eRm (version 1.0-9)

RSM: Estimation of rating scale models

Description

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

Usage

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

Value

Returns an object of class 'Rm', 'eRm' and contains the log-likelihood value, the parameter estimates and their standard errors.

loglik

Conditional log-likelihood.

iter

Number of iterations.

npar

Number of parameters.

convergence

See code output in nlm.

etapar

Estimated basic item difficulty parameters (item and category 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.

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 RSM. 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.

Author

Patrick Mair, Reinhold Hatzinger

Details

The design matrix approach transforms the RSM into a partial credit model and estimates the corresponding basic parameters by using CML. Available methods for RSM-objects are print, coef, model.matrix, vcov, 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,PCM,LRtest

Examples

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