Week 7 In-Class Exercises, Pattern analysis Pt II

Comparing point patterns
This exercise will introduce functions found in the Geostatistical Analyst toolbar.

Introduction

The lab is organized around the following question in the Callalli data:

We know that obsidian is found about 15 km to the southwest of the area, but that chert cobbles are found in the local geology and the cobbles can be found in streambeds. We noted during fieldwork that chert artifacts are commonly found along the banks of the streams where there appeared to have been chert tool manufacture occurring. Obsidian appeared to be primarily located in discrete deposits that were imported from the source region.

On the principal of least effort we might expect that larger artifacts, particularly cores and concentrations of flakes, would be encountered close to the rivers in the case of chert but not in the case of obsidian. We could structure this in terms of hypothesis testing (H0: no relationships between weight of artifacts and proximity to streams; H1: concentrations of heavy chert artifacts are found in proximity to streams). However, a visual exploration of the relationship is also informative.

PART I. Point pattern exploration tools

• Download Lithics_Lab2_AllArchID.zip
• Unzip, add to project
  
• View the Attribute Table.
  

The Lithics_Lab2_All_ArchID table is constructed the same way as we created the Ceram_Lab2_All_ArchID last week. It is a de-normalized table where points were created for every artifact from our lab analysis using the best spatial provenience available.

Note that there are 390 artifact rows.

Look at the Attribute Table and observe the types of data involved. We have projectile points and other lithic tools, and a small sample of flakes. It turns out these flakes are only from a couple of sites, so lets exclude them. Also, we only want to work with Chert and Obsidian, so first we will select out the Chert non flakes using the Definition Query.

• Right-click Lithics_Lab2_All _ArchID and choose Properties... > Definition Query

• Try to construct a query that selects Chert from the Lit_Mat category and excludes cases where Form = Flake Complete, AND also it selects Lit_Mat = Chert and excludes cases where Form = Flake Broken.

• Build this query by clicking the buttons. You shouldn't have to type anything.
• Click Verify
  

Your query should look something like

("Lit_Mat" = 'Chert' AND "Form" <> 'Flake Complete') and ("Lit_Mat" = 'Chert' AND "Form" <> 'Flake Broken')

Build it yourself so you remember how… don't just copy that text!

• Back in ArcMap click the name of the Lithics_Lab2_All_ArchID layer and rename it: Chert_Tools (this set has cores in it too, but just call it tools for simplicity)
  

• Copy and paste the layer (right-click > Copy. Edit menu > Paste)

• Right-Click Properties > Definition Query
• Redefine this layer as Lit_Mat = Obsidian, but no flakes (same as Chert for Form).
• rename this layer Obsidian_Tools
  

Note that we can now work with subsets of that single table without altering the original table. How many records are found in each Attribute Table?

B. Spatially explore the table values by Frequency.

First, turn on the Geostatistical Analyst. This takes two steps

1. Turn it on under Tools Menu > Extensions… > check Geostatistical Analyst
2. Display the Geostatistical Analyst toolbar from your Toolbar (right-click blank area)

• Choose Geostatistical Analyst > Explore Data… Histogram

We have Coinciding Samples… Choose “Include All”.
Why do we have spatially coinciding samples?

• Select Obsidian Tools on the left field and Wt_g10 on the right.

• Look at the histogram. Note that frequency and weight are plotted.

• Click and drag a box over the right-most columns. What weight group do you think you have just selected?

• Look back at your map display and note the points that are selected.

• Open the Attribute table for the Obsidian Tools layer and click the “Selected” button at the bottom.

Note that you can interactively select by

1. spatial position in the map (using the blue selection arrow)
   
2. attribute characteristics from the table
3. frequency (histogram) of values in Explore window

This tool is very useful for data exploration and pattern recognition.

This display also allows you to include histograms as well as values like Count, Mean, St. Dev., etc. on your map layout (using the Add to Layout button) where you can also export them to PDF for use in Word documents, etc.

Part II. Mapping Clusters and Interpolating patterns

A. Cluster/Outlier Analysis: Anselin Local Moran's I

Apply the Cluster/Outlier Analysis function that we used in lab last week

• Make sure no records are selected in any layer:
• Selection Menu > Clear Selected Features
• Next go to Toolbox > Spatial Statistics > Mapping Clusters > Cluster / Outlier Analysis with Rendering…

Input Feature: Chert Tools…
Input Field: Wt_g10
Output Layer File (click the Folder and name it: ChertWtLyr1)
Output Feature Class (click the Folder and name it: ChertWt1)

• Run the analysis. Add the ChertWtLyr to the map if necessary.
• Run the same analysis again with Obsidian and call it ObsidianWtLyr1

Look at the patterns. Zoom and and investigate the red and blue dots. These are features with statistically significant autocorrelation (positive or negative).
The values are Z scores which means that the numbers reflect standard deviations. For example, at a 95% confidence level you cannot reject the null hypothesis (of random distribution) unless the Z scores are in excess of +/- 1.96 (1 stan dev).

• Return to the Geostatistical Analyst > Explore Data… > Histogram function
• Remember to Include All with Coinciding Samples.
• Back the map view select the high or low Spatial Autocorrelation areas with the Select arrow.
  

Look at those values in the Histogram and in the Attribute table. Can you figure out why they have high/low spatial autocorrelation values?

B. Interpolation with IDW.

The Geostatistical Analyst provides tools for examining these kinds of patterns in detail.

1. Geostatistics is premised on the concept discussed as the First Law of Geography: All things are related, but near things are more related than distant things.
2. The assumption in geostatistics is that groups of points that are the same distance and direction from each other will contain similar differences in the value of the variable (attribute) measured at those points.
3. Furthermore, geostatistics assumes that it is possible to predict through interpolation the values for unmeasured points based on their distance and direction from known points.
4. The semivariogram cloud is a graph that depicts the value differences between groups of points found at different distances from each other.

In this brief introduction we will simply produce an IDW surface using the default values and compare it visually to the known patterns.

• Geostatistical Analyst > Geostatistical Wizard….
• Choose Feature: ChertTools and Attribute: Wt_g10
• Next… Choose Include All…

We don't have time to explore all the feature here, but this window is concerned with the directionality and magnitude of the interpolation.

• Click the top-left button "Optimize Power Value". Click Next…

This window displays the interpolation algorithm and allows you to reject specific interpolated (predicted) values that diverge from the Measured values.

• Click Finish…
  

• The resulting display should be renamed "Chert IDW" and moved down to near the bottom of the map layers (so the rivers are showing, etc).
• Repeat the above process with Obsidian and Wt_g10

Study the results. Compare the Clusters/Outliers results (red/blue dots) with the geostatistical wizard output.

It is somewhat difficult to compare the concentrations of heavy chert and obsidian artifacts from these rasters because they obscure each other.

• Right-click the Chert IDW output and click Data… > Export to Vector…
• Repeat with Obsidian IDW.
• Color the contours lines different colors and you can really see the patterns.
  

You can compare the prediction strength in both layers

• Right click Chert IDW > Compare… choose Obsidian IDW on the right side. Note the different RMS errors.

There are other powerful interpolation tools in the Geostatistical Analyst including kriging and semivariogram production. If you choose to use these methods you should research the most appropriate interpolator for your task.
The Subset function is also quite powerful in Geostatistical Analyst. It allows you to set aside a portion of your data for validation purposes. We will use this function in the coming weeks in the locational modeling exercise.