Supplementary Methods
Our analysis began by constructing the correlation matrices reproduced as Tables S2 –
S6. They are suitable for initial exploration and screening, but they use only ranks, do not make
use of all the available natural scale values, and the resulting correlation coefficients do not have
a direct interpretation as the change in outcome per unit change in the predictor.
Hence our next analysis was bivariate regression analysis. This has the virtue that it does
use available natural scale values, and that its coefficients (given in our Tables 1 and 2) do
permit interpretation as the change in outcome per unit change in the predictor. It has the
disadvantages that, in evaluating each independent variable one at a time, it ignores (fails to
control for) other variables, does not even try to address the question of whether all variables are
simultaneously important, and thereby may accept apparent effects of a variable that may be due
to its correlation with other uncontrolled variables.
We then went on to multiple regression analysis (both conventional and robust), which
shares with bivariate analysis the virtues of using natural scale values and of yielding coefficients
permitting interpretation as the change in outcome per unit change in predictor. The robust
coefficients are giving in Tables 1 and 2, and they are compared with the conventional
coefficients in Table S7. A further virtue of this approach is that the bivariate and multivariate
regression coefficients, both presented in Tables 1 and 2, may then be directly compared with
each other; differences between corresponding coefficients indicate effects of evaluating all
variables simultaneously, as opposed to evaluating them independently while ignoring other
variables.
Finally, in order to control for the background assumption of linear effects (and also the
assumptions of additive and non-interacting effects), we carried out the tree analysis, which does
not make those assumptions.
Comparison of these analyses yields the following conclusions:
The correlation matrices and the bivariate regressions (see Tables S4 and S5, and Tables
1 and 2, respectively) agree in signs and in significance/non-significance of all effects of all
variables, on both the deforestation outcome and the forest replacement outcome, for both the
81-entry and the 69-entry datasets.
The robust and conventional multiple regression analyses agree in signs and in
significance/non-significance and in values of all regression coefficients until the third or fourth
decimal places (Table S7).
Comparison of bivariate regression and multiple regression is possible from the left and
right sides respectively of Tables 1 and 2. For the deforestation outcome, there are qualitatively
no differences in signs or in signficance/non-significance of effects for six variables; the sole
difference is that distance emerges as significant in multiple regression but not in bivariate
regression. For the forest replacement outcome, for four variables the signs and significance/non-
2
significance of effects remain qualitatively the same; for one variable (age) the effect reverses in
sign; and one variable (rainfall) is significant by bivariate but not by multivariate regression,
while three variables (latitude, makatea, and distance) are significant by multiple regression but
not by bivariate regression. For variables yielding the same signs and significance between
bivariate and multiple regression, corresponding coefficients lie mostly within a factor of 2 of
each other. That is, considering all variables simultaneously does have some effect (hence
multiple regression was worth doing), but bivariate regression still detects two-thirds (10 out of
16) of the effects (hence multiple regression still leaves intact the majority of the conclusions
drawn from simpler methods).