Background: Perceptual measures such as speech intelligibility are known to be biased, variant and subjective, to which an automatic approach has been seen as a more reliable alternative. On the other hand, automatic approaches tend to lack explainability, an aspect that can prevent the widespread usage of these technologies clinically. Aims: In the present work, we aim to study the relationship between four perceptual parameters and speech intelligibility by automatically modelling the behaviour of six perceptual judges, in the context of head and neck cancer. From this evaluation we want to assess the different levels of relevance of each parameter as well as the different judge profiles that arise, both perceptually and automatically. Methods and Procedures: Based on a passage reading task from the Carcinologic Speech Severity Index (C2SI) corpus, six expert listeners assessed the voice quality, resonance, prosody and phonemic distortions, as well as the speech intelligibility of patients treated for oral or oropharyngeal cancer. A statistical analysis and an ensemble of automatic systems, one per judge, were devised, where speech intelligibility is predicted as a function of the four aforementioned perceptual parameters of voice quality, resonance, prosody and phonemic distortions. Outcomes and Results: The results suggest that we can automatically predict speech intelligibility as a function of the four aforementioned perceptual parameters, achieving a high correlation of 0.775 (Spearman's [rho]). Furthermore, different judge profiles were found perceptually that were successfully modelled automatically. Conclusions and Implications: The four investigated perceptual parameters influence the global rating of speech intelligibility, showing that different judge profiles emerge. The proposed automatic approach displayed a more uniform profile across all judges, displaying a more reliable, unbiased and objective prediction. The system also adds an extra layer of interpretability, since speech intelligibility is regressed as a direct function of the individual prediction of the four perceptual parameters, an improvement over more black box approaches.