LPCM function

Estimation of linear partial credit models

This function computes the parameter estimates of a linear partial credit model (LRSM) for polytomuous item responses by using CML estimation. UTF-8

LPCM(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 LPCM. 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 LPCM can be viewed as a more parsimonous PCM, 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 LPCM-objects are:

print, coef, model.matrix, vcov,summary, logLik, person.parameters.

Returns

Returns on 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.

• 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.

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.

Author(s)

Patrick Mair, Reinhold Hatzinger

See Also

LRSM,LLTM

Examples

#LPCM for two measurement points and two subject groups
#20 subjects, 2*3 items
G <- c(rep(1,10),rep(2,10))                   #group vector
res <- LPCM(lpcmdat, mpoints = 2, groupvec = G)
res
summary(res)