Disease modelling is an essential tool to describe disease progression and its heterogeneity across patients. Usual approaches use continuous data such as biomarkers to assess progression. Nevertheless, categorical or ordinal data such as item responses in questionnaires also provide insightful information about disease progression. In this work, we propose a disease progression model for ordinal and categorical data. We built it on the principles of disease course mapping, a technique that uniquely describes the variability in both the dynamics of progression and disease heterogeneity from multivariate longitudinal data. This extension can also be seen as an attempt to bridge the gap between longitudinal multivariate models and the field of Item Response Theory. Application to the Parkinson's Progression Markers Initiative cohort illustrates the benefits of our approach: a fine-grained description of disease progression at the item level, as compared to the aggregated total score, together with improved predictions of the patient's future visits. The analysis of the heterogeneity across individual trajectories highlights known disease trends such as tremor dominant (TD) or postural instability and gait difficulties (PIGD) subtypes of Parkinson's disease.