equate function

performs Stocking-Lord Equating

Computes linear transformation constants to equate a set of GRM/GPCM item parameters to a target scale using a test characteristic curve equating procedure (Stocking & Lord, 1983)

equate(ipar.to, ipar.from, theta, model = "GRM", start.AK = c(1, 0), 
  lower.AK = c(0.5, -2), upper.AK = c(2, 2))

Arguments

• ipar.to: a data frame containing target item parameters in the following order: a, cb1, cb2,..., cb(maxCat-1)
• ipar.from: a data frame containing to-be-equated item parameters in the following order: a, cb1, cb2,..., cb(maxCat-1)
• theta: a theta grid
• model: IRT model, either "GRM" or "GPCM"
• start.AK: a vector of starting values, c(A, K) where A is a multiplicative constant and K is an additive constant
• lower.AK: a vector of lower limits, c(A, K) where A is a multiplicative constant and K is an additive constant
• upper.AK: a vector of upper limits, c(A, K) where A is a multiplicative constant and K is an additive constant

Details

Computes linear transformation constants (A and K) that equate a set of item parameters (ipar.from) to the scale defined by a target item parameters (ipar.to) by minimizing the squared difference between the test characteristic curves (Stocking & Lord, 1983). The minimization is performed by the nlminb function (in stats).

Returns

returns a vector of two elements, c(A, K) where A is a multiplicative constant and K is an additive constant

References

Stocking, M. L. & Lord, F. M. (1983). Developing a Common Metric in Item Response Theory. Applied Psychological Measurement, 7(2), 201-210.

Author(s)

Seung W. Choi choi.phd@gmail.com

Note

The item parameters are assumed to be on the theta metric (0,1). The number of category threshold parameters may differ across items but not greater than (maxCat-1).

See Also

tcc

Examples

##ipar.to is a data frame containing "target" item parameters
##ipar.from is a data frame containing "to-be-equated" item parameters
## Not run: AK <- equate(ipar.to,ipar.from)
#AK[1] contains the multiplicative constant
#AK[2] contains the additive constant