This page contains some analysis of the Maxent model for Esox_americanus, created Fri Sep 09 23:47:19 EDT 2011 using Maxent version 3.3.3e. If you would like to do further analyses, the raw data used here is linked to at the end of this page.

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 0.881 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 | 0.031 | Fixed cumulative value 1 | 0.594 | 0.002 | 0.000 | 1.145E-17 |

5.000 | 0.099 | Fixed cumulative value 5 | 0.405 | 0.014 | 0.067 | 1.601E-28 |

10.000 | 0.165 | Fixed cumulative value 10 | 0.300 | 0.045 | 0.105 | 1.09E-40 |

0.311 | 0.013 | Minimum training presence | 0.691 | 0.000 | 0.000 | 3.688E-12 |

17.502 | 0.270 | 10 percentile training presence | 0.214 | 0.100 | 0.171 | 2.365E-53 |

24.359 | 0.354 | Equal training sensitivity and specificity | 0.167 | 0.166 | 0.219 | 4.005E-64 |

16.866 | 0.261 | Maximum training sensitivity plus specificity | 0.220 | 0.093 | 0.162 | 4.127E-53 |

19.310 | 0.293 | Equal test sensitivity and specificity | 0.200 | 0.121 | 0.200 | 1.335E-53 |

16.150 | 0.252 | Maximum test sensitivity plus specificity | 0.226 | 0.090 | 0.143 | 4.083E-54 |

3.443 | 0.077 | Balance training omission, predicted area and threshold value | 0.456 | 0.010 | 0.038 | 1.121E-25 |

9.248 | 0.153 | Equate entropy of thresholded and original distributions | 0.313 | 0.045 | 0.105 | 2.999E-38 |

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.

The following table gives estimates of relative contributions of the environmental variables to the Maxent model. To determine the first 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. For the second estimate, for each environmental variable in turn, the values of that variable on training presence and background data are randomly permuted. The model is reevaluated on the permuted data, and the resulting drop in training AUC is shown in the table, normalized to percentages. As with the variable jackknife, variable contributions should be interpreted with caution when the predictor variables are correlated.

Variable | Percent contribution | Permutation importance |
---|---|---|

drainsize | 34.3 | 38 |

wetland | 17.1 | 4.7 |

gradient | 14.9 | 23.6 |

rivbasin | 6.1 | 4.8 |

geology | 4.3 | 4 |

pctdist | 4.2 | 5.7 |

strahler | 3.9 | 0.7 |

velocity | 3.6 | 0.5 |

sinuosity | 2.9 | 2.8 |

pasture | 2.7 | 4.1 |

flow | 2 | 2.8 |

forest | 1.4 | 1.7 |

cropland | 1.2 | 2.9 |

barren | 0.7 | 1.3 |

imperv | 0.5 | 1.2 |

shrub | 0.2 | 1.2 |

The data used in the above analysis is contained in the next links. Please see the Help button for more information on these.

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 1.187, training AUC is 0.906, unregularized training gain is 1.354.

Unregularized test gain is 1.218.

Test AUC is 0.887, standard deviation is 0.013 (calculated as in DeLong, DeLong & Clarke-Pearson 1988, equation 2).

Algorithm terminated after 500 iterations (22 seconds).

The follow settings were used during the run:

421 presence records used for training, 105 for testing.

10328 points used to determine the Maxent distribution (background points and presence points).

Environmental layers used: barren cropland drainsize flow forest geology(categorical) gradient imperv pasture pctdist rivbasin(categorical) shrub sinuosity strahler(categorical) velocity wetland

Regularization values: linear/quadratic/product: 0.050, categorical: 0.250, threshold: 1.000, hinge: 0.500

Feature types used: product linear quadratic hinge threshold

responsecurves: true

outputdirectory: D:\MaxEnt_Fish_NC\StatewideOutput

samplesfile: D:\MaxEnt_Fish_NC\SWEOPoints\SW_AllEO_20.csv

environmentallayers: D:\MaxEnt_Fish_NC\SWEnvRaster

randomtestpoints: 20

Command line used:

Command line to repeat this species model: java density.MaxEnt nowarnings noprefixes -E "" -E Esox_americanus responsecurves outputdirectory=D:\MaxEnt_Fish_NC\StatewideOutput samplesfile=D:\MaxEnt_Fish_NC\SWEOPoints\SW_AllEO_20.csv environmentallayers=D:\MaxEnt_Fish_NC\SWEnvRaster randomtestpoints=20 -t geology -t rivbasin -t strahler