Checking Type Locations

Submitted by dylan on Mon, 2009-04-20 22:18.

Just Checking

```-- NAD27 to NAD83
echo 119d7\'4\"W 36d23\'13\"N | cs2cs +proj=latlong +datum=NAD27 +to +proj=latlong +datum=NAD83 -f "%.6f"
```
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Main Characterization and Monitoring Sites

Submitted by dylan on Tue, 2009-03-10 06:28.

Comparison of Slope and Intercept Terms for Multi-Level Model II: Using Contrasts

Submitted by dylan on Tue, 2009-02-17 04:43.

Premise

Small update to a similar thread from last week, on the comparison of slope and intercept terms fit to a multi-level model. I finally figured out (thanks R-Help mailing list!) how to efficiently use contrasts in R. The C() function can be called within a model formula, to reset the base level of an un-ordered factor. The UCLA Stats Library has an extensive description of this topic here. This approach can be used to sequentially test for differences between slope and intercept terms from a multi-level model, by re-setting the base level of a factor. See example data and figure below.

Note that the multcomp package has a much more robust approach to this type of operation. Details below.

Example Multi-Level Data

# need these
library(lattice)

# replicate an important experimental dataset
set.seed(10101010)
x <- rnorm(100)
y1 <- x[1:25] * 2 + rnorm(25, mean=1)
y2 <- x[26:50] * 2.6 + rnorm(25, mean=1.5)
y3 <- x[51:75] * 2.9 + rnorm(25, mean=5)
y4 <- x[76:100] * 3.5 + rnorm(25, mean=5.5)
d <- data.frame(x=x, y=c(y1,y2,y3,y4), f=factor(rep(letters[1:4], each=25)))

# plot
xyplot(y ~ x, groups=f, data=d,
auto.key=list(columns=4, title='Beard Type', lines=TRUE, points=FALSE, cex=0.75),
type=c('p','r'), ylab='Number of Pirates', xlab='Distance from Land')

Example Multi-Level Model II

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Aggregating Soil Survey Information: Available Water Holding Capacity

Submitted by dylan on Sat, 2009-01-31 23:53.

4km Grid of AWC: generated using PostGIS/GRASS, based on USDA-NCSS SSURGO data.

Horizon thickness-weighted mean AWC (available water holding capacity), aggregated to a 4km grid, based on the detailed (SSURGO) soil survey database. Each grid cell is the component percentage / area fraction weighted mean of profile AWC. The variation in AWC tracks several important parent material induced patterns: with lower AWC in residual soils formed on steep granitic terrain (south flank of Sierra Nevada), and higher AWC in residual soils formed on the gentler slopes of meta-volcanic and meta-sedimentary terrain (central and northern flanks of Sierra Nevada). The higher AWC values one the east side of the San Joaquin Valley correspond with the characteristically finer soils formed from coast range alluvium. High AWC values of the Sacramento Valley correspond with the fine textured soils derived from a mixture of coast range alluvium, and meta-volcanic/sedimentary alluvium from the Sierra Nevada.

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Scaling Soil Survey

Submitted by dylan on Sat, 2009-01-31 20:56.

Background and Justification

Comparison of Slope and Intercept Terms for Multi-Level Model

Submitted by dylan on Thu, 2009-01-29 18:23.

Premise

When the relationship between two variable is (potentially) dependent on a third, categorical variable ANCOVA (analysis of covariance), or some variant, is commonly used. There are several approaches to testing for differences in slope/intercepts (in the case of a simple linear model) between levels of the stratifying variable. In R the following formula notation is usually used to test for interaction between levels of a factor (f) and the relationship between two continuous variables x and y: y ~ x * f. A simple graphical exploration of this type of model can be done through examination of confidence intervals computed for slope and intercept terms, for each level of our grouping factor (f). An example of a fictitious dataset is presented below. Note that this a rough approximation for testing differences in slope/intercept within a multi-level model. A more robust approach would take into account that we are trying to make several pair-wise comparisons, i.e. something akin to Tukey's HSD. Something like this can be done with the multcomp package. For any real data set you should always consult a real statistician.

Example Multi-Level Model: each panel represents a model fit to y ~ x, for group f

Example Multi-Level Data

# need this for xyplot()
library(lattice)

# make some fake data:
x <- rnorm(100, mean=3, sd=6)
y <- x * runif(100, min=1, max=7) + runif(100, min=1.8, max=5)
d <- data.frame(x, y, f=rep(letters[1:10], each=10))

# check it out
xyplot(y ~ x | f, data=d, type=c('p','r'))

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Some Ideas on Interpolation of Categorical Data

Submitted by dylan on Thu, 2009-01-15 04:36.

Premise

Wanted to make something akin to an interpolated surface for some spatially auto-correlated categorical data (presence/absence). I quickly generated some fake spatially auto-correlated data to work with using r.surf.fractal in GRASS. These data were converted into a binary map using an arbitrary threshold that looked about right-- splitting the data into something that looked 'spatially clumpy'.

Fig. 1: Simulated auto-correlated, categorical variable, with sampling points and derived voronoi polygons.

I had used voronoi polygons in the past to display connectivity of categorical data recorded at points, even though sparsely sampled areas tend to be over emphasized. Figure 1 shows the fake spatially auto-correlated data (grey = presence /white = not present), sample points (yellow boxes), and voronoi polygons. The polygons with thicker, red boundaries represent the "voronoi interpolation" of the categorical feature.

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Submitted by dylan on Tue, 2008-12-30 02:45.

Found some interesting material today, mostly related to evaluation of statistical tests and such.

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Python Image Module Example: How much ink on that page?

Submitted by dylan on Fri, 2008-12-26 21:26.

Premise:
Thought it would be fun to compute how much ink a given poster requires, per unit area of paper, when sending to the department large-format printer. The Python Imaging Library provides several modules suitable for low-level operation on image data. A simple (and probably very inefficient) script was developed to compute the white/black percentage of an image. A script like this could be used to adjust a per-poster "ink cost", which would hopefully prevent people from wasting ink. Obviously, this computation is scale-dependent, so standardized rasterization parameters would have to be set in order for the "ink cost" calculation to be fair. More generalized or efficient approaches are always welcomed.

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Characterization of Terrain Shape, Microclimate, and Canopy Cover

Submitted by dylan on Thu, 2008-12-18 21:26.
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