Summary

1. Unconstrained ordination is commonly used in ecology to visualize multivariate data, in particular, to visualize the main trends between different sites in terms of their species composition or relative abundance.
2. Methods of unconstrained ordination currently used, such as non-metric multidimensional scaling, are algorithm-based techniques developed and implemented without directly accommodating the statistical properties of the data at hand. Failure to account for these key data properties can lead to misleading results.
3. A model-based approach to unconstrained ordination can address this issue, and in this study, two types of models for ordination are proposed based on finite mixture models and latent variable models. Each method is capable of handling different data types and different forms of species response to latent gradients. Further strengths of the models are demonstrated via example and simulation.
4. Advantages of model-based approaches to ordination include the following: residual analysis tools for checking assumptions to ensure the fitted model is appropriate for the data; model selection tools to choose the most appropriate model for ordination; methods for formal statistical inference to draw conclusions from the ordination; and improved efficiency, that is model-based ordination better recovers true relationships between sites, when used appropriately.