Soc/Anth 597 Spatial Demography March 14, GeoDa 0.95i Exercise A. Stephen A. Matthews. Outline. 1. Background

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1 Soc/Anth 597 Spatial Demography March 14, 2006 GeoDa 0.95i Exercise A Stephen A. Matthews Outline 1. Background 2. Data set introduced (GDANEPAL.SHP) 3. GeoDa introduced Task 1: Start GeoDa Task 2: Open the GDANEPAL.SHP dataset Task 3: Familiarization with GeoDa Task 4: Select a map and variable(s) Task 5: Construct a spatial weights matrix (first order Queens contiguity) Task 6: Generate a point shape file from an area shape file Task 7: Use Map Tools to change selection criteria and map appearance Task 8: Generate simple statistical graphs and explore dynamic maps Task 9: Produce scatterplots and explore options (e.g., exclusion) Task 10: Use selected Map options Task 11: Explore Options in more detail with a Moran s I scatterplot. 4. Mapping and Spatial Autocorrelation Exercises Task 12: Explore the different mapping options in GeoDa Task 13: Explorations with global spatial autocorrelation univariate Moran Task 14: Explorations with local spatial autocorrelation multivariate Moran In this handout all commands are printed in Courier New (Bold)

2 1. Background GeoDa is a trademark of Luc Anselin. GeoDa is a collection of software tools designed for exploratory spatial data analysis (ESDA) based on dynamically linked windows, and this software replaces the DynESDA Extension for Arcview 3.x. GeoDa is freestanding and does not require a specific GIS system. GeoDa has evolved from efforts to couple SpaceStat and DynESDA with ESRI products (e.g., Arcview 3.x) via extensions. GeoDa adheres to ESRI s shapefiles as the standard for storing the information, using MapObjects LT2 technology for spatial data access, mapping and querying. Luc Anselin suggests for extended course notes and examples dealing with an introduction to spatial data analysis, and requests that users please report anything that seems like a bug to anselin@uiuc.edu (or post to the Openspace mailing list: mailto:openspace@sal.agecon.uiuc.edu). This outline developed for the exercise draws on the structure of the GeoDa 0.9 User s Guide (February 2003) available from (under Spatial Tools). 2. Data set introduced GeoDa comes with several data files as samples (e.g., Crime in Columbus [tracts], SIDS in North Carolina [counties]). In this exercise we will use women s health-related data for Nepal. The data set GDANEPAL.SHP is based on district level data from the early and mid 1990s. Geographically, Nepal is divided in to 75 districts, found in five Development Regions and fourteen Zones (see map accompanying the Data Dictionary for GDANEPAL.SHP). The data set includes a selection of demographic and socioeconomic development variables (e.g., gender development index, gender empowerment measures, contraceptive prevalence rates, life expectancy, literacy, infant mortality rates, fertility rates). A complete listing can be found in the Data Dictionary. The exercises that follow are illustrative only and are not intended to cover the fully functionality of GeoDa. Before we begin the lab copy the GDANEPAL.SHP and associated files to your working directory. 2

3 3. GeoDa introduced Task 1: To launch GeoDa click on its icon on the desktop Task 2: Open the GDANEPAL Project a) File > New Project (This opens the GeoDa Project Setting dialog box). b) Browse through the folder to find and select the shape file, GDANEPAL.SHP. c) Select DIST_NAME as the Key Variable (by scrolling and clicking on variable name). The Key Variable must have a unique value for each observation (i.e., in this case district). The unique value is used to implement the link between maps and statistical graphs. d) Click OK. (you will have to click on the left side of the map window and then drag to the center of the map to view the legend area). e) It is a good idea to maximize the GeoDa window. Click on the full screen button for GeoDa,. Note, all windows in GeoDa can be resized and positioned anywhere within the main program window. Task 3: Familiarization with GeoDa The GeoDa menu bar contains twelve (12) menu items 1. File (Project Toolbar) 2. View 3. Edit (Edit Toolbar) 4. Tools (Weights Toolbar) 5. Table 6. Map 7. Explore (Explore Toolbar) 8. Space 9. Regress 10. Options 11. Window 12. Help 3

