Handling datasets with partially observed variables presents significant challenges, particularly when the available information is minimal or nearly absent. Classical imputation methods can introduce bias, as leveraging the observed portion of the data may lead to an overestimation of the less frequent group in the population. In this work, we propose an indirect approach that exploits the partial information present in the data while accounting for the clustered structure induced by the unobserved variable. A simulation study and an educational case study complete the proposed work.