PCM function

Estimation of partial credit models

Estimation of partial credit models

This function computes the parameter estimates of a partial credit model for polytomous item responses by using CML estimation. UTF-8

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.

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.

Returns

Returns an object of class Rm, eRm containing.

  • loglik: Conditional log-likelihood.

  • iter: Number of iterations.

  • npar: Number of parameters.

  • convergence: See code output in nlm.

  • etapar: Estimated basic item difficulty 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.

  • call: The matched call.

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.

Author(s)

Patrick Mair, Reinhold Hatzinger

See Also

RM,RSM,LRtest

Examples

##PCM with 10 subjects, 3 items res <- PCM(pcmdat) res summary(res) #eta and beta parameters with CI thresholds(res) #threshold parameters
  • Maintainer: Patrick Mair
  • License: GPL-3
  • Last published: 2024-03-15

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