4 with the important menu items matched by a button on the toolbar. Toolbar components [Project, Tools, Map Window, Explore, Space and Map] can be moved and docked anywhere within the main program window. For example, The File Menu (Project Toolbar) contains the standard project management commands (e.g., open a new project, close project windows). The Map Window Menu (Map Window Toolbar) allows the user to (a) manipulate maps and layers (e.g., new map, duplicate map, add layer, remove layer), (b) select variables (e.g., univariate or bivariate), and (c) make use of the Windows clipboard. The Window Menu allows the user to rearrange the windows based on three preset designs: cascade (which stacks the windows), tile vertical (which places windows side-by-side) and tile horizontal which arranges them on top of one another. 4

5 Task 4. Select and map a variable. We will create a new second map and then display two variables side by side. In this example;e we will map the percent of women using Depo Provera (DEPO) and the percent of women using Sterlization (STER). a) create a new map select Edit > New Map b) select GDANEPAL.SHP c) click on Open. This generates a new map window. d) to make both maps visible either resize and move their respective windows or select Window > Tile Horizontal. e) Make one map window active by clicking on the map title bar. We will now add a variable for this map. f) To add a variable Edit > Select Variable > 1st Variable. This opens a variable settings dialog box. (Note is mapping or graphing two variables one would have selected a 2 nd variable). g) In the dialog box select the variable of interest (DEPO) by scrolling down the 1 st variable Y listing. h) Notice that the box select variables as default is checked. If the variable is set as a default (i.e., checked) then all mapping or statistical graph options assume this is the focal variable. If this check box is not marked, the variable selection dialog box will open for each mapping or 5

statistical operation. In the example above, DEPO (percent of women using Depo Provera) is selected. Also, note that the variable is found in the GDANEPAL. SHP file. i) Click OK.

This will produce a map something like The legend indicates the number of observations in each category.

6 statistical operation. In the example above, DEPO (percent of women using Depo Provera) is selected. Also, note that the variable is found in the GDANEPAL. SHP file. i) Click OK. j) To produce a basic quantile map of DEPO select Map > Quantile (if DEPO was not checked as the default than select DEPO if necessary). k) Accept 4 classes/groups in the dialog box by clicking on OK. This will produce a map something like The legend indicates the number of observations in each category. The legends are pre-coded using color schemes suggested using the ColorBrewer picker (found at ). Alternatively you can select new colors by double-clicking on any of the colored rectangles in the legend (or Options > Color > Map). l) Repeat steps (e) through (k) this time selecting STER (percent of women using sterilization). 6

Your screen should now look something like this m) Close one map window (e.g., Quantile STER map) by clicking on the. n) Resize the remaining map window as necessary.

7 Your screen should now look something like this m) Close one map window (e.g., Quantile STER map) by clicking on the. n) Resize the remaining map window as necessary. o) Reset or clear the map using Map > Reset (this returns the map window to the simple locator map showing district boundaries. The View Menu (drop-down menu) contains two options to control the items shown in the program interface and toolbar. View > Toolbar (default is that all six toolbars are visible) and View > Status Bar (default is on ). The Tools Menu (drop-down menu) contains three submenus for (a) constructing and analyzing spatial weights, (b) converting shapefiles such as converting polygon files to point or centroid files and point files to polygon files (Thiessen polygons), and (c) data export. We will explore some of Tools commands now. Task 5. Construct a spatial weights file and explore some properties of this file. a) To construct a spatial weights file select Tools > Weights > Create. This opens up the Creating Weights dialog box. In the example below, the general weights (output) file is saved as a.gal file, GDANEPW1.GAL (Note, you will save it to another directory, C:\TEMP). 7

8 The weights file used DISTRICT as the ID variable and the contiguity weight is based on first order (1) Queen s contiguity. b) Click on Create. c) To explore characteristics of the weights file select Tools > Weights > Properties. This opens up a Weights Characteristics dialog box where one can browse for the relevant file (in the example above, GDANEPW1.GAL). After selecting the file click on OK. This generates a connectivity histogram similar to the one below. d) The histogram can be queried by clicking on a vertical bar. For example, if one selected the vertical bar 2:3 neighbors then the bar would be highlighted and the 14 districts with 2 or 3 neighbors would be highlighted on the map on Nepal (typically districts on the Nepali border). 8

e) Close the histogram window by clicking on the and deselect the selected districts by clicking anywhere on the map but outside of the Nepal country boundary. Task 6.

