Replication Data for: Generative AI and Topological Data Analysis of Longitudinal Panel Data

This paper constructs an approach to analyzing longitudinal panel data which combines topological data analysis (TDA) and generative AI applied to graph neu- ral networks (GNNs). TDA is deployed to identify and analyze unobserved topological heterogeneities of a dataset. TDA-extracted information is quantified into a set of measures, called functional principal components. These measures are used to analyze the data in four ways. First, the measures are construed as moderators of the data and their statistical effects are estimated through a Bayesian framework. Second, the mea- sures are used as factors to classify the data into topological classes using generative AI applied to graph neural networks constructed by construing the data as graphs. The classification uncovers patterns in the data which are otherwise not accessible through statistical approaches. Third, the measures are used as factors that condition the ex- traction of latent variables of the data through a deployment of a generative AI model. Fourth, the measures are used as labels for classifying the graphs into classes used to offer a GNN-based effective dimensionality reduction of the original data . The paper uses a portion of the MIDs dataset (from 1946 to 2010) as a running example to briefly illustrate its ideas and steps. (2024-10-10)