LLTM {eRm}R Documentation

Estimation of linear logistic test models

Description

This function computes the parameter estimates of a linear logistic test model (LLTM) for binary item responses by using CML estimation.

Usage

LLTM(X, W, mpoints = 1, groupvec = 1)

Arguments

X Input 0/1 data matrix or data frame; rows represent individuals (N in total), columns represent items.
W Design matrix for the Rasch model. 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

Details

Through appropriate definition of W the LLTM can be viewed as a more parsimonous Rasch model, 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 LLTM-objects are print, coef, model.matrix, vcov, summary.

Value

Returns on object of class eRm and contains the log-likelihood value, the parameter estimates and their standard errors.

model Type of model.
loglik The log-likelihood.
df Degrees of freedom.
iter Number of iterations required.
etapar Estimated basic item parameters.
se_eta Standard errors of the estimated basic item parameters.
hessian Hessian matrix.
betapar Estimated item parameters.
LR The log-likelihood test statistic for the model.
W Design matrix.
mpoints Number of measurement points.
ngroups Number of groups.

Note

NA's are not allowed in X, the category coding must start with 0 (lowest category).

Author(s)

Patrick Mair, Reinhold Hatzinger

References

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.

See Also

print.eRm,coef.eRm,vcov.eRm,model.matrix.eRm,summary.eRm

Examples


#LLTM for two measurement points 
#100 persons, 2*10 items, W generated automatically

data(lltmdat)                                         
res <- LLTM(lltmdat, mpoints = 2)
res

[Package eRm version 0.3.2 Index]