pcIRT (version 0.1)

weight_test: Test for the scoring weights in the unidimensional polytomous Rasch model

Description

This functions tests the fit of fixed scoring parameters in a unidimensional polytomous Rasch model.

Usage

weight_test(MPRMobj, score_param)
## S3 method for class 'wt':
summary(object, \dots)
## S3 method for class 'wt':
print(x, \dots)

Arguments

MPRMobj

Object of class MPRM

score_param

Numerical vector with the scoring parameters that are tested

object

object of class wt

x

{object of class wt}

...

...

Value

• emp_Chi2
  $\chi^2$ distributed value of the Likelihood Ratio test
• df
  degrees of freedom of the test statistic
• pval
  p value of the test statistic
• unconstrLoglikelihood
  log-likelihood of the unconstrained model
• constrLoglikelihood
  log-likelihood of the constrained model
• unconstrNrPar
  number of estimated parameters in the unconstrained model
• constrNrPar
  number of estimated parameters in the constrained model
• unconstrItempar
  estimated item parameters of the unconstrained model
• constrItempar
  estimated item parameters of the constrained model
• unconstrScoreParameter
  estimated scoring parameters of the unconstrained model

Details

If the unidimensional polytomous Rasch model fits the data, the weight test can be performed to test whether assumed scoring parameters are appropriate. An unconstrained unidimensional polytomous Rasch model is calculated including estimation of scoring parameters. Furthermore a constrained unidimensional polytomous Rasch model is estimated with fixed scoring parameters (according to the input). Subsequently a Likelihood Ratio test tests the fit of the fixed scoring parameters.

References

Fischer, G. H. (1974). Einfuehrung in die Theorie psychologischer Tests [Introduction to test theory]. Bern: Huber.

See Also

MPRM dLRT

Examples

#simulate data set
simdat <- simMPRM(rbind(matrix(c(-1.5,0.5,0.5,1,0.8,-0.3, 0.2,-1.2), ncol=4),0), 500)

#estimate MPRM item parameters
res_mprm <- MPRM(simdat$datmat)

#tests the scoring parameter 0.5 for the unidimensional polytomous model
res_weight <- weight_test(res_mprm,  score_param=c(0.5))
summary(res_weight)