No abstract

The part of responses that is absent in the nonequivalent groups with anchor test (NEAT) design can be managed to a planned missing scenario. In the context of small sample sizes, we present a machine learning (ML)-based imputation technique called chaining random forests (CRF) to perform equating tasks within the NEAT design. Specifically, seven CRF-based imputation equating methods are proposed based on different data augmentation methods. The equating performance of the proposed methods is examined through a simulation study. Five factors are considered: (a) test length (20, 30, 40, 50), (b) sample size per test form (50 versus 100), (c) ratio of common/anchor items (0.2 versus 0.3), and (d) equivalent versus nonequivalent groups taking the two forms (no mean difference versus a mean difference of 0.5), and (e) three different types of anchors (random, easy, and hard), resulting in 96 conditions. In addition, five traditional equating methods, (1) Tucker method; (2) Levine observed score method; (3) equipercentile equating method; (4) circle-arc method; and (5) concurrent calibration based on Rasch model, were also considered, plus seven CRF-based imputation equating methods for a total of 12 methods in this study. The findings suggest that benefiting from the advantages of ML techniques, CRF-based methods that incorporate the equating result of the Tucker method, such as IMP_total_Tucker, IMP_pair_Tucker, and IMP_Tucker_cirlce methods, can yield more robust and trustable estimates for the “missingness” in an equating task and therefore result in more accurate equated scores than other counterparts in short-length tests with small samples.

This study proposes an empirical ensemble equating (3E) approach that collectively selects, adopts, weighs, and combines outputs from different sources to take and combine advantage of equating techniques in various score intervals. The ensemble idea was demonstrated and tailored to the Non-Equivalent groups with Anchor Test (NEAT) equating. A simulation study based on several published settings was conducted. Three outcome measures – average bias, its absolute value, and root mean square difference – were used to evaluate the selected methods’ performance. The 3E approach outperformed other counterparts in most given conditions, while the cautions, such as tuning weights and assuming possible scenarios for using the proposed approach were also addressed.