irtreliability: Marginal and Test Reliability Coefficients with Item Response...

In irtreliability: Item Response Theory Reliability

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))

Example output

Loading required package: stats4
Loading required package: lattice

Iteration: 1, Log-Lik: -8451.768, Max-Change: 0.49027
Iteration: 2, Log-Lik: -8336.191, Max-Change: 0.25156
Iteration: 3, Log-Lik: -8312.465, Max-Change: 0.13431
Iteration: 4, Log-Lik: -8305.747, Max-Change: 0.07985
Iteration: 5, Log-Lik: -8303.312, Max-Change: 0.04955
Iteration: 6, Log-Lik: -8302.352, Max-Change: 0.02996
Iteration: 7, Log-Lik: -8301.823, Max-Change: 0.01076
Iteration: 8, Log-Lik: -8301.766, Max-Change: 0.00714
Iteration: 9, Log-Lik: -8301.743, Max-Change: 0.00473
Iteration: 10, Log-Lik: -8301.730, Max-Change: 0.00176
Iteration: 11, Log-Lik: -8301.728, Max-Change: 0.00115
Iteration: 12, Log-Lik: -8301.727, Max-Change: 0.00076
Iteration: 13, Log-Lik: -8301.727, Max-Change: 0.00034
Iteration: 14, Log-Lik: -8301.726, Max-Change: 0.00030
Iteration: 15, Log-Lik: -8301.726, Max-Change: 0.00019
Iteration: 16, Log-Lik: -8301.726, Max-Change: 0.00016
Iteration: 17, Log-Lik: -8301.726, Max-Change: 0.00014
Iteration: 18, Log-Lik: -8301.726, Max-Change: 0.00010
Iteration: 19, Log-Lik: -8301.726, Max-Change: 0.00008

Calculating information matrix...

irtreliability documentation built on May 2, 2019, 8:33 a.m.