Interpreting percent contribution vs lamba of optimal model in ENMeval

[Jane Anderson]

I'm confused on the interpretation of the percent contribution and lambdas of the feature classes in the optimal model (based on AICc = 0). I understand from the ENMeval vignette that the feature classes with lambda = 0 were not used in the optimal model. However, these feature classes still have a contribution? I'm unclear how that is possible if they were not used. One of my variables (Bio15) shows a 20% contribution, despite a lambda = 0. I really appreciate any insight or help anyone can offer!

> var.importance(Csaic.opt)

  variable percent.contribution permutation.importance

1   bio_11               3.3285                 0.4957

2   bio_12              13.9899                39.1823

3   bio_13               2.3037                16.3896

4   bio_14               0.6292                 0.0000

5   bio_15              20.6543                 0.0000

6   bio_18              51.4599                43.9324

7   bio_19               4.7034                 0.0000

8    bio_3               0.1377                 0.0000

9    bio_6               2.7934                 0.0000

> Csaic.opt@lambdas

 [1] "bio_11, 1.5721085363948009, 167.360000610352, 275.959991455078"

 [2] "bio_12, -15.386469845576093, 134.279998779297, 4122.2001953125"

 [3] "bio_13, 10.925711186656258, 55.4000015258789, 1139.16003417969"

 [4] "bio_14, 1.4799199554384825, 0.0, 73.5999984741211"             

 [5] "bio_15, 0.0, 30.0400009155273, 175.320007324219"               

 [6] "bio_18, 8.554906989476683, 17.0, 768.760009765625"             

 [7] "bio_19, 0.0, 0.0, 2803.56005859375"                            

 [8] "bio_3, -0.45630754720573957, 51.136360168457, 83.5199966430664"

 [9] "bio_6, 0.0, 98.6800003051758, 226.850006103516"                

[10] "linearPredictorNormalizer, 7.927417524185016"                  

[11] "densityNormalizer, 15.642019759272474"                         

[12] "numBackgroundPoints, 10078"                                    

[13] "entropy, 8.298090207214834"   

[Jamie M. Kass]

The percent contribution statistics measures what the contribution of each variable is at every iteration of model building. Maxent builds lots of models during its learning process and only keeps variables that resist regularization (i.e., shrinkage of coefficient to 0) until the very end of model building. While this process is happening, the contribution of each variable to each model is recorded. That’s why you can see a positive contribution for variables with lambda of 0. The “variable importance” stat is different. It builds models with and without that variable many times and evaluates the results to calculate “importance”. You can find details about these in the Maxent tutorial on the American Museum of Natural History Maxent website.

Jamie Kass
PhD Candidate
City College of NY

[Jane Anderson]

That makes sense. Thanks so much, I really appreciate it!

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C. Jane Anderson, Ph.D.

www.ecojane.org