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In this work, we attempt to predict the composition-structure relationship in alkali aluminoborate glasses by using a recent statistical mechanics-based model that has previously been applied to predict the structure of binary modifier-former and ternary modifier-former-former oxide glasses. However, the structure of glasses with network intermediates such as Al2O3 has not yet been predicted with this approach. We thus extend the statistical mechanics-based model to predict composition-structure relations in Na2O-Al2O3-B2O3 glasses with different structural assumptions regarding the role of high-coordinated aluminum species. This ternary glass system was chosen since its structure has been thoroughly investigated in literature and is thus the best system for training the statistical mechanics-based model. To test and validate the model parameters established in the Na2O-Al2O3-B2O3 glass system, we accurately predict the structural speciation in Cs2O-Al2O3-B2O3 and Li2O-Al2O3-B2O3 glasses with the same parameters for Al-B interactions.