discr_test: Testing item discriminations

In tcl: Testing in Conditional Likelihood Context

Testing item discriminations

Description

Computes gradient (GR), likelihood ratio (LR), Rao score (RS) and Wald (W) test of hypothesis of equal item discriminations against the alternative that at least one item discriminates differently (only for binary data).

Usage

discr_test(X)

Arguments

X	Data matrix.

Details

The tests are based on the following model suggested in Draxler, Kurz, Gürer, and Nolte (2024)

\text{logit} \big( E(Y) \big ) = \tau + \alpha + \delta (r - 1),

where E(Y) ist the expected value of a binary response (of a person to an item), r = 1, \dots, k - 1 is the person score, i.e., number of correct responses of that person when responding to k items, \tau is the respective person parameter and \alpha and \delta are two parameters referring to the respective item. The parameter \alpha represents a baseline, i.e., the easiness or attractiveness of the respective item in person score group r = 1. The parameter \delta denotes the constant change of the attractiveness of that item between successive person score groups. Thus, the model assumes a linear effect of the person score r on the logit of the probability of a correct response.

The four test statistics are derived from a conditional likelihood function in which the \tau parameters are eliminated by conditioning on the observed person scores. The hypothesis to be tested is formally given by setting all \delta parameters equal to 0. The alternative assumes that at least one \delta parameter is not equal to 0.

Value

A list of test statistics, degrees of freedom, and p-values.

test	A numeric vector of gradient (GR), likelihood ratio (LR), Rao score (RS), and Wald test statistics.
df	A numeric vector of corresponding degrees of freedom.
pvalue	A vector of corresponding p-values.
call	The matched call.

References

Draxler, C., Kurz. A., Gürer, C., & Nolte, J. P. (2024). An improved inferential procedure to evaluate item discriminations in a conditional maximum likelihood framework. Manuscript submitted for publication.

See Also

invar_test, change_test, and LLTM_test.

Examples

## Not run: 
##### Dataset PISA Mathematics data.pisaMath {sirt} #####

library(sirt)
data(data.pisaMath)
y <- data.pisaMath$data[, grep(names(data.pisaMath$data), pattern = "M" )]

res <- discr_test(X = y)
# $test
# GR     LR     RS      W
# 72.430 73.032 76.725 73.470
#
# $df
# GR LR RS  W
# 10 10 10 10
#
# $pvalue
#       GR        LR        RS         W
# "< 0.001" "< 0.001" "< 0.001" "< 0.001"
#
# $call
# discr_test(X = y)


## End(Not run)

tcl documentation built on Sept. 17, 2024, 1:08 a.m.