LRSM {eRm}

Estimation of linear rating scale models

Description

This function computes the parameter estimates of a linear rating scale model (LRSM) for polytomuous item responses by using CML estimation.

Usage

LRSM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE,
   etaStart)

Arguments

X

Input data matrix or data frame; rows represent individuals (N in total), columns represent items. Missing values are inserted as NA.

W

Design matrix for the LRSM. If omitted, the function will compute W automatically.

mpoints

Number of measurement points.

groupvec

Vector of length N which determines the group membership of each subject, starting from 1

se

If TRUE, the standard errors are computed.

sum0

If TRUE, the parameters are normalized 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

Through appropriate definition of W the LRSM can be viewed as a more parsimonous RSM, on the one hand, e.g. by imposing some cognitive base operations to solve the items. One the other hand, linear extensions of the Rasch model such as group comparisons and repeated measurement designs can be computed. If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc. measurement point are added column-wise in X.

If W is user-defined, it is nevertheless necessary to specify mpoints and groupvec. It is important that first the time contrasts and then the group contrasts have to be imposed.

Available methods for LRSM-objects are: print, coef, model.matrix, vcov,summary, logLik, person.parameters.

Value

Returns an object of class 'eRm' containing:

loglik

Conditional log-likelihood.

iter

Number of iterations.

npar

Number of parameters.

convergence

See code output in nlm.

etapar

Estimated basic item parameters (item and category 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.

groupvec

Group membership vector.

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

LLTM,LPCM

Examples

#LRSM for two measurement points
#20 subjects, 2*3 items, W generated automatically,
#first parameter set to 0, no standard errors computed.

res <- LRSM(lrsmdat, mpoints = 2, groupvec = 1, sum0 = FALSE, se = FALSE)
res