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Article information
2025 , Volume 30, ¹ 1, p.51-63
Avdeenko T.V., Timofeeva A.Y.
Method for optimal grouping of factor levels in ANOVA model
Purpose. The purpose of this work is to formulate the problem of grouping factor levels in the ANOVA model. The model has a fixed number of factor level groups that establish a mixed integer linear programming problem for finding a global optimum. Methodology. The problem of grouping the levels of input factors in the ANOVA model can be considered as a special case of feature selection, where the features are paired comparisons between factor levels. Such problem can be solved by embedded methods (CAS-ANOVA algorithm) or wrapper methods (agglomerative merging method). Globally optimal solution (according to the given criterion) can be found using these methods in particular cases. In contrast, the proposed linearization-based approach always leads to the best solution. Results. Two methods were proposed for linearizing of the explained sum of squares for grouping levels in ANOVA model. The linearization methods were compared in terms of computation time. A comparative study of methods for grouping factor levels was carried out using the example of barley yield analysis. Findings. The second linearization method, which includes a smaller number of binary variables, has advantages in terms of computation time. The proposed approach, in contrast to the CAS-ANOVAalgorithm and the agglomerative merging method, ensures the achievement of a global optimum. Due to computational complexity, an application of this method is recommended when the optimal number of factor level groups is small.
[link to elibrary.ru]
Keywords: analysis of variance, CAS-ANOVA, grouping, factor level, linearization, global optimum
doi: 10.25743/ICT.2025.30.1.006
Author(s):
Avdeenko Tatiana Vladimirovna
Dr. , Professor
Position: Professor
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20, prospekt K. Marksa
E-mail: avdeenko@corp.nstu.ru
SPIN-code: 1085-2099Timofeeva Anastasiia Yurievna
PhD.
Position: Associate Professor
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20 Prospekt K. Marksa
E-mail: a.timofeeva@corp.nstu.ru
SPIN-code: 8980-1611 References:
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Bibliography link:
Avdeenko T.V., Timofeeva A.Y. Method for optimal grouping of factor levels in ANOVA model // Computational technologies. 2025. V. 30. ¹ 1. P. 51-63
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