tcl (version 1.0.1)

LLTM_test: Testing linear restrictions on parameter space of item parameters of RM.

Description

Computes Wald (W), likelihood ratio (LR), Rao score (RS) and gradient (GR) test statistics for hypotheses defined by linear restrictions on parameter space of the item parameters of RM.

Usage

LLTM_test(data, W)

Value

A list of class tcl of test statistics, degrees of freedom, and p-values.

test

A numeric vector of Wald (W), likelihood ratio (LR), Rao score (RS), and gradient (GR) test statistics.

df

Degrees of freedom.

pvalue

A vector of corresponding p-values.

data

Data matrix.

call

The matched call.

Arguments

data

Data matrix.

W

Design matrix of LLTM.

Details

The RM item parameters are assumed to be linear in the LLTM parameters. The coefficients of the linear functions are specified by a design matrix W. In this context, the LLTM is considered as a more parsimonious model than the RM. The LLTM parameters can be interpreted as the difficulties of certain cognitive operations needed to respond correctly to psychological test items. The item parameters of the RM are assumed to be linear combinations of these cognitive operations. These linear combinations are defined in the design matrix W.

References

Fischer, G. H. (1995). The Linear Logistic Test Model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, Recent Developments, and Applications (pp. 131-155). New York: Springer. Fischer, G. H. (1983). Logistic Latent Trait Models with Linear Constraints. Psychometrika, 48(1), 3-26.

See Also

change_test, and invar_test.

Examples

if (FALSE) {
# Numerical example assuming no deviation from linear restriction

# design matrix W defining linear restriction
W <- rbind(c(1,0), c(0,1), c(1,1), c(2,1))

# assumed eta parameters of LLTM for data generation
eta <- c(-0.5, 1)

# assumed vector of item parameters of RM
b <- colSums(eta * t(W))

y <- eRm::sim.rasch(persons = rnorm(400), items = b - b[1])  # sum0 = FALSE

res <- LLTM_test(data = y, W = W )

res$test # test statistics
res$df # degrees of freedoms
res$pvalue # p-values

}