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

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

Arguments

X

Input 0/1 data matrix or data frame; rows represent individuals (N in total), columns represent items. Missing values have to be inserted as NA.

W

Design matrix for the LLTM. 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. If groupvec=1, no group contrasts are imposed.

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 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.

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 LLTM-objects are:
print, coef, model.matrix, vcov,summary, logLik, person.parameters.

Value

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 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

LRSM,LPCM

Examples

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#LLTM for 2 measurement points
#100 persons, 2*15 items, W generated automatically
res1 <- LLTM(lltmdat1, mpoints = 2)
res1
summary(res1)

#Reparameterized Rasch model as LLTM (more pasimonious)
W <- matrix(c(1,2,1,3,2,2,2,1,1,1),ncol=2)              #design matrix
res2 <- LLTM(lltmdat2, W = W)
res2
summary(res2)

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