed. Moreover, these proportions are internally constrained into the interval [0.001; 0.999] to ensure valid computation of Delta scores. The computation is made in three steps: (a) the proportions of success are transformed into Delta scores; (b) the major axis of the ellipse made by the Delta points is determined and its intercept and slope parameters are obtained; (c) the perpendicular distances (between each Delta point and the major axis) are computed. See Angoff (1982) and Angoff and Ford (1973) for further details. Option anchor sets the items which are considered as anchor items for computing the perpndicular distances. Only anchor items are used to compute the intercept and slope parameters of the major axis. anchor must hold integer values specifying the column numbers of the corresponding anchor items. It is primarily designed to perform item purification.

References

Angoff, W. H. (1982). Use of difficulty and discrimination indices for detecting item bias. In R. A. Berck (Ed.), Handbook of methods for detecting item bias (pp. 96-116). Baltimore, MD: Johns Hopkins University Press. Angoff, W. H., and Ford, S. F. (1973). Item-race interaction on a test of scholastic aptitude. Journal of Educational Measurement, 2, 95-106.

See Also

difTID, dichoDif

Examples

# Loading of the verbal data
 data(verbal)

 # Computing proportions of success
 props <- cbind(colMeans(verbal[verbal[,26]==0,1:24]),
   colMeans(verbal[verbal[,26]==1,1:24]) )

 # Perpendicular distances 
 trItemDiff(props)

 # Removing item 6 from the set of anchor items
 trItemDiff(props, anchor=c(1:5,7:24))