Testing the Local Independence Assumption of the Rasch Model WithQ₃-Based Nonparametric Model Tests

Abstract

Local independence is a central assumption of commonly used item response theory models. Violations of this assumption are usually tested using test statistics based on item pairs. This study presents two quasi-exact tests based on the [Formula: see text] statistic for testing the hypothesis of local independence in the Rasch model. The proposed tests do not require the estimation of item parameters and can also be applied to small data sets. The authors evaluate the tests with three simulation studies. Their results indicate that the quasi-exact tests hold their alpha level under the Rasch model and have higher power against different forms of local dependence than several alternative parametric and nonparametric model tests for local independence.

Adaptation and psychometric evaluation of the Fear of COVID-19 Scale in the general Colombian population

“…This limited performance of the item is not new because, in a sample of the general Italian population, covariance was observed item 1 ("I am more afraid of coronavirus-19") and item 5 ("When I see news and stories about coronavirus-19 on social networks, I get nervous or anxious"; Soraci et al, 2020). This finding suggests an item with local dependence that could compromise the scale's reliability (Christensen et al, 2017;Debelak & Koller, 2020). Along the same lines, a study in Saudi Arabia (Alyami et al, 2020) found a significant error covariance for items 1 and 2 ("My hands get wet when I think about COVID-19").…”

“…Thus, a 6-item scale (Fear COVID-6) was obtained. This consideration is significant since local dependency assumption violations can inflate reliability estimators and generate other construct validity problems (Debelak & Koller, 2020).…”

Academic Achievement and Peer Tutoring in Mathematics: A Comparison Between Primary and Secondary Education

“…A post hoc analysis was run using Scheffe's test (MacDonald & Gardner, 2000). As Debelak and Koller (2019) state, several requirements must be fulfilled before using parametric methods in a study. To this purpose, a Kolmogorov-Smirnoff test was conducted using the pretest scores to ensure that students' scores followed a normal distribution.…”

A Rasch Analysis of the School-Related Well-Being (SRW) Scale: Measuring Well-Being in the Transition from Primary to Secondary School

“…Performing a Rasch analysis, different indicators of the quality of the measurement are evaluated. A first step is checking the internal construct validity, through the exam of some general assumptions concerning the item response theory models [40][41][42], i.e., monotonicity [43,44], local independence [45][46][47], unidimensionality [48,49], and absence of differential item functioning (DIF) or item bias [50,51]. The DIF is related to another key assumption of the Rasch model, relating to the fact that the item parameter estimates should not depend on the person sample, and vice versa.…”