Autocorrelation in GAM and GRASP

Autocorrelation in GAM and GRASP models is an important topic of discussion since these models are being widely used in predictive animal and plant distribution models in the discipline of ecology.

The most widely used statistical models in the fields of ecological modeling, biodiversity and conservation are Generalized Linear Models (GLM) and GAM (General Additive Model) which is a semi-parametric extension of GLM. GRASP stands for Generalized Regression Analysis and Spatial Prediction (http://www.cscf.ch/grasp/grasp-s/welcome.html). GRASP is a combination of advanced S Plus functions and GIS (Geographical Information System) Many of these applications can be run through the software “R” (www.r-project.org).

What is Autocorrelation?

Autocorrelation describes correlation between a process, say Xt, at a different point of time Xs. The autocorrelation function can be depicted in a formula as

where Xt has the variance σ2 and mean μ. E is the expected value. The result will range between -1 and 1. 1 indicates perfect correlation while -1 indicates perfect anti-correlation. You must note that the function should be well defined.

If you use time series data in regression analysis, autocorrelation of residuals will be a problem area, since it will lead to an upward bias in the statistical significance of coefficient estimates. A Durbin Watson test can be used to detect the presence of autocorrelation. You can use Durbin’s h statistic, if your explanatory variables include a lagged dependent variable. To avoid autocorrelation related problems you may use differencing of data and lag structures in estimation. (http://en.wikipedia.org/wiki/Autocorrelation)

Biogeographical Predictions of Distributions of Species

Biographical predictions of distribution of species are very important in assessing the impact of changing environmental conditions on the distribution of species, eco systems and natural communities. Many of the statistical models ignore the important issues related to the distribution of species like spatial autocorrelation, dispersal and migration, and biotic and environmental interactions. When modeling spatial distribution of species following the things should be taken into consideration (GLF+06).

1. Links with ecological theory
2. Incorporation of spatial concept
3. Optimal use of artificially generated data and existing data
4. Integration of environmental and ecological interactions
5. Prediction of errors and uncertainties and
6. Prediction of the distribution of communities

In most of the spatial analyses, spatial autocorrelation is an important source of bias. Although GAM, CTA and GLM models are vulnerable to spatial autocorrelation the performance of GAM and CTA models are better. The reliability of niche modeling can be improved if certain procedures and techniques, such as ‘null model approach,’ are taken into consideration during the modeling process (SAK06).

GRASP Versions

The R version shares the basic idea and architecture of the S Plus version, but has evolved independently in ways specific to the R environment. Both the versions are made available for free to promote the use of spatial predictions in environmental management and other niche modeling.

The Need for Robust Distribution Models

You need robust species’ distribution models and documentation in order to predict the effects of changing environmental conditions on biological communities and ecosystems. Autocorrelation in GAM and GRASP models should be considered seriously. An improved collaborative effort between theoretical and functional ecologists, ecological modelers and statisticians is needed to make better distribution models.

References

GLF+06 – Making better biogeographical predictions of species’ distributions by ANTOINE GUISAN, ANTHONY LEHMANN, SIMON FERRIER, MIKE AUSTIN, JACOB MC. C. OVERTON, RICHARD ASPINALL and TREVOR HASTIE Journal of Applied Ecology
Volume 43 Page 386 – June 2006, (http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2664.2006.01164.x)

SAK06 – Consequences of spatial autocorrelation for niche-based models, P. SEGURADO, M. B. ARAÚJO and W. E. KUNIN, Journal of Applied Ecology, Volume 43 Page 433 – June 2006. (http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2664.2006.01162.x).