Statistics Seminar - 02/05/26

Abstract:

Latent variable models are widely used to represent unobservable processes that drive complex phenomena. Factor models, in particular, capture shared latent structure across multiple outcomes, revealing relationships that are not directly observable. Still, applying them in practice raises challenges such as rotational invariance, which affects identifiability, and the common problem of outcomes measured on different spatial units.

In this talk, I present two methodological contributions addressing these challenges. First, I tackle identifiability in contexts where we want to quantify predefined interactions among specific subsets of outcomes. I develop an estimation framework that decomposes the loadings matrix within a Markov chain Monte Carlo framework, enabling unique estimation of both latent factors and loadings. Second, I address spatial misalignment in Bayesian spatial factor models by introducing a spatial factor model capable of integrating outcomes measured on misaligned areal units (e.g., county and ZIP code levels). By defining a latent factor at the spatial intersection of these units, this method enables granular spatial inference and uncovers localized patterns that would otherwise be obscured in aggregated analyses.

Note:

Contact Prof. JZ at jzhang@math.msstate.edu for additional information.