# EWaldtest: Wald test to check sampling independence under CML. In Nwosu/RM.weights: Weighted Rasch modeling and extensions using Conditional Maximum Likelihood

## Description

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

## Usage

 1 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 sumset (complementary to the one used to estimate b1). se1 Item standard errors (first sub-sample). se2 Item standard errors (second sub-sample).

## 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}{√{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.

## 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.

## Author(s)

Sara Viviani [email protected]

RM.w
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ## 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 ## End(Not run)