Using dynamic structural equations to include lagged and simultaneous interactions in multivariate spatio-temporal models for climate-linked physical, community, and ecosystem models

Oregon Convention Center 

Structural equation models (SEM) allow scientists to hypothesize system linkages in multivariate analyses, and coefficients in a sparse "path matrix" are estimated based on the sample covariance among variables. Conveniently, the path matrix yields a sparse precision matrix and SEM can be fitted as a Gaussian Markov random field (GMRF). I first discuss how SEM can be extended using R-package dsem to represent a nonseparable process including simultaneous and lagged interactions among variables and over time, where the joint path matrix is constructed via the sum of separable path matrices across time-lags. To illustrate, I use dsem to represent ecosystem interactions in the eastern Bering Sea, including linkages from ocean physics through phyto- and zooplankton to fishes, seabirds, and seals. I also introduce a spatial extension using R-package tinyVAST that also includes a separable spatial process. To illustrate, I use tinyVAST to estimate associations between flatfishes and rockfishes and corals and sponges in the Gulf of Alaska and Aleutian Islands. Throughout, I emphasize that SEM provides a natural extension for GMRFs to multivariate settings.