RSM {eRm} R Documentation

## 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)


### 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.

### 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.

### 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.

### 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.

RM,PCM,LRtest
##RSM with 10 subjects, 3 items