Environmental Engineering Reference
In-Depth Information
dependence”. In SDMs, we do not care about SAC per se, but about SAC in the
model's residuals (i.e. unexplained by the environment), because it distorts model
coefficients (Bini et al. 2009; Dormann 2007a). To date it is unclear whether this
residual SAC is mainly due to model misspecification (omission of non-linearity and
interactions), due to variation in sampling coverage, due to omission of important
predictors, or due to ecological processes (territoriality, dispersal). Only with respect
to some of these problems a
statistical
solution can be found. The spatial toolbox is
rich in approaches (Beale et al. 2010; Carl et al. 2008; Dormann et al. 2007; Mahecha
and Schmidtlein 2008). In any case, SDM residuals should be investigated for spatial
autocorrelation, and attempts should be made to correct for it. If spatial models yield
similar coefficient estimates (GLM) as non-spatial models, then there seems to be little
value in “going spatial”: the ranges of the spatial autocorrelation may or may not be
related to the ecological scale of movement or behavioral patterns (Betts et al. 2009;
Dormann 2009).
Tweaking the Model
There are several ways in which the quality of the model can be increased (Maggini
et al. 2006). One important start is to investigate the model residuals. They indicate
whether model assumptions were violated (e.g. when residuals are highly skewed or
their variance is not the same throughout the range of fitted values) or if some non-
linear relationship went unnoticed (residuals may show a hump-shaped trend
against fitted values).
Model diagnostics
13
will also indicate outliers, i.e. data points that have a high
influence on the model coefficients. We can use weights to decrease an outlier's
impact. Weights are also useful when the balance between presences and absences is
very disturbed. Down-weighting the more common category so that model weights
sum to the same value for 0s and 1s has been shown to increase the sensitivity of
binomial models (Maggini et al. 2006). The same approach is recommended when
using pseudo-absences (Elith and Leathwick 2009a).
By including data from other scales or broader geographic coverage, regional or
local SDMs can also be improved. Pearson et al. (2004) used European distribution
and climate data to fit a niche model for four plant species. Predicted probabilities
of occurrence from this model were then used as input variable alongside land-
cover variables in the second-step model for the UK. Thereby the authors avoided
the problem that the climate gradient in the UK is much shorter than of the species'
global distribution.
Assessing Model Performance
To quantify how well our model fits the data, we compare model predictions with
field data (usually on a hold-out sample; e.g. the subset of a cross-validation).
13
Diagnostics for GLMs fitted in R are given by plotting the model object.