This opens a dialog box prompting for the input and output file names. In the example below, the input file is GDANEPAL.SHP while the output file was named GDAPOINT.SHP. b) Click CREATE and then click DONE.

9 e) Close the histogram window by clicking on the and deselect the selected districts by clicking anywhere on the map but outside of the Nepal country boundary. Task 6. Generating a point shape file from an area shape file. a) To convert the district shapefile in to a centroid (point) shapefile use the command Tools > Shape > Polygons to Points. This opens a dialog box prompting for the input and output file names. In the example below, the input file is GDANEPAL.SHP while the output file was named GDAPOINT.SHP. b) Click CREATE and then click DONE. Note, with a point file it is possible to generate spatial weights files based on a distance weight or k-nearest Neighbors (in the example below the number of neighbors to be used is 6). We will not do this. 9

10 Task 7. Use Map Tools to change selection criteria and the appearance of selected entities on maps and graphs. a) Click on the GDANEPAL map title bar to make it active. b) Add the life expectancy (LE) variable using Edit > Select Variable > 1st Variable. c) In the dialog box select the variable of interest (LE) by scrolling up/down the 1 st variable Y listing. d) Click OK. e) To produce a basic quantile map of LE select Map > Quantile. f) Accept 4 classes/groups in the dialog box by clicking on OK. g) We will now use some map selection tools. The most frequently used is Options > Selection Shape. In the first instance choose the Circle selection criteria. There are five different ways to select locations on a map: Point, Rectangle (the default), Polygon, Line and Circle. Note, the selection criteria can also be initiated by right clicking on a map (and note also that zoom and selection color options are available). h) Before making a selection we will change the selection color using Options > Color > Shading This opens up a color dialog box with preset colors and the ability to define other colors. In the examples that follow the selection color was set to black. 10

Click on the map at the approximate location of Kathmandu and

11 i) We will select districts based on a circle drawn around Kathmandu (Nepal s capital). Click on the map at the approximate location of Kathmandu and drag away from the center. Kathmandu After releasing the districts clipped by the circle are selected. 11

12 Task 8. Generate simple statistical graphs and explore dynamic maps (use LE, GDI and CPR). The Explore Menu (Explore Toolbar) contains traditional statistical graphics used in exploratory data analysis (EDA): Histogaram, Scatterplot, Boxplot, Parallel Coordinate Plot, 3D Scatterplot, and Conditional Plot. The latter three will not be discussed in this handout but feel free to explore. These EDA and ESDA tools are invoked in the same manner. After selecting from the Explore menu, the variable selection dialog box appears (unless the default was set earlier). We will first create a box plot. a) Click on the GDANEPAL map title bar to make it active. b) Change the default variable to the gender empowerment index (GDI) variable using Edit > Select Variable > 1st Variable. c) In the dialog box select the variable of interest (GDI) by scrolling up/down the 1 st variable Y listing. d) Click OK. e) Select Explore > Box Plot for the variable GDI f) Select Window > Tiled Vertical Produces a map something like 12

Notice that the selected districts on the map appear in yellow on the bar chart. There appears to be considerable spatial variation in GDI even among districts close to Kathmandu.

13 Notice that the selected districts on the map appear in yellow on the bar chart. There appears to be considerable spatial variation in GDI even among districts close to Kathmandu. The Options Menu contains ways to customize the graphs (e.g., categories in a histogram, or changing the hinge for a box plot, or the use of raw or standardized data in scatterplots). We will add a histogram for the Contraceptive Prevalence Rate (CPR) g) Click on the GDANEPAL map title bar to make it active. h) Change the default variable to CPR using Edit > Select Variable > 1st Variable. i) In the dialog box select the variable of interest (CPR) by scrolling up/down the 1 st variable Y listing. j) Click OK. k) Add a histogram for the Contraceptive Prevalence Rate (CPR) using Explore > Histogram. l) Experiment with sizing and positioning windows (and using Windows > Tile Vertical) 13

