Dependence among variables and unobserved heterogeneity are common features of multivariate count data. We propose a model-based clustering approach for this setting based on a Poisson factor mixture model, which combines a low-dimensional latent structure with a finite mixture specification. This enables simultaneous dimension reduction and clustering while providing interpretable latent representations of count profiles. The proposal originates from the UniversITA project, which collected formal written texts from a representative sample of Italian university students. Since university students play a central role in the process of linguistic change, as they are the most educated segment of the youth population, understanding variation in their writing is substantively important for both language research and higher education policy. Texts were annotated for various linguistic features, producing multivariate count data. The fitted model identifies two correlated latent dimensions of writing competence, interpretable as communicative effectiveness and grammatical-linguistic control. Incorporating educational and sociodemographic covariates further reveals distinct student profiles associated with field of study and prior educational background. Beyond this application, the proposed framework can be employed for the analysis of heterogeneous multivariate count data with complex dependence patterns, such as those arising in educational assessments, psychological and behavioral studies, and text analysis.

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