Joint spatio-temporal analysis of multiple response types using the hierarchical generalized transformation model with application to coronavirus disease 2019 and social distancing (2002.09983v3)

Abstract: Social distancing can be described as an effort to maintain a physical distance between individuals and has become a necessary public health measure to combat cornoavirus disease 2019 (COVID-19). Social distancing is known to weaken incidences and deaths due to COVID-19, however, there are detrimental economic and psychological effects. This motivates us to analyze incidences (and deaths) of COVID-19 along with a measure of the health of the US economy (i.e., the adjusted closing price of the Dow Jones Industrial), and a measure of the public interest in COVID-19 through Google Trends data. The model we implement is developed to be easily adapted to a data scientist's preferred method for continuous data, which is done to aid future analyses of this important dataset. This dataset consists of multiple response types (e.g., continuous-valued, count-valued, binomial counts). Thus, we introduce a reasonable easy-to-implement all-purpose method that "converts" a statistical model for continuous responses (the preferred model) into a Bayesian model for multi-response data sets. To do this, we transform the data such that the continuous-valued transformed data can be reasonably modeled using the preferred model and the transformation itself is treated as unknown. The implementation of our approach involves two steps. The first step produces posterior replicates of the transformed data using a latent conjugate multivariate (LCM) model. The second step involves generating values from the posterior distribution implied by the preferred model. We refer to our model as the hierarchical generalized transformation (HGT) model. In a simulation, we demonstrate the flexibility of the HGT model by incorporating two different preferred models: Bayesian additive regression trees (BART) and the spatial mixed effects (spatio-temporal mixed effects) models.