Inferential Permutation Tests for Maximum Entropy Models

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Description

maxent.test performs the permutation tests proposed by Shipley (2010) for maximum entropy models. Two different null hypotheses can be tested: 1) the information encoded in the entire set of constraints C is irrelevant for predicting the probabilities, and 2) the information encoded in subset B of the entire set of constraints C = {A U B} is irrelevant for predicting the probabilities. A plot can be returned to facilitate interpretation.

Usage

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maxent.test(model, obs, sub.c, nperm = 99, quick = TRUE,
alpha = 0.05, plot = TRUE)

Arguments

model

list returned by maxent.

obs

vector, matrix or data frame of observed probabilities of the states (columns).

sub.c

character or numeric vector specifying the subset of constraints B associated with null hypothesis 2. If missing, null hypothesis 1 is tested.

nperm

number of permutations for the test.

quick

if TRUE, the algorithm stops when alpha is outside the confidence interval of the P-value. Can be useful to speed up the routine.

alpha

desired alpha-level for the test. Only relevant if quick is TRUE.

plot

if TRUE, a plot is returned to facilitate interpretation.

Details

maxent.test is a direct translation of the permutation tests described by Shipley (2010). Please refer to this article for details.

Using quick = FALSE will return the true null probability for a given nperm. However, if nperm is large (a rule-of-thumb is >=999 permutations for allowing inference at alpha = 0.05), this can take a very long time. Using quick = TRUE is a much faster and highly recommended alternative if one is only interested in accepting/rejecting the null hypothesis at the specified alpha-level given by argument alpha.

If maxent was run with multiple data sets (i.e. if constr had more than one row), then maxent.test performs the test for all sets simultaneously, following the ‘omnibus’ procedure described by Shipley (2010).

The following measure of fit between observed and predicted probabilities is returned:

fit = 1 - (sum(o_ij - p_ij)^2 / sum(o_ij - q_ij)^2)

where o_ij, o_ij, and q_ij are the observed, predicted and prior probabilities of state i from data set j, respectively, S is the number of states, and D the number of data sets (i.e. rows in obs). A value of 1 indicates perfect predictive capacity, while a value near zero indicates that the constraints provide no additional information beyond what is already contained in the prior q (Sonnier et al. 2009).

Value

fit

measure of fit giving the predictive ability of the entire set of constraints C, beyond that already provided by the prior distribution.

fit.a

measure of fit giving the predictive ability of the subset of constraints A, beyond that already provided by the prior distribution; only returned if sub.c is specified

r2

Pearson r^2 between observed and predicted probabilities, using the entire set of constraints C

r2.a

Pearson r^2 between observed and predicted probabilities, using the subset of constraints A; only returned if sub.c is specified

r2.q

Pearson r^2 between observed and prior probabilities; only returned when sub.c is missing

obs.stat

observed statistic used for the permutation test; see Shipley (2010)

nperm

number of permutations; can be smaller than the specified nperm when quick is TRUE

pval

P-value

ci.pval

approximate confidence intervals of the P-value

Warning

maxent.test is a computationally intensive function. The tests can take a very long time when nperm is large and quick = FALSE. It is highly recommended to use quick = TRUE because of this, unless you are interested in obtaining the true null probability.

Author(s)

Etienne Laliberté etiennelaliberte@gmail.com

http://www.elaliberte.info

References

Sonnier, G., Shipley, B., and M. L. Navas. 2009. Plant traits, species pools and the prediction of relative abundance in plant communities: a maximum entropy approach. Journal of Vegetation Science in press.

Shipley, B. (2010) Inferential permutation tests for maximum entropy models in ecology. Ecology in press.

See Also

maxent to run the maximum entropy model that is required by maxent.test.

Another faster version of maxent.test for multicore processors called maxent.testMC is available from Etienne Laliberté (etiennelaliberte@gmail.com). It's exactly the same as maxent.test but makes use of the multicore, doMC, and foreach packages. Because of this, maxentMC only works on POSIX-compliant OS's (essentially anything but Windows).

Examples

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# example with tussock dataset
traits <- tussock$trait[, c(2:7, 11)] # use only continuous traits
traits <- na.omit(traits) # remove 2 species with NA's
abun <- tussock$abun[, rownames(traits)] # abundance matrix
abun <- t(apply(abun, 1, function(x) x / sum(x) )) # relative abundances
agg <- functcomp(traits, abun) # community-aggregated traits
traits <- t(traits) # transpose matrix

# run maxent on site 1 (first row of abun), all species
pred.abun <- maxent(agg[1,], traits)

## Not run: 
# do the constraints give predictive ability?
maxent.test(pred.abun, obs = abun[1,], nperm = 49)

# are height, LDMC, and leaf [N] important constraints?
maxent.test(pred.abun, obs = abun[1,], sub.c = c("height",
"LDMC", "leafN"), nperm = 49)

## End(Not run)