Interpretation of output

[Heiko]

Hello friends.

I am confused because I keep reading different interpretations of Maxent's output.

To understand why the new default is now "cloglog" I read Philipps et al. (2017): Opening the black box: an open-source release of Maxent.
I still didnt really grasp it. But they write: "[...] Maxent's default output scaling is a model of probability of presence".

But then in other papers (e.g. Guillera-Arroita et al. (2014): Maxent is not a presence-absence method. A comment on Thibaud et al. In: Methods Ecol Evol 5 (11), S. 1192–1197) they state:
"Maxent does not estimate probabilities" and "Here, we again emphasize that it is not possible to estimate occurrence probabilities from a PB data set and that hence the default logistic output does not represent probabilities either."

So now I am completely confused. Could somebody please tell me:

1) What is the exact definition of the logistic and the cloglog output and
2) What is the difference between those two.

I am not looking for a high profile mathematical explanation but rather for an ecological meaning behind the outcome.

Thank you so much!!

[Jamie M. Kass]

In addition to the paper (which I admit can be difficult to grasp with the first reading, and an elementary understanding of the underlying math), this updated tutorial provides some helpful language under the heading "Output formats":

http://biodiversityinformatics.amnh.org/open_source/maxent/Maxent_tutorial2017.pdf

I still think there is room for improvement though, and I think a discussion on the forum regarding interpretation of the new output and its relation to ecology is warranted.

Jamie

[Heiko]

Thank you Jamie.

They say "The default output is cloglog, which is the easiest to conceptualize: it gives an estimate between 0 and 1 of probability of presence."

Probability of presence. So that does not mean RELATIVE probability of presence right?
Other authors (see my initial post) seem to rigorously disagree.

If anyone with a deeper understanding of the math behind MaxEnt can comment on this, this would be highly appreciated.

Thank you!
Heiko

[Jamie M. Kass]

Heiko,

Yes, I see your point, and I agree that better (more accessible) documentation is needed here. I think that cloglog can be interpreted as probability of presence under certain assumptions. Whether we as modelers can make these assumptions in a valid way is, I think, the topic of debate. As no one has yet published any commentary on this approach, or used maxnet in a published application (to my knowledge), it’s hard to know how everyone in the field feels about it. I guess we can wait and see what others say. Until then, if you prefer to play it safe, the logistic transformation has a lot written about it, and it is more or less clear what the assumptions are (mainly, that prevalence is 0.5 throughout study extent unless you modify it — though it still remains a static prevalence across space). With either or these transformations, the goal is to be able to compare values across species, which is impossible with the raw values.

Jamie

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[Francisco Rodriguez Sanchez]

Hi,

I think the best way to understand the new statistical approach in Maxent is to read the papers by Renner & Warton, Fithian & Hastie, etc, that first analysed the relationship between Maxent and inhomogeneous point process models:

Warton, David I.; Shepherd, Leah C. Poisson point process models solve the “pseudo-absence problem” for presence-only data in ecology. Ann. Appl. Stat. 4 (2010), no. 3, 1383--1402. doi:10.1214/10-AOAS331. https://projecteuclid.org/euclid.aoas/1287409378

Fithian, William; Hastie, Trevor. Finite-sample equivalence in statistical models for presence-only data. Ann. Appl. Stat. 7 (2013), no. 4, 1917--1939. doi:10.1214/13-AOAS667. https://projecteuclid.org/euclid.aoas/1387823304

Renner, I. W. and Warton, D. I. (2013), Equivalence of MAXENT and Poisson Point Process Models for Species Distribution Modeling in Ecology. Biometry, 69: 274–281. https://doi.org/10.1111/j.1541-0420.2012.01824.x

Renner, I. W., Elith, J., Baddeley, A., Fithian, W., Hastie, T., Phillips, S. J., Popovic, G. and Warton, D. I. (2015), Point process models for presence-only analysis. Methods Ecol Evol, 6: 366–379. https://doi.org/10.1111/2041-210X.12352

Aarts, G., Fieberg, J. and Matthiopoulos, J. (2012), Comparative interpretation of count, presence–absence and point methods for species distribution models. Methods in Ecology and Evolution, 3: 177–187. https://doi.org/10.1111/j.2041-210X.2011.00141.x

If you don't want to get into too much statistical detail, the review by Renner et al. Methods Ecol Evol (2015) is probably one of the best introductions.

Hope this helps

Paco

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[Ahmed El-Gabbas]

Hello,

After about two years of the publication of the new maxent version, how should the cloglog prediction be interpreted? Do you think it can be (cautiously) interpreted as probability of occurrence?

This quote is from Maxent's tutorial: "The cloglog value corresponding to a raw value of r is 1-exp(-c·r).  .....   The default output is cloglog, which is the easiest to conceptualize: it gives an estimate between 0 and 1 of probability of presence.  Note that probability of presence depends strongly on details of the sampling design, such as the quadrat size and (for vagile organisms) observation time; cloglog output estimates probability of presence assuming that the sampling design is such that typical presence localities have an expected abundance of one individual per quadrat, which results in a probability of presence of about 0.63."

I think this assumption is hardly met or simply unknown using opportunistic sightings. I found some researches still interpret cloglog predictions as (relative) probability of occurrence (under some assumptions), do you think this makes sense?

Cheers,
Ahmed

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[Jamie M. Kass]

I think that if you can clearly explain why your study meets all the assumptions necessary, and you have a good understanding of point process models, you might be able to argue for interpretting your output as probability of presence. However, without absence data, this is generally difficult. Think about it this way. If I am modeling some general signal based on 1's and 0's with a logistic regression and I only have 1's, can I confidently say my result can predict the probability of finding a 1? Usually the answer is no, but point process models work a bit differently, and understanding this difference is key to making any such interpretations. If you are unsure or simply don't know if your system can meet these assumptions, the safest thing is to refer to the output as a relative occurrence rate (when using "raw" output for maxent.jar or "exponential" for maxnet after normalizing) or refer to cloglog or logistic transformations as an estimate of suitability. If that sounds vague to you, it is vague for a reason -- because we are assuming some or all assumptions have not been met to call it a probability of presence. But the results can still be useful, as long as our intepretation does not overextend itself.

Jamie Kass
JSPS Postdoctoral resesrcher, OIST
Okinawa, Japan