This paper employs a geometric approach for describing population heterogeneity representations of different discrete data models. The case of a 2 x 2 contingency table is considered in details. The paper provides geometric representations for log-linear, latent class, Grade of Membership and Rasch models in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The approach generalizes 2 x 2 case to higher dimensions, i.e., to 2 J tables with \(J \ge 3\). A discussion of similarities and differences among the models is included.