Computation of Andersen's Likelihood-Ratio Test

This function applies the Likelihood Ratio Test of Andersen. Note that all persons with raw score equal to "median" are assigned to the lower group in cases of a median split. Is is also allowed to split after "mean" or submit any dichotomous vector as split criteria.

tmt_lrtest(object, split = "median", cores = NULL, se = TRUE, ...)

Arguments

object

it is necessary to submit an object of the function mst or nmst

split

default is the split criteria "median" of the raw score, optional are "mean" or any dichotomous vector

cores

submit integer of cores you would like to apply

se

logical: if true, the standard error is estimated

...

further arguments for the tmt_rm function

Value

List with following entries

data_orig

Submitted data frame with item responses

betapars_subgroup

List of item parameters (difficulty) for each subgroup

se.beta_subgroup

List of standard errors of the estimated item parameters

model

Used model ((mst) for Rasch model with multistage design)

LRvalue

LR-value

df

Degrees of freedoms for the test statistic

pvalue

P-value of the likelihood ratio test

loglik_subgroup

Log-likelihoods for the subgroups

split_subgroup

List of split vector for each subgroup

call

Submitted arguments for the function (matched call)

fitobj

List of objects from subgroup estimation

References

• Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38(1), 123-140.

• Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.

See also

tmt_rm

Author

Jan Steinfeld

Examples

# example for tmt_lrtest
#############################################################################
# Example Rasch model and Likelihood Ratio Test
#############################################################################
dat <- tmt:::sim.rm(theta = 100, b = 10, seed = 1111)
#> Warning: It is necessary to set a seed for both theta and beta if no vector is passed. The specified seed was used for the theta parameters, the following is used for beta: 1112
dat.rm <- tmt_rm(dat = dat)
dat.lrt <- tmt_lrtest(dat.rm)
summary(dat.lrt)
#> 
#> Likelihood ratio test (Andersen):
#> 
#> Value (Chi^2):  21.545
#> df (Chi^2):  9
#> p-value:  0.01