irtreliability {irtreliability}

Marginal and Test Reliability Coefficients with Item Response Theory

Description

A function to estimate marginal and test reliability from estimated item response theory models.

Usage

irtreliability(input, model, cats, relcoef = "trc", nquad = 49, SE = TRUE)

Arguments

input

An object of class SingleGroupClass from package mirt.

model

A character vector indicating the item response theory model used, options are "GPCM" and "3-PL".

cats

A numeric vector indicating the number of possible categories for each item.

relcoef

A character vector indicting which reliability coefficients to calculate, options are "mrc" for the marginal reliability coefficient and "trc" for the test reliability coefficient.

nquad

The number of Gauss-Hermite quadrature points to be used.

SE

A logical vector denoting whether the standard errors for the reliability coefficient estimates should be calculated.

Value

An S4 object of class 'relout' which includes the following slots

est

The estimated coefficient.

cov

The estimated variance.

pder

The partial derivatives of the coefficient with respect to the item parameters.

type

The type of coefficient.

Author(s)

[e-mail]

References

Andersson, B. and Xin, T. (2018). Large Sample Confidence Intervals for Item Response Theory Reliability Coefficients. Educational and Psychological Measurement, 78, 32-45.
Cheng, Y., Yuan, K.-H. and Liu, C. (2012). Comparison of reliability measures under factor analysis and item response theory. Educational and Psychological Measurement, 72, 52-67.
Green, B. F., Bock, R. D., Humphreys, L. G., Linn, R. L. and Reckase, M. D. (1984). Technical guidelines for assessing computerized adaptive tests. Journal of Educational Measurement, 21, 347-360.
Kim, S. (2012). A note on the reliability coefficients for item response model-based ability estimates. Psychometrika, 77, 153-162.
Kim, S. and Feldt, L. S. (2010). The estimation of the IRT reliability coefficient and its lower and upper bounds, with comparisons to CTT reliability statistics. Asia Pacific Education Review, 11, 179-188.

Examples

#Generate 2-PL data
set.seed(14)
akX <- runif(15, 0.5, 2)
bkX <- rnorm(15)
data2pl <- matrix(0, nrow = 1000, ncol = 15)

for(i in 1:1000){
	ability <- rnorm(1)
	data2pl[i,1:15] <- (1 / (1 + exp(-akX *(ability - bkX)))) > runif(15)
}

#Estimate the 2-PL IRT model with package mirt
library(mirt)
sim2pl <- mirt(data.frame(data2pl), 1, "gpcm", SE = TRUE)
mrc2pl <- irtreliability(sim2pl, "GPCM", rep(2, 15), relcoef = "mrc")
trc2pl <- irtreliability(sim2pl, "GPCM", rep(2, 15))