Assess Predictor Importance and Quantify Model Significance in a Fitted Generalized Dissimilarity Model.

This function uses matrix permutation to perform model and predictor significance testing and to estimate predictor importance in a generalized dissimilarity model. The function can be run in parallel on multicore machines to reduce computation time.

Usage

gdm.varImp(spTable, geo, splines = NULL, knots = NULL,
predSelect = FALSE, nPerm = 50, pValue=0.05, parallel = FALSE, cores = 2,
sampleSites = 1, sampleSitePairs = 1, outFile = NULL)

Arguments

spTable

A site-pair table, same as used to fit a gdm.

geo

Similar to the gdm geo argument. The only difference is that the geo argument does not have a default in this function.

splines

Same as the gdm splines argument. Note that the current implementation requires that all predictors have the same number of splines.

knots

Same as the gdm knots argument.

predSelect

Set to TRUE to perform predictor selection using matrix permutation and backward elimination. Default is FALSE. When predSelect = FALSE results will be returned only for a model fit with all predictors.

nPerm

Number of permutations to use to estimate p-values. Default is 50.

pValue

The p-value to use for predictor selection / elimination. Default is 0.05.

parallel

Whether or not to run the matrix permutations and model fitting in parallel. Parallel processing is highly recommended when either (i) the nPerms argument is large (>100) or (ii) a large number of site-pairs (and / or variables) are being used in model fitting (note computation demand can be reduced using subsampling - see next arguments). The default is FALSE.

cores

When the parallel argument is set to TRUE, the number of cores to be registered for parallel processing. Must be <= the number of cores in the machine running the function. There is no benefit to setting the number of cores greater than the number of predictors in the model.

sampleSites

The fraction (0-1, though a value of 0 would be silly, wouldn't it?) of sites to retain from the full site-pair table. If less than 1, this argument will completely remove a fraction of sites such that they are not used in the permutation routines.

sampleSitePairs

The fraction (0-1) of site-pairs (i.e., rows) to retain from the full site-pair table - in other words, all sites will be used in the permutation routines (assuming sampleSites = 1), but not all site-pair combinations. In the case where both the sampleSites and the sampleSitePairs argument have values less than 1, sites first will be removed using the sampleSites argument, followed by removal of site-pairs using the sampleSitePairs argument. Note that the number of site-pairs removed is based on the fraction of the resulting site-pair table after sites have been removed, not on the size of the full site-pair table.

outFile

An optional character string to write the object returned by the function to disk as an .RData object (".RData" is not required as part of the file name). The .RData object will contain a single list with the name of "outObject". The default is NULL, meaning that no file will be written.

Value

A list of four tables. The first table summarizes full model deviance, percent deviance explained by the full model, the p-value of the full model, and the number of permutations used to calculate the statistics for each fitted model (i.e., the full model and each model with predictors removed in succession during the backward elimination procedure if predSelect=T). The remaining three tables summarize (1) predictor importance, (2) predictor significance, and (3) the number of permutations used to calculate the statistics for that model, which is provided because some GDMs may fail to converge for some permutations / predictor combinations and you might want to know how many permutations were used when calculating statistics. Or maybe you don't, you decide.

Predictor importance is measured as the percent decrease in deviance explained between the full model and the deviance explained by a model fit with that predictor permuted. Significance is estimated using the bootstrapped p-value when the predictor has been permuted. For most cases, the number of permutations will equal the nPerm argument. However, the value may be less should any of the models fit to them permuted tables fail to converge.

If predSelect=FALSE, the tables will have values only in the first column.

Details

To test model significance, first a model is fit using all predictors and un-permuted environmental data. Any predictor for which the sum of the I-spline coefficients sum to zero is preemptively removed. Next, the environmental data are permuted nPerm times (by randomizing the order of the rows) and a GDM is fit to each permuted table. Model significance is determined by comparing the deviance explained by GDM fit to the un-permuted table to the distribution of deviance explained values from GDM fit to the nPerm permuted tables. To assess predictor significance, this process is repeated for each predictor individually (i.e., only the data for the predictor being tested is permuted rather than the entire environmental table). Predictor importance is quantified as the percent change in deviance explained between a model fit with and without that predictor permuted. If predSelect=TRUE, this process continues by next permutating the site-pair table nPerm times, but removing one predictor at a time and reassessing predictor importance and significance. At each step, the least important predictor is dropped (backward elimination) and the process continues until all non-significant predictors are removed, with significance level being set by the user and the pValue argument.

References

Ferrier S, Manion G, Elith J, Richardson, K (2007) Using generalized dissimilarity modelling to analyse and predict patterns of beta diversity in regional biodiversity assessment. Diversity & Distributions 13, 252-264.

Fitzpatrick, MC, Sanders NJ, Ferrier S, Longino JT, Weiser MD, and RR Dunn. 2011. Forecasting the Future of Biodiversity: a Test of Single- and Multi-Species Models for Ants in North America. Ecography 34: 836-47.

Author

Matt Fitzpatrick and Karel Mokany

Examples

##fit table environmental data
##set up site-pair table using the southwest data set
sppData <- southwest[c(1,2,13,14)]
envTab <- southwest[c(2:ncol(southwest))]
sitePairTab <- formatsitepair(sppData, 2, XColumn="Long", YColumn="Lat",
sppColumn="species", siteColumn="site", predData=envTab)
#> Warning: No abundance column was specified, so the biological data are assumed to be presences.
#> Aggregation function missing: defaulting to length

## not run
#modTest <- gdm.varImp(sitePairTab, geo=T, nPerm=50, parallel=T, cores=10, predSelect=T)
#barplot(sort(modTest$`Predictor Importance`[,1], decreasing=T))