Modelling algorithm Algorithm Notes R package(s) References
Multivariate regression tree (MRT) multiresponse extention of classification and regression tree (CART) mvpart (discont.) Nieto-Lugilde et al 2018, Norberg et al 2019
Multiresponse multivariate adaptive regression splines (MMARS) multiresponse version of multivariate adaptive regression splines (MARS) MDA, EARTH Nieto-Lugilde et al 2018, Norberg et al 2019
Constrained linear ordination (CLO) similar to generalized linear model (GLM) VGAM Nieto-Lugilde et al 2018, Norberg et al 2019
Constrained quadratic ordination (CQO) generalized linear model (GLM) with quadratic response VGAM Nieto-Lugilde et al 2018, Norberg et al 2019
Constrained additive ordination (CAO) similar to generalized additive model (GAM) VGAM Nieto-Lugilde et al 2018, Norberg et al 2019
Multiresponse artificial neural networks (MANN) a type of machine learning NNET, neuralnet Nieto-Lugilde et al 2018, Norberg et al 2019
Multivariate stochastic neural network (MISTN) a type of machine learning MISTNET Harris 2015, Nieto-Lugilde et al 2018, Norberg et al 2019, Zhang et al 2018
Hierarchical Bayesian Modelling (HBM) a relatively newer application of Bayesian algorithms spBayes, BayesComm, HMSC, boral, or rosalia D’Amen et al 2017, Nieto-Lugilde et al 2018, Norberg et al 2019, Ovaskainen et al 2017, Warton et al (2015), Wilkenson et al 2019, Zhang et al 2018
Latent variable model (LVM) Bayesian implementation; overlap with HBM R2jags, gllvm Hui et al 2015, Warton et al 2015, Ovaskainen et al 2017
Generalized dissimilarity modelling (GDM) use continuous functions to model community patterns by considering variation in species along environmental gradients gdm D’Amen et al 2017, Nieto-Lugilde et al 2018, Norberg et al 2019
Gradient forest (GF) community level extension of Random Forest gradientForest Nieto-Lugilde et al 2018, Norberg et al 2019
Region of common profile (RCP) Less frequently applied in ecology RCPmod Lyons et al 2017
Generalized joint attribute modelling (GJAM) not commonly applied; conflicting evidence on predictive performance (Zhang et al 2018) gjam Zhang et al 2018, Norberg et al 2019