Qval (version 1.2.1)

Wald.test: the Wald test for two q-vectors

Description

This function flexibly provides the Wald test for any two q-vectors of a given item in the Q-matrix, but requires that the two q-vectors differ by only one attribute. Additionally, this function needs to accept a CDM.obj.

Usage

Wald.test(CDM.obj, q1, q2, i = 1)

Value

An object of class htest containing the following components:

statistic

The statistic of the Wald test.

parameter

the degrees of freedom for the Wald-statistic.

p.value

The p value

Arguments

CDM.obj

An object of class CDM.obj. @seealso CDM.

q1

A q-vector

q2

Another q-vector

i

the item needed to be validated

Details

$$ Wald = \left[\mathbf{R} \times P_{i}(\mathbf{\alpha})\right]^{'} (\mathbf{R} \times \mathbf{V}_{i} \times \mathbf{R})^{-1} \left[\mathbf{R} \times P_{i}(\mathbf{\alpha})\right] $$

Examples

library(Qval)
set.seed(123)

K <- 3
I <- 20
N <- 500
IQ <- list(
  P0 = runif(I, 0.0, 0.2),
  P1 = runif(I, 0.8, 1.0)
)
Q <- sim.Q(K, I)
data <- sim.data(Q = Q, N = N, IQ = IQ, model = "GDINA", distribute = "horder")

CDM.obj <- CDM(data$dat, Q)

q1 <- c(1, 0, 0)
q2 <- c(1, 1, 0)

## Discuss whether there is a significant difference when 
## the q-vector of the 2nd item in the Q-matrix is q1 or q2.
Wald.test.obj <- Wald.test(CDM.obj, q1, q2, i=2)

print(Wald.test.obj)