invar_test  R Documentation 
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 twosided alternative that at least one item parameter differs between the two groups.
invar_test(X, splitcr = "median", model = "RM")
X 
Data matrix. 
splitcr 
Split criterion which is either "mean", "median" or a numeric vector x.

model 
RM, PCM, RSM 
Note that items are excluded for the computation of GR,LR, and W due to inappropriate response patterns within subgroups and for computation of RS due to inappropriate response patterns in the total data. If the model is identified from the total data but not from one or both subgroups only RS will be computed. If the model is not identified from the total data, no test statistic is computable.
A list of test statistics, degrees of freedom, and pvalues.
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 pvalues. 
deleted_items 
A list with numeric vectors of item numbers that were excluded before computing corresponding test statistics. 
call 
The matched call. 
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. (2020). The Gradient Test and its Finite Sample Size Properties in a Conditional Maximum Likelihood and Psychometric Modeling Context. Communications in StatisticsSimulation and Computation, 119.
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. 325352). New York: Springer.
change_test
, and LLTM_test
.
## Not run:
##### 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$pvalue # pvalues
res$deleted_items # excluded items
$test
GR LR RS W
14.492 14.083 13.678 12.972
$df
GR LR RS W
7 7 7 7
$pvalue
GR LR RS W
"0.043" "0.050" "0.057" "0.073"
$deleted_items
$deleted_items$GR
[1] "none"
$deleted_items$LR
[1] "none"
$deleted_items$RS
[1] "none"
$deleted_items$W
[1] "none"
$call
invar_test(X = y, splitcr = x, model = "RM")
## End(Not run)
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