14 m) Using the box plot select those districts that score low on GDI. This will require you to select data points by holding down the SHIFT KEY and draging to create a selection rectangle (or with the SHIFT KEY held down click on each individual data point). The selected (highlighted) districts in the box plot are dynamically linked to the Map and Histogram windows see below. Notice that many of the districts also have low contraceptive prevalence rates (CPR) not surprisingly perhaps and that these districts are predominantly in the Far West and Mid West Development Regions of Nepal (see Data Dictionary). n) Close (delete) the histogram and box-plot by clicking on the respective boxes. o) Deselect the districts on the map by clicking once inside the map window but outside of the Nepal shape. 14

Task 9. To produce a scatterplot of the contraceptive prevalence rate versus per capita income and explore the use of exclusion. By definition a scatterplot requires two variables.

15 Task 9. To produce a scatterplot of the contraceptive prevalence rate versus per capita income and explore the use of exclusion. By definition a scatterplot requires two variables. In this example we will produce a scatterplot of contraceptive prevalence rate (CPR) and per capita income in Nepali Rupees (PCNRS). a) To add two variables use Edit > Select Variable. This opens a variable settings dialog box. b) In the dialog box select the variables of interest, CPR by scrolling down the 1 st variable Y listing, and PCNRS by scrolling down the 2nd variable X listing. Notice that the box select variables as default is checked. Then click OK. c) To produce the scatterplot of CPR against PCNRS use Explore > Scatterplot d) Position windows using Windows > Tile Vertical 15

e) To select those districts that report per capita income of less than 5000 Nepal Rupees, Left click near the 5,000 PCNRS and then drag to make a rectangle.

16 e) To select those districts that report per capita income of less than 5000 Nepal Rupees, Left click near the 5,000 PCNRS and then drag to make a rectangle. f) To make a rectangle dynamic press CTRL (control), click and drag, then release. The box will flash and then become active. This box can be moved around the scatterplot by moving the cursor (joystick). Click on the scatterplot to make the selection permanent. g) An important option in the use of scatterplots is the ability to exclude selected data points. This is initiated using the command Options > Exclude Selected. This option allows for the visual inspection of the effects of outliers and leverage points on the regression slope. h) In the example below the three districts making up Kathmandu Valley have been selected on the life expectancy map the easiest way to make the selection is with the Scatterplot window active, click and drag a rectangle around the three data points in the top-right area of the scatterplot graph Or with the Map window active and the SHIFT KEY pressed down click on the three districts of choice. You may need to zoom in to the map to make the selections requiring that you 16

4) With the SHIFT-KEY pressed down, Left-Click on the three districts of interest.

17 1) Right-Click on the map and select Zoom In. 2) Left-Click and drag to form a zoom window. 3) Right-Click on the map and select Point. 4) With the SHIFT-KEY pressed down, Left-Click on the three districts of interest. 5) Right-Click on the map and select Full Extent. The Zoomed in map with the three selected districts is shown below i) To exclude the three Kathmandu Valley observations use Options > Exclude Selected. One can see changes in the relationship (slope) between CPR and PCNRS. 17

j) Another option when using scatterplots is the creation of the graph based on standardized data values. This is initiated using Options > Scatterplot > Standardized Data.

18 j) Another option when using scatterplots is the creation of the graph based on standardized data values. This is initiated using Options > Scatterplot > Standardized Data. Note, you may need to redraw the scatterplot using Options > Exclude once or twice to view the plot above. k) Close (delete) the scatterplot by clicking on the. l) Maximize the Map window by clicking on the. m) Deselect the districts on the map by clicking once inside the map window but outside of the Nepal shape. Note, we will return to techniques for spatial autocorrelation analysis after we have used a few more GeoDa tools. Task 10. Use selected Map options and other features of GeoDa. The Map Menu allows the user to create four standard choropleth maps: quantile maps, percentile map, box map and standard deviational map. We generated a quantile map of life expectancy (LE) earlier in this session. Cartograms can also be generated in GeoDa (we will not cover these in this exercise). 18

19 a) To reset or clear the map use Map > Reset (this returns the map window to the simple locator map showing only district boundaries). b) The Smooth and Map Movie command implement specialized mapping functions. