A joint spatial factor analysis model to accommodate data from misaligned areal units with application to Louisiana social vulnerability.

With the threat of climate change looming, the public health community has an interest in identifying communities at the highest risk of devastation based not only on geographic features but also on social characteristics. Indices of community social vulnerability can be created by applying a spatial factor analysis to a set of relevant social variables measured for each community; however, current spatial factor analysis methodology is ill-equipped to handle spatially misaligned data. We introduce a joint spatial factor analysis model that can accommodate spatial data from two distinct partitions of a geographic space and identify a common set of latent factors underlying them. By defining the latent factors over the intersection of the two partitions, the model minimizes loss of information. Using simulated data constructed to mimic the spatial structure of our real data, we confirm the reliability of the model and demonstrate its superiority over competing ad hoc methods for dealing with misaligned data in spatial factor analysis. Finally, we construct an index of community social vulnerability for each census tract in Louisiana, a state prone to environmental disasters, which could be exacerbated by climate change, by applying the joint spatial factor analysis model to a set of misaligned social indicator data from the state. To demonstrate the utility of this index, we integrate it with Louisiana flood insurance claims data to identify communities that may be at particularly high risk during natural disasters, based on both social and geographic features.