Estimating hidden populations by transferring knowledge from geographically misaligned levels

The estimation of hidden sub-populations is a hard task that appears in many fields. For example, public health planning in Brazil depends crucially of the number of people who holds a private health insurance plan and hence rarely uses the public services. Different sources of information about these sub-populations may be available at different geographical levels. The available information can be transferred between these different geographic levels to improve the estimation of the hidden population size. In this study, we propose a model that use individual level information to learn about the dependence between the response variable and explanatory variables by proposing a family of link functions with asymptotes that are flexible enough to represent the real aspects of the data and robust to departures from the model. We use the fitted model to estimate the size of the sub-population at any desired level. We illustrate our methodology estimating the sub-population that uses the public health system in each neighborhood of large cities in Brazil.