Ranking of six candidate path models relating socio-economic variables to the (<i>i</i>) proportional (pENV) and (<i>ii</i>) absolute environmental impact rank (aENV) based on the Bayesian Information Criterion (BIC).

(i) For pENV, models A, D and E have high adjusted goodness-of-fit index (AGFI). Model A is the most highly ranked relative to other models in the candidate set based on BIC weights (wBIC), with lower support for models D and E. All remaining models have little support. (ii) For aENV, only models D and F have high AGFI. Model D is the most highly ranked relative to other models in the candidate, and with less support for model F. All remaining models have little support. Shown also are the model degrees of freedom (df), associated model Chi-square value (χ2), and the difference between the top-ranked model's BIC and that of the model under consideration (ΔBIC). Model variables include environmental rank (pENV or aENV), total human population size rank (pop), purchasing power parity-adjusted Gross National Income (gni) rank and governance quality rank (gov) (see text for details). Each model is described by the hypothetical causal paths between socio-economic indicators and environmental impact. Refer to Fig. S4 for full path model details.