eRm: PCM – R documentation

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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.

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.

Examples

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

eRm

Extended Rasch Modeling

v1.0-2

GPL-3

Authors

Patrick Mair [cre, aut], Reinhold Hatzinger [aut], Marco J. Maier [aut], Thomas Rusch [ctb], Rudolf Debelak [ctb]

Initial release

2021-02-11

PCM