# Statistical analyses for survey against raster?

I am somewhat of a newbie to geostatistical analyses, but pretty familiar with GIS and remote sensing packages. I was wondering if anyone had suggestions on appropriate geostatistical analyses for a particular data set. The data set consists of a large-scale survey at the land plot level consisting of questions related to political participation (an ordinal scale), and raster data from a binary landcover classification of forest cover. The survey data I am envisioning joining to a .shp file of landplot boundaries. I had wondered about either converting the vector to raster and analyzing raster against raster, or converting the landsat landcover map into a vector and analyzing vector x vector.

The research question is whether political participation (potentially plus other variables) affects the presence of forest cover. What I´m imagining is some sort of multivariate linear regression in terms of the survey data, but when it comes to adding in the values from the raster I´m somewhat stymied. In doing some background research on potential approaches, it seems like looking at discrete variation might be the way to go.

I´m using ArcGIS 10 and Erdas 2011.

• I am curious to know the underlying theory. Do you mean to suggest something like voting for the Green Party causes a tree to grow? Maybe each vote for a Communist kills a kitten, too... – whuber Jul 30 '12 at 15:18

To begin with, I would recommend raster-based analysis. Remote sensing data such as NLCD is notorious for being problematic in simple and multiple linear regression (e.g. data distribution, unrealistic p-values due to large n, etc). Alternatively, there are powerful nonparametric regression methods, such as randomForest that can be used with unruly remote sensing and mixed, ordinal datasets

You can analyze a scenario like what you described by using a Fishnet (Data Management) and Zonal Statistics as Table (Spatial Analyst) in ArcGIS 10. For example, the attached image shows a raster of binary burn data and a 1 acre fishnet in blue. This analysis also required precipitation, elevation, and various site indices--all of which were raster data. These predictors then can be used to form a regression equation along with the response variable, which happened to be binary tree cover data. Here is a stepwise example to help generate some ideas for you:

1. Create a fishnet (Data Management) over your area of interest taking into account your scale of interest (e.g. for land cover datasets, 1 ac cells are common)
2. Convert any vector data to raster data.
3. Use Zonal Statistics as Table (Spatial Analyst) to calculate, for example, the mean pixel value within the fishnet cells.
4. Repeat Zonal stats until your response and predictors have all been analyzed and tables have been produced for each.
7. Export the fishnet attribute table to a .csv
8. Using a statistical package that can handle nonparametric regression (in this case R), read in the .csv
9. Run randomForest in stats package.

Here is some simple code in R that might help:

``````# Random Forest regression
require(randomForest) 