eRm (version 0.9-2)

PCM: Estimation of partial credit models

Description

This function computes the parameter estimates of a partial credit model for polytomous item responses by using CML estimation.

Usage

PCM(X, W, se = TRUE, sum0 = TRUE, etaStart)

Arguments

X

Input data matrix or data frame with item responses (starting from 0); rows represent individuals, columns represent items. Missing values are inserted as NA.

W

Design matrix for the PCM. If omitted, the function will compute W automatically.

se

If TRUE, the standard errors are computed.

sum0

If TRUE, the parameters are normed to sum-0 by specifying an appropriate W. If FALSE, the first parameter is restricted to 0.

etaStart

A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used.

Value

• Returns an object of class Rm, eRm containing.
• loglik
  Conditional log-likelihood.
• iter
  Number of iterations.
• etapar
  Estimated basic item parameters.
• se.eta
  Standard errors of the estimated basic item parameters.
• betapar
  Estimated item-category (easiness) parameters.
• se.beta
  Standard errors of item parameters.
• hessian
  Hessian matrix if se = TRUE.
• W
  Design matrix.
• X
  Data matrix.
• X01
  Dichotomized data matrix.

Details

Through specification in W, the parameters of the categories with 0 responses are set to 0 as well as the first category of the first item. Available methods for PCM-objects are print, coef, model.matrix, vcov, plot, summary, logLik, person.parameters, plotICC, LRtest.

References

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer. Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20. Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.

See Also

RM,RSM,LRtest

Examples

##PCM with 10 subjects, 3 items
data(pcmdat)
res <- PCM(pcmdat)
res  
summary(res)                #eta and beta parameters with CI
thresholds(res)             #threshold parameters