This article investigates a family of centrality models for urban networks that incorporate both topological and non-topological factors. Since centrality is inherently recursive, these models can be formulated as fixed-point equations, which we refer to as shifted eigenproblems. Assuming a correlation between node centrality and occupancy, we discuss how experimental data can be used to estimate model parameters via least-squares methods. Furthermore, such data would allow us to infer the intrinsic attraction of each node, as well as the occupancy induced by must-visit points of interest, a task that is conceptually challenging. Once the model parameters are fitted and validated, our framework can be used to assess the impact of urban interventions, such as introducing a must-visit point of interest at a specific node or enhancing its intrinsic attraction. The resulting sensitivity analysis is therefore highly relevant for urban planning decisions. We also provide explicit formulas to facilitate this analysis.