tcl (version 1.0.1)

change_test: Tests in context of measurement of change using LLTM.

Description

Computes gradient (GR), likelihood ratio (LR), Rao score (RS) and Wald (W) test statistics for hypotheses on parameters expressing change between two time points.

Usage

change_test(data)

Value

A list of class tcl 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 vector of corresponding p-values.

data

Data matrix.

call

The matched call.

Arguments

data

Data matrix containing the responses of n persons to 2k binary items. Columns 1 to k contain the responses to k items at time point 1, and columns (k+1) to 2k the responses to the same k items at time point 2.

Details

Assume all items be presented twice (2 time points) to the same persons. The data matrix X has n rows (number of persons) and 2k columns considered as virtual items. Assume a constant shift of item difficulties of each item between the 2 time points represented by one parameter. The shift parameter is the only parameter of interest. Of interest is the test of the hypothesis that the shift parameter equals 0 against the two-sided alternative that it is not equal to zero.

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

invar_test, and LLTM_test.

Examples

if (FALSE) {
# Numerical example with 400 persons and 4 items
# presented twice, thus 8 virtual items

# Data y generated under the assumption that shift parameter equals 0
# (no change from time point 1 to 2)

# design matrix W used only for example data generation
#     (not used for estimating in change_test function)
W <- rbind(c(1,0,0,0,0),
  c(0,1,0,0,0),
  c(0,0,1,0,0),
  c(0,0,0,1,0),
  c(1,0,0,0,1),
  c(0,1,0,0,1),
  c(0,0,1,0,1),
  c(0,0,0,1,1))

# eta Parameter, first 4 are nuisance, i.e. , easiness parameters of the 4 items
# at time point 1, last one is the shift parameter.
eta <- c(-2,-1,1,2,0)

y <- eRm::sim.rasch(persons = rnorm(400), items = colSums(eta * t(W)))

res <- change_test(data = y)

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

}