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

In akurz1/tcl: Testing in Conditional Likelihood Context

Description

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

Usage

LLTM_test(X, W)

Arguments

X	data matrix.
W	design matrix of LLTM.

Details

The RM item parameters are assumed to be linear in the LLTM parameters. The coefficients of linear functions are specified by a design matrix W. In this context, the LLTM is considered as a more parsimonous 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.

Value

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

test	a numeric vector of gradient (GR), likelihood ratio (LR), Rao score (RS), and Wald test statistics.
df	degrees of freedom.
pvalue	a numeric vector of corresponding p-values.
call	the matched call.

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

# 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(X = y, W = W )

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

akurz1/tcl documentation built on Oct. 22, 2021, 4:10 p.m.