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1. Detecting arrays for effects of multiple interacting factors

   https://doi.org/10.1016/j.ic.2024.105202  

   Colbourn, Charles J; Syrotiuk, Violet R (December 2024, Information and Computation)

   Detecting arrays provide test suites for complex engineered systems in which many factors interact. The determination of which interactions have a significant impact on system behaviour requires not only that each interaction appear in a test, but also that its effect can be distinguished from those of other significant interactions. In this paper, compact representations of detecting arrays using vectors over the finite field are developed. Covering strong separating hash families exploit linear independence over the field, while the weaker elongated covering perfect hash families permit some linear dependence. For both, probabilistic analyses are employed to establish effective upper bounds on the number of tests needed in a detecting array for a wide variety of parameters. The analyses underlie efficient algorithms for the explicit construction of detecting arrays. 

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2. Mixed-Level Covering, Locating, and Detecting Arrays via Cyclotomy

   Akhtar, Yasmeen; Colbourn, Charles J; Syrotiuk, Violet R (June 2024, Springer)

   Hoffman, Frederick; Holliday, Sarah; Rosen, Zvi; Shahrokhi, Farhad; Wierman, John (Ed.)

   For a finite field of order.q, and.v a divisor of.q − 1, additive translates of a cyclotomic vector yield a.q × q cyclotomic array on.v symbols. For every positive integer.t, for certain.q sufficiently large with respect to.v, such a cyclotomic array is always a covering array of strength.t. Asymptotically such arrays have far too many rows to be competitive with certain other covering array constructions. Nevertheless, for small values of .t , this cyclotomic method produces smallest known covering arrays for numerous parameters suitable for practical application. This paper extends these ideas and shows that cyclotomy can produce covering arrays of higher index, and locating and detecting arrays with large separation. Computational results also demonstrate that certain cyclotomic arrays for the same order.q but different values of .v can be juxtaposed to produce mixed-level covering, locating, and detecting arrays. 

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3. Scalable level-wise screening experiments using locating arrays

   https://doi.org/10.1080/00224065.2023.2220973  

   Akhtar, Yasmeen; Zhang, Fan; Colbourn, Charles J; Stufken, John; Syrotiuk, Violet R (October 2023, Journal of Quality Technology)

   Alternative design and analysis methods for screening experiments based on locating arrays are presented. The number of runs in a locating array grows logarithmically based on the number of factors, providing efficient methods for screening complex engineered systems, especially those with large numbers of categorical factors having different numbers of levels. Our analysis method focuses on levels of factors in the identification of important main effects and two-way interactions. We demonstrate the validity of our design and analysis methods on both well-studied and synthetic data sets and investigate both statistical and combinatorial properties of locating arrays that appear to be related to their screening capability. 

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4. A Novel Method for Detecting Intersectional DIF: Multilevel Random Item Effects Model with Regularized Gaussian Variational Estimation

   https://doi.org/10.1017/psy.2025.10046  

   Ren, He; Lyu, Weicong; Wang, Chun; Xu, Gongjun (September 2025, Psychometrika)

   Abstract Differential item functioning (DIF) screening has long been suggested to ensure assessment fairness. Traditional DIF methods typically focus on the main effects of demographic variables on item parameters, overlooking the interactions among multiple identities. Drawing on the intersectionality framework, we define intersectional DIF as deviations in item parameters that arise from the interactions among demographic variables beyond their main effects and propose a novel item response theory (IRT) approach for detecting intersectional DIF. Under our framework, fixed effects are used to account for traditional DIF, while random item effects are introduced to capture intersectional DIF. We further introduce the concept of intersectional impact, which refers to interaction effects on group-level mean ability. Depending on which item parameters are affected and whether intersectional impact is considered, we propose four models, which aim to detect intersectional uniform DIF (UDIF), intersectional UDIF with intersectional impact, intersectional non-uniform DIF (NUDIF), and intersectional NUDIF with intersectional impact, respectively. For efficient model estimation, a regularized Gaussian variational expectation-maximization algorithm is developed. Simulation studies demonstrate that our methods can effectively detect intersectional UDIF, although their detection of intersectional NUDIF is more limited. 

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5. Robustness of Recovery in Locating Array-based Screening Experiments

   Seidel, S. A.; Colbourn, C. J.; Syrotiuk, V.R. (January 2019, Spring Simulation Multiconference)

   Locating arrays (LAs) are experimental designs for screening interactions in engineered systems. LAs are often highly unbalanced, requiring advanced techniques to recover the terms that significantly influence system performance. While perfect recovery is achieved in the absence of noise, real systems are noisy. Therefore, in this paper, we study the robustness of recovery in the presence of noise. Using known models to generate synthetic data, we investigate recovery accuracy as a function of noise. Separation is introduced into LAs to allow more coverage for each t-way interaction; when separation is higher, recovery in noisy scenarios should improve. We find that locating arrays are able to recover the influential terms even with high levels of noise and that separation appears to improve recovery. Under the pessimistic assumption that noise depends on the range of responses, it is no surprise that terms with small coefficients become indistinguishable from noise. 

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