More on Maxent

```More on Maxent
Env. Variable importance:
Ma xent attempts to determine
variable importance a couple
ways:
•During modeling, Maxent asks
how much “gain” occurs
•During iterations, Maxent
increases gain of the model by
modifying coefficient for a
single feature based on input
environmental data
• Gain is related to information
added by an environ. variable
• Maxent can then determine
percent contribution of the env.
variable to whole the model
More on Maxent
Env. Variable importance
caveats
• Percent contribution
outputs don’t take into
account covariances across
environmental layers
• Variale importance is
based on Maxent algorithm!
It might be different using a
different method!
• Interpret with caution
• Permutation importance a
new measure.
Env. Variable importance:
• Maxent attempts to determine
variable importance a couple
ways:
• jackknifing is another method
to determine environmental layer
importance
• It is a leave-one-layer out
without replacement procedure
• How much “gain” occurs if we
use individual layers or
combinations?
• Which layer contributes the
most gain when used
individually?
Env. Variable importance:
• comparing test and train variable
importance is useful
• Note that precip6190_ann is the best
predictor for test but not train when
used alone
• Suggests that transferability of
monthly values lower than annual
values
• Note, length of red bar indicates
gain using all variables
• If blue bar is shorter than red,
corresponding loss of gain
(explanation) when variable omitted.
How to read these graphs
• Each graph shows the range of
values for the pixels in the
environment layers you used on
the x-axis
• Probability of presence is
shown on the y-axis (0 to 1)
• eg., tmax6190_annshows that
for low tmaxs, probability of
occurrence is ~1, which drops
towards 0 around 22.5 C.
• Plots do not take into account
correlation among variables
• Maxent produces a second
graph with individual variables
run separately
New Maxent Goodies
The Explain Tool
• New in Maxent 3.3
• Shows for any point
where the value is on
all response curves
• Can be used to see
how env. Variables
matter in different
areas.
• Haven’t had a chance
to use this much
How do we know when models are
“realistic” or, better put, of
“reasonable quality”, or even better
put… “valid”?
Two Types of Error in Distributional Predictions
Actual geographic distribution
Two Types of Error in Distributional Predictions
Predicted geographic distribution
Two Types of Error in Distributional Predictions
Actual geographic distribution
Predicted geographic distribution
Two Types of Error in Distributional Predictions
Actual geographic distribution
Predicted geographic distribution
Overprediction,
or Commission
Underprediction,
or Omission
Two Types of Error in Distributional Predictions
Objective: To Minimize Both Forms of Error
Two Types of Error in Distributional Predictions
Objective: To Minimize Both Forms of Error
To evaluate model quality you need to:
1. Generate an ‘independent’ set of data
There are at least two strategies to do so:
- Collect New Data
- Split your data into two sets, one set used in
training, one set used in model testing.
2. Generate a model with the training data
3. Quantify error components with a confusion matrix by
utilizing the testing data
Actually
Present
Actually
Absent
Predicted
Present
a
b
Predicted
Absent
c
d
a & d = correct predictions
b = commission error
(false positives,
overprediction)
c = omission error
(false negatives,
underprediction)
Measuring Omission Redux
• Omission error is “easy” to measure if you have a test and
training datset
• Training dataset to create model
• Test dataset to verify if suitable habitats include the “pixels”
that also contain the test locations.
• If yes, then omission error is low.
Measuring Commission Error Redux
• Measuring commission error is much trickier
• We don’t know anything about true absences, because we
only collected presence data
• How to measure commission error?
• In Maxent, the commission error is measured in reference to
the “background” (all pixels)
• And we are therefore distinguishing presence from “random”
rather than presence from absence
EXAMPLE MODELS THAT YOU MIGHT NOT BELIEVE
High Omission
LowCommission
We know the model gets
this wrong. How? Explain
in terms of omission,
commission and in terms of
true/false presence/absence
Zero Omission
High Commission
This one probably gets
something wrong too.
Also explain….
Zero Omission
No Commission
Overfitting
And this one too…
Omission Error (% of
occurrence points outside the
predicted area)
Some stochastic algorithms (e.g. GARP) produce different
models with the same input data. Good models find
minimization between commission/omission error. So can
find those models.
