# equate: performs Stocking-Lord Equating In lordif: Logistic Ordinal Regression Differential Item Functioning using IRT

## Description

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)

## Usage

 ```1 2``` ``` 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).

## Value

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

## 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).

## Author(s)

Seung W. Choi <[email protected]>

## References

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

`tcc`

## Examples

 ```1 2 3 4 5``` ```##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 contains the multiplicative constant #AK contains the additive constant ```

### Example output

```Loading required package: mirt

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

format.pval, units