Skabbholmen data from: Concurrent ordination: Simultaneous unconstrained and constrained latent variable modeling

In community ecology, unconstrained ordination can be used to indirectly explore drivers of community composition, while constrained ordination can be used to directly relate predictors to an ecological community. However, existing constrained ordination methods do not explicitly account for community composition that cannot be explained by the predictors, so that they have the potential to misrepresent community composition if not all predictors are available in the data.
We propose and develop a set of new methods for ordination and Joint Species Distribution Modelling (JSDM) as part of the Generalized Linear Latent Variable Model (GLLVM) framework, that incorporate predictors directly into an ordination. This includes a new ordination method that we refer to as concurrent ordination, as it simultaneously constructs unconstrained and constrained latent variables. Both unmeasured residual covariation and predictors are incorporated into the ordination by simultaneously imposing reduce...