eRm (version 0.9-2)

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)

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.

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.
• etapar
  Estimated basic item 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.

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.parameters, plotICC, plotjointICC, LRtest, Waldtest.

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
data(raschdat1)
res <- RM(raschdat1, sum0 = FALSE)
print(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)
print(res)
summary(res)     
res$W                                       #generated design matrix
                       
#Rasch model with missing values
data(raschdat2)
res <- RM(raschdat2)
print(res)
summary(res)