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The performance of inbred lines in advanced endogamous generation is commonly evaluated in successive generations of testing and selection, which we defined as "multistage field trials" (MSFT). MSFT data routinely exhibit heterogeneity of (co)variances at several levels due to genetic and/or statistical imbalance. Nowadays, mixed models have been widely used to deal with unbalanced data. However, few studies on common bean have addressed the use of a mixed model approach with modeling of (co)variance structures for random effects in MSFT. Furthermore, factor analysis and genotype‐ideotype distance (FAI‐BLUP) selection index was originally proposed using best linear unbiased predictions from individual analysis. In this regard, we aimed to study the implications of modeling (co)variance structures for random effects in the estimation of genetic parameters and evaluate the accuracy and efficiency of inbred line selection by the modeled FAI‐BLUP approach. A total of five trials were evaluated from 2018 to 2020. The results revealed that the unstructured covariance matrix fitted better for grain yield, whereas the matrix with uniform correlation and heterogeneity of variances fitted better for grain aspect and plant architecture. The modeled FAI‐BLUP approach increased the values of selection accuracy and selection efficiency. Our results suggest that modeling the different structures of (co)variances and selecting the best‐performing genotypes by modeled FAI‐BLUP approach should be used in common bean assays involving unbalanced data. Core Ideas: Genetic and/or statistical imbalance is a reality of plant breeding programs.Selecting the best fitted (co)variance structure for unbalanced data increased the selection accuracy.Low magnitude estimates of genetic correlation indicated the predominance of the complex part of the G × E interaction.The modeled FAI‐BLUP approach increased the selection efficiency by an average of 13.95%. [ABSTRACT FROM AUTHOR]