RM.weights (version 2.0)

EWaldtest: Wald test to check sampling independence under CML.

Description

This function performs a Wald test of sampling independence on item severity parameters.

Usage

EWaldtest(b1, b2, se1, se2)

Arguments

b1

Item severity vector estimated on the first sample subset.

b2

Item severity vector estimated on the second sample subset (complementary to the one used to estimate b1).

se1

Item standard errors (first sub-sample).

se2

Item standard errors (second sub-sample).

Value

A list with the following elements:

z	The z-statistics of the Wald test.
p	Computed p-value of the Wald test.
tab	Descriptive table with test results.

Details

This function computes the Wald test to check if the sampling independence assumption holds. The test statistics is $$ z = \frac{\hat{b}_1 - \hat{b}_2}{\sqrt{Var(\hat{b}_1) + Var(\hat{b}_2)}}, $$ where \(\hat{b}_1\) and \(\hat{b}_2\) are the ML item parameter estimates computed on two, randomly extracted and complementary, sub-samples of the overall sample, and \(Var(\hat{b}_1)\) and \(Var(\hat{b}_2)\) the corresponding variances.

The null hypothesis is of parameter estimates equality while the alternative hypothesis is bilateral (\(b_1 \neq b_2\)).

The sampling independence assumption implies that item severity parameter estimates do not depend on the analysed samples, but only on the severity of the items themselves. One way to check for this assumption is to extract two (complementary) random samples from the original sample and run the Wald test, or, more accurately, to extract B random sub-samples and observe the p-values distribution for each item.

See Also

RM.w

Examples

# NOT RUN {
data(data.FAO_country3)
# Questionnaire data and weights
XX.country3 = data.FAO_country3[,1:8]
wt.country3 = data.FAO_country3$wt

# Split the sample in two random sub-samples
n = nrow(XX.country3)
samp1 = sample(1:n, n/2)
samp2 = setdiff(1:n, samp1)
# Fit two Rasch models on the two sub-samples
rr1 = RM.w(XX.country3[samp1, ], wt.country3[samp1])
rr2 = RM.w(XX.country3[samp2, ], wt.country3[samp2])
# Test sampling independence
EWaldtest(rr1$b, rr2$b, rr1$se.b, rr2$se.b)$tab
# }