100
For species with a
fair number of
occurrence data this
is a typical curve
0
100
Commission Index (% of area
predicted present)
Omission Error (% of occurrence points
outside the predicted area)
100
Distribution of a species
in an area
High Omission
Low Commission
Zero Omission
High Commission
Zero Omission
No Commission
Overfitting
0
100
Commission Index (% of area
predicted present)
The question now is, which of these models are good and
which ones are bad?
100
Omission Error (% of occurrence
points outside the predicted area)
Models with high
omission error are
(not capturing
environment of
known occurrences)
0
100
Commission Index (% of area
predicted present)
The question now is, which of these models are good and
which ones are bad?
Omission Error (% of occurrence
points outside the predicted area)
100
Region of
the best
models
overfitting
0
overprediction
100
Commission Index (% of area
predicted present)
The following discussion made a big
assumption: That models results are
binary – either suitable or unsuitable.
HOWEVER…
SOME TOOLS PRODUCE
CONTINUOUS MEASURES
OF SUITABLE on a scale from 0
(unsuitable) to 100 (really suitable)
Like Maxent… the tools we’ll use.
So how to Threshold ?
(eg convert a continuous map into a binary one)
• Lots of potential thresholds to choose. Some
of the most common are:
– Fixed (eg. all maxent values 10-100 are suitable, all 0-10
are not. Note … arbitrary)
– Lowest presence threshold (threshold that requires the
lowest possible suitable area that still includes all training
occurrence data points)
– Sensitivity-specificity equality (where true positive and
true negative fraction are equal)
HOW TO READ SOME OF THE MAXENT
OUTPUTS PART 2 – RECEIVER OPERATOR
CURVES.
WHAT THEY ARE, AND WHAT THEY MEAN.
AS BEST AS I CAN REMEMBER (and explain)
Remember, we have test data to use to find errors
of commission and omission
to see how the model performs
actual value
p
n
total
p'
True
Positive
False
Positive
(commission)
P'
n'
False
Negative
(omission)
True
Negative
N'
prediction
outcome
total
P
N
- We can caculate the true positive rate (TPR) as TP/P
- We can calculate the false positive rate (FPR) as FP/N
- We can calculate accuracy (ACC) = (TP + TN) / (P + N)
A
B
C
C'
TP=63
FP=28
91
TP=77
FP=77
154
TP=24
FP=88
112
TP=88
FP=24
112
FN=37
TN=72
109
FN=23
TN=23
46
FN=76
TN=12
88
FN=12
TN=76
88
100
100
200
100
100
200
100
100
200
100
100
200
TPR = 0.63
TPR = 0.77
TPR = 0.24
TPR = 0.88
FPR = 0.28
FPR = 0.77
FPR = 0.88
FPR = 0.24
ACC = 0.68
ACC = 0.50
ACC = 0.18
ACC = 0.82
TPR is also called sensitivity
1-FPR is also called specificity
WE CAN PLOT THE TPR against 1-FPR:
This is called a Receiver-Operator Characteristic Curve
- Comes from information theory
ACC VALUES ARE GREAT WHEN YOU HAVE THRESHOLDED YOUR
MAXENT RESULT. WHAT ABOUT VALUES OVER MULTIPLE THRESHOLDS?
-You calculate your ACC value at all thresholds
- low thresholds overpredict (high commission errors)
- high thresholds underpredict (high omission errors)
- you get a curve of under to overprediction – this is the ROC curve
- the area under the curve is a good indicator of model performance
-You want AUC values close to 1
- Another graph showing how omission increases with
increasing threshold.
- Background (kind of pseudoabsences) go the other
direction since you are predicting more absence as you increase
threshold
- You are looking at specificity versus sensitivity across thresholds
HOW TO READ SOME OF THE MAXENT
OUTPUTS PART 2 – RECEIVER OPERATOR
CURVES.
WHAT THEY ARE, AND WHAT THEY MEAN.
People often report AUC values as measures of
model performance and you can too. With
caveats:
1. AUCs vary dependening whether a species
is widespread or narrowly distributed
2. The choice of the “geographic window of
extent” for modeling matters
3. AUCs are typically inflated due to spatial
autocorrelation
4. So interpret “good” model results with
caution.
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