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)
Arguments
X
Input data matrix or data frame with item responses (starting from 0); rows represent individuals (N in total), columns represent items.
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
Value
Returns on object of class eRm and contains the log-likelihood value,
the parameter estimates and their standard errors.
modelType of model.
loglikThe log-likelihood.
dfDegrees of freedom.
iterNumber of iterations required.
etaparEstimated basic item parameters.
se_etaStandard errors of the estimated basic item parameters.
hessianHessian matrix.
betaparEstimated item parameters.
LRThe log-likelihood test statistic for the model.
WDesign matrix.
mpointsNumber of measurement points.
ngroupsNumber of groups.
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, i.e. X(T1)|X(T2)|... Available methods for LRSM-objects are print, coef,
model.matrix, vcov, summary.
References
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations,
Recent Developements, and Applications. Springer.