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.

Examples

Run this code

# 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)

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