# convert: Item Parameters Conversion In equateIRT: IRT Equating Methods

## Description

Converts item and person parameters using equating coefficients.

## Usage

 `1` ```convert(A, B, coef = NULL, person.par = NULL) ```

## Arguments

 `A` equating coefficient A. `B` equating coefficient B. `coef` vector of item parameters return by function `modIRT`. `person.par` vector of person parameters estimates.

## Details

Difficulty parameters b are converted using transformation b*A+B; discrimination parameters a are converted using transformation a/A; guessing parameters c are not transformed.

Person parameters θ are converted using transformation θ*A+B.

## Value

A list with components

 `coef` vector of item parameters transformed. `person.par` vector of person parameters transformed

Michela Battauz

## References

Battauz, M. (2015). equateIRT: An R Package for IRT Test Equating. Journal of Statistical Software, 68, 1–22.

Kolen, M.J. and Brennan, R.L. (2014). Test equating, scaling, and linking: methods and practices, 3rd ed., New York: Springer

`itm`, `modIRT`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```# conversion using direct coefficients # three-parameter logistic model # direct equating coefficients between forms 1 and 2 using the Stocking-Lord method data(est3pl) test <- paste("test", 1:5, sep = "") mod3pl <- modIRT(coef = est3pl\$coef, var = est3pl\$var, names = test, display = FALSE) l12 <- direc(mod1 = mod3pl[1], mod2 = mod3pl[2], method = "Stocking-Lord") convert(A = l12\$A, B = l12\$B, coef = coef(mod3pl\$test1)) # the conversion of item parameters is obtained also using itm(l12) # conversion using bisector coefficients # two-parameter logistic model # direct equating coefficients using the "Haebara" method data(est2pl) test <- paste("test", 1:5, sep = "") mod2pl <- modIRT(coef = est2pl\$coef, var = est2pl\$var, names = test, display = FALSE) direclist2pl <- alldirec(mods = mod2pl, method = "Haebara") # compute chain equating coefficients for path 1,2,3,4 pth1 <- paste("test", 1:4, sep = "") chainec1 <- chainec(direclist = direclist2pl, pths = pth1) # compute chain equating coefficients for path 1,5,4 pth2 <- c(paste("test", c(1,5,4), sep = "")) chainec2 <- chainec(direclist = direclist2pl, pths = pth2) # create a list of objects of class ceqc ecall <- c(chainec1, chainec2) # compute bisector and weighted bisector coefficients allec <- bisectorec(ecall = ecall, weighted = TRUE, unweighted = TRUE) summary(allec) eqc14<-eqc(allec, link = "test1.test4", path = "bisector") convert(A = eqc14\$A, B = eqc14\$B, coef = coef(mod2pl\$test1), person.par = seq(-3, 3, 0.5)) ```