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eRm

MLoef

Martin-Löf's Likelihood-Ratio-Test

Description

This Likelihood-Ratio-Test is based on item subgroup splitting.

Usage

MLoef(robj, splitcr = "median")

Arguments

`robj`	An object of class `'Rm'`.
`splitcr`	Split criterion to define the item groups. `"median"` and `"mean"` split items in two groups based on their items' raw scores. `splitcr` can also be a vector of length k (where k denotes the number of items) that takes two or more distinct values to define groups used for the Martin-Löf Test.

Details

This function implements a generalization of the Martin-Löf test for polytomous items as proposed by Christensen, Bjørner, Kreiner & Petersen (2002), but does currently not allow for missing values.

If the split criterion is "median" or "mean" and one or more items' raw scores are equal the median resp. mean, MLoef will assign those items to the lower raw score group. summary.MLoef gives detailed information about the allocation of all items.

summary and print methods are available for objects of class 'MLoef'.

An ‘exact’ version of the Martin-Löf test for binary items is implemented in the NPtest function.

Value

MLoef returns an object of class MLoef containing:

`LR`	LR-value
`df`	degrees of freedom
`p.value`	p-value of the test
`fullModel`	the overall Rasch model
`subModels`	a list containing the submodels
`Lf`	log-likelihood of the full model
`Ls`	list of the sub models' log-likelihoods
`i.groups`	a list of the item groups
`splitcr`	submitted split criterion
`split.vector`	binary allocation of items to groups
`warning`	items equalling median or mean for the respective split criteria
`call`	the matched call

Author(s)

Marco J. Maier, Reinhold Hatzinger

References

Christensen, K. B., Bjørner, J. B., Kreiner S. & Petersen J. H. (2002). Testing unidimensionality in polytomous Rasch models. Psychometrika, (67)4, 563–574.

Fischer, G. H., and Molenaar, I. (1995). Rasch Models – Foundations, Recent Developements, and Applications. Springer.

Rost, J. (2004). Lehrbuch Testtheorie – Testkonstruktion. Bern: Huber.

Examples

# Martin-Löf-test on dichotomous Rasch model using "median" and a user-defined
# split vector. Note that group indicators can be of character and/or numeric.
splitvec <- c(1, 1, 1, "x", "x", "x", 0, 0, 1, 0)

res <- RM(raschdat1[,1:10])

MLoef.1 <- MLoef(res, splitcr = "median")
MLoef.2 <- MLoef(res, splitcr = splitvec)

MLoef.1

summary(MLoef.2)

eRm

Extended Rasch Modeling

v1.0-2

GPL-3

Authors

Patrick Mair [cre, aut], Reinhold Hatzinger [aut], Marco J. Maier [aut], Thomas Rusch [ctb], Rudolf Debelak [ctb]

Initial release

2021-02-11