Maxent model for culicifacies

This page contains some analysis of the Maxent model for culicifacies, created Fri Sep 17 13:47:11 EDT 2010 using Maxent version 3.2.1. If you would like to do further analyses, the raw data used here is linked to at the end of this page.

Analysis of omission/commission

The following picture shows the omission rate and predicted area as a function of the cumulative threshold. The omission rate is is calculated both on the training presence records, and (if test data are used) on the test records. The omission rate should be close to the predicted omission, because of the definition of the cumulative threshold.

The next picture is the receiver operating characteristic (ROC) curve for the same data. Note that the specificity is defined using predicted area, rather than true commission (see the paper by Phillips, Anderson and Schapire cited on the help page for discussion of what this means). This implies that the maximum achievable AUC is less than 1. If test data is drawn from the Maxent distribution itself, then the maximum possible test AUC would be 0.978 rather than 1; in practice the test AUC may exceed this bound.

Some common thresholds and corresponding omission rates are as follows. If test data are available, binomial probabilities are calculated exactly if the number of test samples is at most 25, otherwise using a normal approximation to the binomial. These are 1-sided p-values for the null hypothesis that test points are predicted no better than by a random prediction with the same fractional predicted area. The "Balance" threshold minimizes 6 * training omission rate + .04 * cumulative threshold + 1.6 * fractional predicted area.

Cumulative threshold	Logistic threshold	Description	Fractional predicted area	Training omission rate	Test omission rate	P-value
1.000	0.007	Fixed cumulative value	0.175	0.000	0.174	1.739E-11
5.000	0.042	Fixed cumulative value	0.086	0.000	0.174	3.434E-17
10.000	0.088	Fixed cumulative value	0.054	0.014	0.217	3.945E-19
8.991	0.080	Minimum training presence	0.059	0.000	0.217	1.731E-18
34.579	0.474	10 percentile training presence	0.012	0.097	0.391	1.064E-21
18.866	0.179	Equal training sensitivity and specificity	0.028	0.028	0.261	3.045E-22
16.741	0.153	Maximum training sensitivity plus specificity	0.032	0.014	0.261	3.8E-21
1.016	0.007	Equal test sensitivity and specificity	0.174	0.000	0.174	1.583E-11
6.515	0.056	Maximum test sensitivity plus specificity	0.073	0.000	0.174	1.724E-18
2.217	0.017	Balance training omission, predicted area and threshold value	0.128	0.000	0.174	5.579E-14
13.054	0.117	Equate entropy of thresholded and non-thresholded distributions	0.042	0.014	0.217	5.607E-21

Pictures of the model

This is a representation of the Maxent model for culicifacies. Warmer colors show areas with better predicted conditions. White dots show the presence locations used for training, while violet dots show test locations. Click on the image for a full-size version.

Response curves

These curves show how each environmental variable affects the Maxent prediction. The curves show how the logistic prediction changes as each environmental variable is varied, keeping all other environmental variables at their average sample value. Click on a response curve to see a larger version. Note that the curves can be hard to interpret if you have strongly correlated variables, as the model may depend on the correlations in ways that are not evident in the curves. In other words, the curves show the marginal effect of changing exactly one variable, whereas the model may take advantage of sets of variables changing together.

In contrast to the above marginal response curves, each of the following curves represents a different model, namely, a Maxent model created using only the corresponding variable. These plots reflect the dependence of predicted suitability both on the selected variable and on dependencies induced by correlations between the selected variable and other variables. They may be easier to interpret if there are strong correlations between variables.

Analysis of variable contributions

The following table gives a heuristic estimate of relative contributions of the environmental variables to the Maxent model. To determine the estimate, in each iteration of the training algorithm, the increase in regularized gain is added to the contribution of the corresponding variable, or subtracted from it if the change to the absolute value of lambda is negative. As with the jackknife, variable contributions should be interpreted with caution when the predictor variables are correlated.

Variable	Percent contribution
bio_3	24.3
hwsd	19.8
bio_1	16.5
bio_19	11.7
bio_12	7.8
bio_15	6
bio_7	5.9
bio_4	2.3
bio_18	0.8
bio_2	0.8
h_slope	0.7
bio_17	0.7
h_flowacc	0.6
bio_14	0.5
h_topoind	0.4
alt	0.3
h_flowdir	0.2
bio_10	0.2
bio_11	0.1
h_aspect	0.1
bio_9	0
bio_8	0
bio_13	0
bio_16	0
bio_6	0
bio_5	0

The following picture shows the results of the jackknife test of variable importance. The environmental variable with highest gain when used in isolation is hwsd, which therefore appears to have the most useful information by itself. The environmental variable that decreases the gain the most when it is omitted is hwsd, which therefore appears to have the most information that isn't present in the other variables.

The next picture shows the same jackknife test, using test gain instead of training gain. Note that conclusions about which variables are most important can change, now that we're looking at test data.

Lastly, we have the same jackknife test, using AUC on test data.

Raw data outputs and control parameters

The data used in the above analysis is contained in the next links. Please see the Help button for more information on these.
The model applied to the training environmental layers
The coefficients of the model
The omission and predicted area for varying cumulative and raw thresholds
The prediction strength at the training and (optionally) test presence sites
Results for all species modeled in the same Maxent run, with summary statistics and (optionally) jackknife results

Regularized training gain is 3.285, training AUC is 0.995, unregularized training gain is 3.692.
Unregularized test gain is 2.130.
Test AUC is 0.936, standard deviation is 0.026 (calculated as in DeLong, DeLong & Clarke-Pearson 1988, equation 2).
Algorithm terminated after 500 iterations (27 seconds).

The follow parameters and settings were used during the run:
72 presence records used for training, 23 for testing.
10072 points used to determine the Maxent distribution (background points and presence points).
Environmental layers used: alt bio_1 bio_10 bio_11 bio_12 bio_13 bio_14 bio_15 bio_16 bio_17 bio_18 bio_19 bio_2 bio_3 bio_4 bio_5 bio_6 bio_7 bio_8 bio_9 h_aspect h_flowacc h_flowdir h_slope h_topoind hwsd(categorical)
Command line:
Feature types used: Linear Quadratic Hinge
Regularization multiplier is 1.0
Regularization values: linear/quadratic/product: 0.130 categorical: 0.250 hinge: 0.500
Species file is C:\Maxent\SEAsian_species\Culicifacies\culicifacies_17Sept2010.csv
Environmental variables from C:\Desktop_Garp\Garp\SEandCAsia
Output directory is C:\Maxent\SEAsian_species\Culicifacies\culicifacies_red_04167
Output format is Logistic
Output file type is .asc
Maximum iterations is 500
Convergence threshold is 1.0E-5
Random test percentage is 25
Jackknife selected
Remove duplicates selected
Make pictures selected
Create response curves selected