32
Brendan Moyle
in its presence. Large swings in the value of a coefficient in a new model tend to
indicate multicollinearity. Nonetheless, if forecasting is the goal of the model, the
Hendry method may not be appropriate. Although the Hendry method generates
models that have high explanatory power, the models do not necessarily have
good predictive power. Other approaches to the reduction in the number of explanatory variables and lowering of the influence of multicollinearity may be
better at predicting but usually will be worse at explaining the data at hand.
In most applications, it is useful to contrast several different models, especially
those that have similar explanatory power. For instance, Moyle (1997) used a
variation of the model presented below. In developing the model below, it was
suspected that body mass might have a nonlinear relationship with extinction risk
because it ranges over five orders of magnitude. Formal testing for nonlinearity
showed that the linear assumption for body mass was valid. Nonetheless, transformations to smooth the relationship were performed and the model reestimated.
Not surprisingly, the fact that a raw linear relationship was valid meant the model
was robust to either the raw body mass or the log-transformed body mass. Different models reveal whether the inferences of the model are robust as well as adding
to the knowledge of the conservation manager. As with all statistical models,
diagnostic tests on the explanatory variables are required, and ideally, some crossvalidation information on the values of the parameters should be generated (see
Elith, this volume).
The Model
Body mass was measured in kilograms, and the data were obtained mostly from
the work of Atkinson and Millener (1991). When body mass is not recorded in this
chapter, Dunning’s data (1993) were used instead. This created the potential for a
measurement bias as the two sources did not always agree on the body mass
values. Complicating this issue is the fact the body mass estimates for many birds
are based on museum samples or show great dependence on well-studied populations. Hence estimates of body mass have not been generated by representative
samples of these species.
Species and subspecies endemic to the Chatham Islands (CHATHAM) were
recorded as a dummy variable (i.e., represented as a binary variable). The working
hypothesis was that species that are endemic to a small island have higher extinction risks (Pimm et al. 1988). Trophic level might also be related to extinction risk.
Species at the top of the food chain might require a larger range to maintain a
viable population. Herbivorous bird species in New Zealand may be less able to
defend themselves against mammalian predators than more aggressive birds in
higher trophic levels. The guilds used in the study of Atkinson and Millener
(1991) were classed into four trophic levels and tested for statistical significance.
For reasons of parsimony, only the top trophic level (TROPH1) and the bottom
trophic level (TROPH4) were retained in this model.
Another factor that may be relevant for New Zealand species is flying ability.
As many birds that are unable to fly are also relatively heavy, the variable most
Brendan Moyle
in its presence. Large swings in the value of a coefficient in a new model tend to
indicate multicollinearity. Nonetheless, if forecasting is the goal of the model, the
Hendry method may not be appropriate. Although the Hendry method generates
models that have high explanatory power, the models do not necessarily have
good predictive power. Other approaches to the reduction in the number of explanatory variables and lowering of the influence of multicollinearity may be
better at predicting but usually will be worse at explaining the data at hand.
In most applications, it is useful to contrast several different models, especially
those that have similar explanatory power. For instance, Moyle (1997) used a
variation of the model presented below. In developing the model below, it was
suspected that body mass might have a nonlinear relationship with extinction risk
because it ranges over five orders of magnitude. Formal testing for nonlinearity
showed that the linear assumption for body mass was valid. Nonetheless, transformations to smooth the relationship were performed and the model reestimated.
Not surprisingly, the fact that a raw linear relationship was valid meant the model
was robust to either the raw body mass or the log-transformed body mass. Different models reveal whether the inferences of the model are robust as well as adding
to the knowledge of the conservation manager. As with all statistical models,
diagnostic tests on the explanatory variables are required, and ideally, some crossvalidation information on the values of the parameters should be generated (see
Elith, this volume).
The Model
Body mass was measured in kilograms, and the data were obtained mostly from
the work of Atkinson and Millener (1991). When body mass is not recorded in this
chapter, Dunning’s data (1993) were used instead. This created the potential for a
measurement bias as the two sources did not always agree on the body mass
values. Complicating this issue is the fact the body mass estimates for many birds
are based on museum samples or show great dependence on well-studied populations. Hence estimates of body mass have not been generated by representative
samples of these species.
Species and subspecies endemic to the Chatham Islands (CHATHAM) were
recorded as a dummy variable (i.e., represented as a binary variable). The working
hypothesis was that species that are endemic to a small island have higher extinction risks (Pimm et al. 1988). Trophic level might also be related to extinction risk.
Species at the top of the food chain might require a larger range to maintain a
viable population. Herbivorous bird species in New Zealand may be less able to
defend themselves against mammalian predators than more aggressive birds in
higher trophic levels. The guilds used in the study of Atkinson and Millener
(1991) were classed into four trophic levels and tested for statistical significance.
For reasons of parsimony, only the top trophic level (TROPH1) and the bottom
trophic level (TROPH4) were retained in this model.
Another factor that may be relevant for New Zealand species is flying ability.
As many birds that are unable to fly are also relatively heavy, the variable most