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

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 on parameters expressing change between two time points.

Usage

change_test(X)

Arguments

X	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. Test of hypothesis that shift parameter equals zero against the two-sided alternative that shift parameter is not equal to zero.

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

invar_test, and LLTM_test.

Examples

# 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 exmaple 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
# (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(X = y)

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.