invar_test: Test of invariance of item parameters between two groups.

In akurz1/tcl: Testing in Conditional Likelihood Context

Description

Computes gradient (GR), likelihood ratio (LR), Rao score (RS) and Wald (W) test statistics for hypothesis of equality of item parameters between two groups of persons against a two-sided alternative that at least one item parameter differs between the two respected groups.

Usage

invar_test(X, splitcr = "median", model = "RM")

Arguments

X	data matrix.
splitcr	split criterion which is either "mean", "median" or a numeric vector x. "mean" corresponds to division of the sample according to the mean of the person score. "median" corresponds to division of the sample according to the median of the person score. x has length equal to number of persons and contains zeros and ones indicating group membership of the persons.
model	RM, PCM, RSM

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	degrees of freedom.
pvalue	a numeric vector of corresponding p-values.
call	the matched call.

References

Draxler, C. (2010). Sample Size Determination for Rasch Model Tests. Psychometrika, 75(4), 708–724.

Draxler, C., & Alexandrowicz, R. W. (2015). Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model. Psychometrika, 80(4), 897–919.

Draxler, C., Kurz, A., & Lemonte, A. J. (2019). The Gradient Test and its Finite Sample Size Properties in a Conditional Maximum Likelihood and Psychometric Modeling Context. Submitted for publication.

Glas, C. A. W., & Verhelst, N. D. (1995a). Testing the Rasch Model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch Models: Foundations, Recent Developments, and Applications (pp. 69–95). New York: Springer.

Glas, C. A. W., & Verhelst, N. D. (1995b). Tests of Fit for Polytomous Rasch Models. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch Models: Foundations, Recent Developments, and Applications (pp. 325-352). New York: Springer.

Lemonte, A. J. (2016). The Gradient Test. Another Likelihood-Based Test. London:Academic Press.

Terrell, G. R. (2002). The Gradient Statistic. Computing Science and Statistics, 34(34), 206–215.

See Also

change_test, and LLTM_test.

Examples

##### Rasch Model #####
y <- eRm::sim.rasch(persons = rnorm(400), c(0,-3,-2,-1,0,1,2,3))
x <- c(rep(1,200),rep(0,200))

res <- invar_test(y, splitcr = x, model = "RM")

res$test # test statistics
res$df # degrees of freedoms
res$pvalue # p-values

akurz1/tcl documentation built on Oct. 22, 2021, 4:10 p.m.