RM: Estimation of Rasch Models

In eRm: Extended Rasch Modeling

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)

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.

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.

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.

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.

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)

eRm documentation built on March 19, 2024, 3:06 a.m.