User modeling is a key topic in many applications, mainly social networks and information retrieval systems. To assess the effectiveness of a user modeling approach, its capability to classify personal characteristics (e.g., the gender, age, or consumption grade of the users) is evaluated. Due to the fact that some of the attributes to predict are multiclass (e.g., age usually encompasses multiple ranges), assessing fairness in user modeling becomes a challenge since most of the related metrics work with binary attributes. As a workaround, the original multiclass attributes are usually binarized to meet standard fairness metrics definitions where both the target class and sensitive attribute (such as gender or age) are binary. However, this alters the original conditions, and fairness is evaluated on classes that differ from those used in the classification. In this article, we extend the definitions of four existing fairness metrics (related to disparate impact and disparate mistreatment) from binary to multiclass scenarios, considering different settings where either the target class or the sensitive attribute includes more than two groups. Our work endeavors to bridge the gap between formal definitions and real use cases in bias detection. The results of the experiments, conducted on four real-world datasets by leveraging two state-of-the-art graph neural network-based models for user modeling, show that the proposed generalization of fairness metrics can lead to a more effective and fine-grained comprehension of disadvantaged sensitive groups and, in some cases, to a better analysis of machine learning models originally deemed to be fair. The source code and the preprocessed datasets are available at the following link: https://github.com/erasmopurif/toward-responsible-fairness-analysis.