Fast model-based ordination with copulas

Visualising data is a key step in data analysis, allowing researchers to find patterns, and assess and communicate the results of statistical modelling. In ecology, visualisation is often challenging when there are many variables (often for different species or other taxonomic groups) and they are not normally distributed (often counts or presence–absence data). Ordination is a common and powerful way to overcome this hurdle by reducing data from many response variables to just two or three, to be easily plotted. Ordination is traditionally done using dissimilarity-based methods, most commonly non-metric multidimensional scaling (nMDS). In the last decade, however, model-based methods for unconstrained ordination have gained popularity. These are primarily based on latent variable models, with latent variables estimating the underlying, unobserved ecological gradients. Despite some major benefits, a drawback of model-based ordination methods is their speed, as they typically take much longer to return a result than dissimilarity-based methods, especially for large sample sizes. We introduce copula ordination, a new, scalable model-based approach to unconstrained ordination. This method has all the desirable properties of model-based ordination methods, with the added advantage that it is computationally far more efficient. In particular, simulations show copula ordination is an order of magnitude faster than current model-based methods, and can even be faster than nMDS for large sample sizes, while being able to produce similar ordination plots and trends as these methods.