Inference and Model Fitting for Spatial Point Process
(back to Bert Loosmore's home page)
This page details my research related to improving how spatial point process statistics are used in ecological research. Part of this work was for my Master's thesis, but additional research is continuing. Our results so far have been published as:
Loosmore, N. B. and Ford, E.D. (2006) Statistical Inference Using the G or K Point Pattern Spatial Statistics. Ecology 87, 1925-1931.
Exploration of spatial point patterns can potentially provide information about underlying processes of establishment and competition. However, we need to move beyond merely testing observed patterns against CSR and progress to more informative model fitting. In summary, this work is about developing numerical methods for inference and model fitting. While some analytical approaches exist (such as psuedolikelihood methods), as of yet they are only available for certain classes of models. Numerical approaches should allow for more generic spatial models to be evaluated.
If you use my script, or have any questions or comments, please e-mail me (nhl `at' u.washington.edu) about it! I'm obviously interested in what people are doing for spatial point pattern analysis.
Files and Resources:
The R script for using the CEDL method (version 1.0) for the G and K/L point pattern statistics, and a user's guide (*.pdf).
My short page about the wind river canopy crane data set.
Areas of Current Research (started 5/17/07):
These are things that I'm currently working on and hope to release a new version of the script soon!
- adding a t_{min} parameter and a 'wrapper' function to deal with larger data sets (done 5/22/07 - see test code below)
- evaluating if the total rss can be used as a method to assess model fit
- investigating how to make the code run faster, especially for large data sets
- fixing outstand bug requests (please e-mail me if you have any!)
- adding some simple error checking
- what is the proper distance range to use when evaluating an observed pattern?
- allowing rectangular (and other?) data sets to be evaluated
- enhance the capability to generate other types of patterns, maybe by passing a reference to the appropriate function?
The following code is test code only! Please use with caution, and contact me with any questions. It contains partial and not fully tested implementations of some of these improvements.
- Version 1.02 for using the CEDL method, which implements the t_{min} parameter (see below) for the K statistic. Updated release notes.
- Version 1.01 for using the CEDL method, which implements the t_{min} parameter for the G statistic. The purpose here is two fold, first one might want to only test a null hypothesis over a certain range of distances, and second, it allows a method to process large pattern one section of distances at a time. See the release notes for a more complete description of changes. (last updated 5/20/07)
Areas of Future Research:
- more work to identify what scale means and how to best detect it.
- more research into the differences between the G and K statistics and where each is most applicable.
- a simulation study to evaluate power as a function of the point intensity. How many points of a given pattern are needed to adequately detect it?
- understanding the ramifications of using different values for $t_{max}$ for the G and K statistics.
- more exploration of the use of the $c$ and $w(t)$ parameters for variance stabilization.
- implementation for the F statistic and plots of non unit square shapes, sizes
- optimize code and submit as a package to CRAN
QERM 550 Lectures:
- Spring quarter 2007 lecture about general MC simulations methods.
- Spring quarter 2005 lecture about making inference when using point pattern statistics.