Model-based ordination with constrained latent variables

1. In community ecology, unconstrained ordination can be used to predict latent variables from a multivariate dataset, which generated the observed species composition. 2. Latent variables can be understood as ecological gradients, which are represented as a function of measured predictors in constrained ordination, so that ecologists can better relate species composition to the environment while reducing dimensionality of the predictors and the response data. 3. However, existing constrained ordination methods do not explicitly account for information provided by species responses, so that they have the potential to misrepresent community structure if not all predictors are measured. 4. We propose a new method for model-based ordination with constrained latent variables in the Generalized Linear Latent Variable Model framework, which incorporates both measured predictors and residual covariation to optimally represent ecological gradients. Simulations of unconstrained and constrained ordination show that the proposed method outperforms CCA and RDA. ### Competing Interest Statement The authors have declared no competing interest.