PCM {eRm} R Documentation

## 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.

### 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.

### Value

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.

### Author(s)

Patrick Mair, Reinhold Hatzinger

### 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.

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


[Package eRm version 1.0-2 Index]