eRm (version 1.0-9)

MLoef: Martin-Löf's Likelihood-Ratio-Test

Description

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

Usage

MLoef(robj, splitcr = "median", etaStart = NULL)

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

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.

etaStart

Optional list of starting values (eta parameters).

Author

Marco J. Maier, Reinhold Hatzinger

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.

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.

See Also

LRtest, Waldtest

Examples

# Martin-Loef-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_1
MLoef_2 <- MLoef(res, splitcr = splitvec)
summary(MLoef_2)