Inference and computational methods for regression models in the presence of partially observed network data or high-dimensional capture-recapture data

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This Discovery research program is concerned with the development of statistical models for respondent-driven sampling (RDS) and capture-recapture experiments to tackle new theoretical and methodological challenges in data analysis. It puts the emphasis on the underlying theory and the computational aspects of new statistical models in the presence of partially observed network data or high-dimensional capture-recapture data. For RDS, we will first tackle the parameter estimation problem of regression models, under a new parameter identification paradigm, when the underlying population network is partially observed. We will propose novel semiparametric estimation methods under mild topological constraints on the structure of the network and under additional model assumptions. We will then relax the topological constraints and propose identification regions for the target parameters under partial identification. Once these principled approaches for RDS regression are developed, a framework for causal inference in RDS studies will be proposed. Further, two new design-based and model-based population size estimators will be developed by modeling the RDS process (i) as a wave-wise sampling design and by averaging over all possible reordering of the recruitment data and (ii) as a capture-recapture `removal' model in which individuals' recruitment probabilities depend on their network sizes, or degrees. In capture-recapture, new models and computational methods will be elaborated to analyze high-dimensional marketing data with an underlying network structure, generated by activating applications on mobile phones, with a focus on the estimation of direct and indirect effects of digital ads on foot traffic under a causal framework. We will adopt the potential outcome framework, with the additional assumption that an individual's exposition to an ad may affect her/his neighbors' decision to visit public places. The computational aspect of this research program will be further developed and implemented in open access software for a wider uptake by researchers and users. This Discovery research program will provide theoretical and methodological foundations for modern analysis of data collected via capture-recapture and RDS. This will offer a new understanding of these designs for data collection and analysis, which will be useful for applications in public health, social sciences, and new areas such as marketing and computational advertising.