In large-scale educational assessments, multiple test forms are commonly administered to ensure test security and operational feasibility. For test scores to be fairly interpreted, results from different forms must be comparable. Traditionally, test equating relies on anchor items that allow adjustments for differences in group ability. However, in many settings, anchor items are unavailable, requiring alternative approaches.

Generalized Kernel Equating (GKE) provides a flexible framework for equating test forms under various data collection designs, including the Non-equivalent Groups with Covariates (NEC) design, which incorporates background variables related to test scores to account for group differences. A methodological challenge arises when some of these background variables are themselves measured using different test forms, potentially introducing discrepancies and bias into the equating process. To address this issue, repeated equating of covariates has been proposed, where compromised covariates are first equated before being incorporated into the primary GKE process.

While previous research has demonstrated the theoretical advantages of repeated equating of covariates and its performance in simulation settings, its longitudinal behavior in real-world high-stakes assessments, where populations and testing conditions evolve over time, is less well known. This study investigates the longitudinal stability of repeated equating of covariates within the GKE-NEC framework in the context of the Czech Republic’s national upper secondary school leaving examination (matura exams). The focus is on the English Language test administered in spring and autumn terms between 2016 and 2024. Students taking the exam in the autumn term systematically differ from those in the spring term, typically showing lower performance and higher rates of repeated attempts. Furthermore, the composition of students selecting non-mandatory subjects such as English varies across years, creating additional challenges for maintaining score comparability over time.

The primary aim of the study is to investigate whether repeated equating of covariates using GKE produces stable equating scores across multiple exam years. Specifically, we analyze (a) the consistency of equated score distributions across years, (b) how changes in student populations influence equated score distributions within the GKE framework, and (c) whether pre-equating covariates enhances the robustness of equated scores over time. By providing empirical evidence from a national high-stakes assessment context, this research contributes to the understanding of covariate-based equating methods in the absence of anchor items.

The study is conducted on data from the Czech national upper secondary school leaving examination, focusing on English Language test scores from spring and autumn administrations between 2016 and 2024. Given the systematic differences between students taking the exam in the two terms, a non-equivalent groups design is assumed. Test equating is conducted using Generalized Kernel Equating (GKE) under the Non-equivalent Groups with Covariates (NEC) design. The main covariates include school type (academic versus non-academic secondary schools), student status (whether this is the first or repeated attempt to pass the exam), and scores from the mandatory Czech Language test. To address the measurement of background variables across multiple test forms, repeated equating of covariates is implemented. First, Czech Language test scores are equated across administrations. Spring administrations across years are equated using an equivalent groups design, justified by the mandatory nature of the test. Subsequently, spring and autumn administrations within each year are equated within the GKE framework using school type and exam attempt as background variables. The resulting equated Czech Language scores are then incorporated into the primary GKE-NEC equating of English Language test scores. Longitudinal analyses focus on changes in equated score distributions across years, the stability of GKE parameters associated with background variables, and the standard errors of equating.

We expect to observe substantial differences in raw score distributions between spring and autumn administrations, reflecting systematic differences in student characteristics and prior achievement. After adjustment using Generalized Kernel Equating under the NEC design, it is expected that test forms that are comparable in terms of difficulty will show better score distribution consistency. Repeated equating of covariates is expected to improve the longitudinal stability of equating scores compared to approaches that include background variables without prior equating. This improvement is expected to be especially important in periods with changes in student composition and test-taking behavior. Incorporating multiple background variables is expected to strengthen the adjustment for group differences and reduce potential bias, though a modest increase in uncertainty may arise due to the multi-step equating process. Overall, the findings are expected to provide empirical evidence supporting repeated equating of covariates within the GKE framework as a practical approach for ensuring score comparability in high-stakes assessment systems without anchor items. The study emphasizes the importance of addressing measurement differences in covariates for ensuring longitudinal score comparability in national examination systems.

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