Bayesian networks to evaluate and test the Raven’s colored progressive matrices

Abstract

The present study explores the inter-item dependencies within Raven’s Colored Progressive Matrices (CPMs) across childhood developmental stages by leveraging different Bayesian Network (BN) models. The data were collected from 255 participants aged 4 to 11 and analyzed using both theory-driven (including transitive independence and various sequential dependence structures) and data-driven approaches. The data-driven BN structure learning was developed by incorporating bootstrap stability analysis and parameter optimization, while the hypothesis comparison was carried out via Bayes factors. Furthermore, the model’s validity and generalizability were examined through the implementation of the leave-one-out cross-validation (LOOCV) approach. The findings revealed that the Sequential Data-Driven Model exhibited consistent superiority over conventional theory-driven hypothesis models. This suggest the presence of complex interrelationships that might challenge the assumption of local independence in psychometric assessments. Furthermore, our cross-validation analyses and model fit findings reveal that robust sequential dependencies and direct item-to-item influences are more stable in kindergarten samples. Conversely, as students progress through primary school, their response patterns become more heterogeneous and variable, likely reflecting a transition toward more flexible and individualized cognitive approaches. In conclusion, these results suggest the presence of complex patterns of item interdependence in the CPMs, thereby establishing the foundation for the development of advanced scoring methodologies and prompting additional investigation into the cognitive processes underlying these dependencies.