eRm (version 1.0-4)

RM: Estimation of Rasch Models

Description

This function computes the parameter estimates of a Rasch model for binary item responses by using CML estimation.

Usage

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

Value

Returns an object of class dRm, 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.

se.eta

Standard errors of the estimated basic item parameters.

betapar

Estimated item (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 0/1 data matrix or data frame; rows represent individuals, columns represent items. Missing values are inserted as NA.

W

Design matrix for the Rasch model. 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

For estimating the item parameters the CML method is used. Available methods for RM-objects are:
print, coef, model.matrix, vcov, summary, logLik, person.parameter, LRtest, Waldtest, plotICC, plotjointICC.

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

RSM,PCM, LRtest, Waldtest

Examples

# Rasch model with beta.1 restricted to 0
res <- RM(raschdat1, sum0 = FALSE)
res
summary(res)
res$W                                       #generated design matrix

# Rasch model with sum-0 beta restriction; no standard errors computed
res <- RM(raschdat1, se = FALSE, sum0 = TRUE)
res
summary(res)
res$W                                       #generated design matrix

#Rasch model with missing values
res <- RM(raschdat2)
res
summary(res)