NR 245

Lab 3: Spatial autocorrelation

 

 

  1. Download the table autocorr from the NR245 folder of the share drive to your account. Join this to your BG_GF_LC2 layer using the BGKEY field (in TOC, right click on BG_GF_LC2>>joins>>tabular join). However, we’re going to need to eliminate one row that has a bunch of zero values for Census data. In my table it is row 5, also ObjectID 5, but it may be different in your table. To find it, look for the MED.HH.INC column and scroll down in it until you find a zero value in that column. That is the row you want to delete. It should be missing all the Census data, starting with MED.HH.INC. Click on the row to highlight (select) it. Then right click on that layer in the table of contents and click selection>>switch selection. Now export (right click>>export data) that selection to a new layer in your geodatabase called BG_GF_Census. When you load the resulting layer in ArcMap you’ll notice it is missing one polygon, which happens to be mostly park land.
  2. Now we’ll run some simple SA analyses. Open Arc toolbox and go to spatial statistics tools>>analyzing patterns>>spatial autocorrelation. Double click on it, choosing BG_GF_census as the input, P_coarseveg as the input field, checking display output graphically, choosing “row” as the type of standardization, and accept all the other defaults. Click OK. You will see summary results in the graphic output window. What is the Moran’s index score? Briefly give the result summarized in the window. Hit close and then look at the results in the toolbox reporting window (the one that now says “completed” at the top). What is the Z score? Keep in mind that the critical values for a z statistic at a 95% confidence level are -1.96 and +1.96. This is because 95% of the area on a standard normal distribution is between -1.96 and 1.96. At the 99% confidence levels those thresholds are positive and negative 2.58. For more info see http://members.tripod.com/~RichardBowles/maths/proportion/proportion.htm.
  3. Now try running SA for some other variables and briefly report each result, including the confidence level at which it is significant for:
    1. P_baresoil
    2. P_water
    3. Median household income (MED_HH_INC)
    4. Robbery rate (Robb05)
  4. Now we’ll do a local hotspot analysis using localmoran. Before doing this, create a new folder in your account called SA in Arc Catalog. In it, create a new geodatabase called SA as well (File>>new>>personal geodatabase). Into your folder copy a symbology file called zscore from here.  Then close Arc Catalog. This hotspot analysis will look at the Moran statistic variably across space. Click on spatial statistics tools>>mapping clusters>>cluster and outlier analysis (Anselin). Choose BG_GF_Census as the input, Robb05 (robbery rate) as the input field, and save the output as a feature class in your SA geodatabase, calling it LISA_rob1. Under standardization, choose “row.” Set distance band to 2000.  Leave everything else at the default values. You should see the new feature class added at the end. Open its symbology window and click “import.” Choose the lyr file you just downloaded and choose to apply it to the LMzInvDst variable. If the symbology import doesn’t work, try doing, try creating your own lyr file at spatial statistics tools>>utilities>>Z score rendering). Take a screencapture and interpret the map you see. Keep in mind that this is mapping Z scores and that the same critical values apply as mentioned earlier. Keep in mind also that for LocalMoran positive and significant (red) values mean similarity of values in space and negative and significant (blue) values mean systematic dissimilarity, or negative spatial autocorrelation. Try this now using the Getis method (spatial statistics tools>>mapping clusters>>hot spot analysis with rendering). Choose the same input layer and field as last time, and for output also save it in SA.mdb, but call it Getis_rob and call the output lyr file the same thing. Also choose a distance band of 2000 meters. When it produces the output, you’ll need to open the symbology window, and use the import button to apply the newly created lyr file to the Zscore field (Gi2000). Take a screencapture and note the differences with the Moran.  You’ll note that the z statistic associated with the output of the Getis statistic has a different interpretation from LocalMoran. It combines information from the original map with the autocorrelation statistics by making areas that are spatially autocorrelated and have high value red and areas that are spatially autocorrelated but with low values blue. If you have time, you can try an alternative approach. Go back to the local Moran tool (cluster and Outlier analysis) and choose everything the same as before, only this time change “conceptualization of spatial relationships” to “polygon contiguity” and leave distance band blank. This means that polygons are considered neighbors only when touching (note this can also be done for the Getis statistic when you use the Hotspot analysis tool without rendering). When it’s done go to symbology and click “import” then choose your z-score layer file used at the beginning of step 4. When it asks for a values field, choose LMzContig. Take a look—you should see a smaller number of autocorrelated polygons than with the original Local Moran.
  5.  Now try the same thing using the parcel layer from last week. Again choose the cluster and outlier analysis, but this time choose parcels_R as the input layer and assessed property value (assessed_tot) as the input variable (note that I had originally suggested using the “price” variable in these instructions; if you’ve already done that, that’s fine—just turn in what you have) choosing “row” standardization and Inverse Distance as the spatial method. Leave the distance band blank. Output this again to your geodatabase. Run it and again, in the symbology window, import the Zscore lyr file. Look at the output and compare it to a graduated color map of price. What is the hoptspot analysis appear to be showing you? Take screencapture of the map showing the z scores. If you have time, try the same parcel level analysis with the local Getis tool (spatial statistics tools>>mapping clusters>>hot spot analysis). Choose the same inputs, but change the name of the ouput to Getis_price, choose inverse distance output, row standardization and a distance band threshold of 500 meters. Again apply the zscore .lyr file but this time choose GiInvDst as the variable to apply it to and look at the difference.
  6. Now we’re going to run a regression in S Plus but look at the residuals to see if they are spatially autocorrelated. Load up the BG_GF_census layer into Splus using File>>import data>>from database (using the instructions of week 1). Go to statistics>>regression>>linear. Input the following model to predict the variation in tree cover, using BG.GF.census as your data set: P.coarse.veg~AVE.HH.SZ+P.HS.+POP00.SQMI+MED.HH.INC+P.SFDH+P.Protland+d2down+d2ramp. Hit apply. You’ll note that one variable (plus the intercept, which you don’t need to worry about) is not significant at the 95% confidence level. You should get a good R-squared for this. Copy the table of results from S Plus into your document and report which variable (there should only be one) is not significant and how you know to drop that variable and rerun it. Rerun the model without that variable and also clicking on the results tab and checking the “residuals” box under “saved results,” choosing BG_GF_Census as the table to save it in. If you look at the BG.GF.Census table after hitting apply, you should see a column at the far end of the table called residuals.  
  7. Now let’s output these back to Arc Map. Go to file>>export data>>to database. Choose Data target as MS Access, brose to your NR245 geodatabase, Choose resid as the output table name, and click on the filter tab, where you will choose the preview columns checkbox, and then select to export (by shift-clicking) only BKGKEY and residuals. Then click OK. If it doesn’t work, it may be because your geodatabase is already open in Arc Catalog or Arc Map.
  8. Now, open Arc Map and load BG-GF-Census as well as the “resid” table you just created. Do a tabular join to join resid to BG_GF_Census. Then, run a quick Moran test on those residuals (you could also do this in Splus, but it’s easier in Arc Map), by going to spatial statistics tools>>analyzing patterns>>spatial autocorrelation. Choose BG_GF_Census as the input table and Residual as the input field and choose to standardize by row. You can leave the distance band blank.  Interpret the results. Are your residuals independent and random, or spatially autocorrelated? Now run a cluster and outlier analysis using the local Moran statistic, like we did above (spatial statistics tools>>mapping clusters>>cluster and outlier analysis). Choose the same table and fields, as you just did, and change standardization to “row.” Then click OK and map the result using the Zscore lyr file again and take a screencapture.
  9. Assemble screencapture and text into a file and upload.