You should still remove all the variables that a highly correlated. r>0.7 is a good start.  

If you are using R, why not try to find the best model using "AIC (package name: AICcModavg)". You could test the possible different combinations of the remaining Bioclimatic variables (as predictor variables) and come up with the best model. You could further evaluate your model and check the AUC values.. 

You should be able to drop some predictors after this. That is if you haven't already done this.

First of all, what specific type of model you are planning on using? Nelson made a good suggestion. You can also use ‘rattle’ package of R to run and validate spatial models.

My suggestion would be do your SDM using, GIS (ArcGis or GRASS), GME for populating a evenly spaced grid with the environmental and species values ( geographical modeling environment, google for download), and run your models using the salford machine learning suite. If you use their implementation of TreeNet or Random Forests, then you do not have to worry about autocorrelation and the algorithm will handle interactions for you. You can even tell it to allow all interactions or just a certain number, you could also penalize them. Then you could easily run your model on all 19 variables. Just after Breiman and the idea of many weak learners  make a good model.  http://projecteuclid.org/euclid.ss/1009213726

Indeed the more variables you use, the higher the AUC. However, above a few variables (1-3)  any additional value only marginally increases the AUC as can be nicely seen in the Jackknife graphs included in the maxent package. However, adding 20 or so additional variables to the best one-three may raise the AUC with 0.05-0.

The simplest and most elegant way to eliminate highly correlated  variables is the hierarchical, stepwise maxent SDM approach as in attached.

Multi-collinearity tests (VIF; Spearman's rank) can be performed on continuous variable and Chi-square on categorical ones to eliminate highly correlated variables. Indeed (bio)climate variables may be highly correlated among each other and with, for example, elevation. However, the issue is which of the two highly correlated variable to remove a prioiri from the SDM.

In case you use GML I may have other hints (ROC) and references.

Please also consider the inherent double bias in the WorldClim data; in effect extrapolations from non- randomly situated weather stations and a non-random selection from the among weather stations (see attached)

hope it helps

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Thanks for the tips Hein. For now i use MaxEnt but i wll try more models to see differences on the performance.

Hello,

When variables are correlated, I generally remove one of a pair where the correlation is higher than 0.7 (trying to evaluate which is the variable that makes less biological sense or that relates less with the species distribution).

Additionally, to evaluate the contribution of each variable separately, I test all the variables individually and keep only those with a p

Hi,

If you actually mean spatial autocorrelation, none of the above deals with spatial dependence.

I think you mean multicollinearity between your predictors. One way to deal with the collinearity is to perform a PCA on your predictors and use the components as your predictors in your model. See http://dx.plos.org/10.1371/journal.pone.0080724.g002

If you want to deal with spatial autocorrelation, then you would need to check your residuals. You can perform a Global Moran's I or Geary's C on them. If there is spatial autocorrelation that would mean you are missing an important underlying process.  

Take care

Robby

I completely agree with Robby R Marrotte. Your question is about collinearity between predictors, not autocorrelation between sampled points and PCA  is a good method to remove collinearity. Any threshold is arbitrary so you should motivate why you used 0.7 instead of 0.69 or 0.71 or 0.8, etc. With PCA components you can consider all the variability of your environment without collinearity problems.

Thanks Robby and Maurizio. PCA is what i will use for the WORLDCLIM dataset.

For the autocorellation of the presence data, what i do is an occurence thinner / remove duplicate records from same pixels.

All data (18000 records) are from literature georeferenced locations.

Another vote for Robby R. Marrotte's answer. Using PCA scored as predictors is a nice way to deal with highly correlated variables (as often is the case in climatic data). Often, I also find that it's fairly easy to look at the variable component loadings to interpret the "new" PCA variable. For example, PC1 might load heavily with temperature variables, whereas PC2 might be reflective of precipitation or moisture (precip*temp) variables, PC3 might be seasonality in temperature, etc. This can usually be figured out simply by looking at the component loadings.

Since you brought up spatial autocorrelation, if you haven't yet, it's essential that you look at the spatial autocorrelation in your data to determine best practice for cross-validation of the models. If your data are highly spatially autocorrelated, you're going to find that random data-split cross-validations will give you highly optimistic error estimates. There are many easy ways to check this, including Moran's I, variograms, etc. It's a critical step if you want a reliable error estimate (e.g. AUC).

Hi,  

I'm currently trying to use Maxent for roadkill analysis, but one of my colleagues raised a question that using spatially correlated datasets in maximum entropy models leads to biased results and the dataset should be tested and correlated occurrences removed.

I have no clue how to test roadkill point dataset for spatial autocorrelation to get rid of correlated points. What's the easiest and the most common way to determine which points need to be removed to avoid the bias? 

If you know / have any information / articles / website for me to look over, please advise on this. 

Your direct advise to solve this issue is greatly appreciated. 

Best,

Bryan