equateIRT (version 2.5.1)

score: Scoring

Description

Relates number-correct scores on two forms.

Usage

score(obj, ...)
# S3 method for eqc
score(obj, method = "TSE", D = 1, scores = NULL, se = TRUE, nq = 30, 
  w = 0.5, theta = NULL, weights = NULL, anchor.type = "internal", ...)
# S3 method for eqclist
score(obj, link = NULL, method = "TSE", D = 1, scores = NULL, se = TRUE, nq = 30, 
  w = 0.5, theta = NULL, weights = NULL, anchor.type = "internal", ...)
# S3 method for ceqc
score(obj, method = "TSE", D = 1, scores = NULL, se = TRUE, nq = 30, 
  w = 0.5, theta = NULL, weights = NULL, anchor.type = "internal", ...)
# S3 method for ceqclist
score(obj, path = NULL, method = "TSE", D = 1, scores = NULL, se = TRUE, nq = 30, 
  w = 0.5, theta = NULL, weights = NULL, anchor.type = "internal", ...)
# S3 method for meqc
score(obj, link = NULL, method = "TSE", D = 1, scores = NULL, se = TRUE, 
  bistype = NULL, nq = 30, w = 0.5, theta = NULL, weights = NULL, 
  anchor.type = "internal", ...)

Value

A data frame containing theta values (only for true score equating), scores in the form chosen as base, equated scores, and standard errors of equated scores.

Arguments

obj

output object from functions direc, alldirec, chainec or bisectorec.

link

a character string with the names of the two forms being linked separated by a dot (e.g. "test1.test3"). Necessary if obj is output of functions alldirec or bisectorec.

path

a character string with the names of the forms that constitute the path separated by a dot (e.g. "test1.test2.test3"). Necessary if obj is output of function chainec.

method

the scoring method to be used. This should be one of "TSE" (the default) for true score equating or "OSE" for observed score equating.

D

constant D of the IRT model used to estimate item parameters.

scores

integer values to be converted.

se

logical; is TRUE standard errors of equated scores are computed.

bistype

bisector type. It should be specified when obj is an output object from function bisectorec. It should be weighted or unweighted. It can be NULL if only one type was computed by function bisectorec.

nq

number of quadrature points used to approximate integrals with observed score equating. Used only if arguments theta and weights are NULL.

w

synthetic weight for population 1. It should be a number between 0 and 1.

theta

vector of ability values used to approximate integrals with observed score equating.

weights

vector of weights used to approximate integrals with observed score equating.

anchor.type

The anchor type, which can be "internal" or "external". External anchors are not implemented for bisector equating coefficients. See details.

...

further arguments passed to or from other methods.

Author

Michela Battauz

Details

If anchor.type is internal, the common items are used for computing the scores; if it is external, the common items are used for computing the equating coefficients but not for computing the scores. External anchors are not implemented for bisector equating coefficients because it is possible that all items are used as achors in one of the paths considered.

This function computes standard error of equated scores with the observed score equating method using \((\alpha_X',\alpha_{V1}',A,B)'\) for the description of \(\beta_{X2,x}(At_m+B)\), and \((\alpha_Y',\alpha_{V2}',A,B)'\) for \(\beta_{Y1,y}(t_m)\) (see Ogasawara, 2003).

References

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

Ogasawara, H. (2001). Item response theory true score equatings and their standard errors. Journal of Educational and Behavioral Statistics, 26, 31--50.

Ogasawara, H. (2003). Asymptotic standard errors of IRT observed-score equating methods. Psychometrika, 68, 193--211.

See Also

alldirec, bisectorec, chainec, direc

Examples

# the following code uses item parameter estimates previously obtained
# for examples that start from item response data see function modIRT

# two-parameter logistic model
data(est2pl)
test<-paste("test", 1:5, sep = "")
mod2pl <- modIRT(coef = est2pl$coef, var = est2pl$var, names = test, display = FALSE)
# direct equating coefficients between forms 1 and 2 using the Haebara method
l12 <- direc(mods = mod2pl, which = c(1,2), method = "Haebara")
# scoring using direct equating coefficients and the true score equating method
score(l12)
# scoring using direct equating coefficients and the observed score equating method
score(l12, method = "OSE")
# specify only scores from 10 to 15
score(l12, method = "OSE", scores = 10:15)
# external anchors and true score equating method
score(l12, anchor.type = "external")
# external anchors and observed score equating method
score(l12, method = "OSE", anchor.type = "external")

# all direct equating coefficients using the Haebara method
direclist2pl <- alldirec(mods = mod2pl, method = "Haebara")
# scoring using direct equating coefficients and the true score equating method
score(direclist2pl, link = "test1.test2")

# 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 <- paste("test", c(1,5,4), sep = "")
chainec2 <- chainec(direclist = direclist2pl, pths = pth2)
# scoring using chain equating coefficients and the true score equating method for score 12
score(chainec1, path = "test1.test2.test3.test4", scores = 12)
score(chainec2, path = "test1.test5.test4", scores = 12)
# scoring using chain equating coefficients, true score equating and external anchors
score(chainec1, path = "test1.test2.test3.test4", anchor.type = "external")
# scoring using chain equating coefficients, observed score equating and external anchors
score(chainec1, path = "test1.test2.test3.test4", method = "OSE", anchor.type = "external")


# 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)
# scoring using weighted bisector equating coefficients and the true score 
# equating method for score 12
score(allec, bistype = "weighted", link = "test1.test4", scores = 12)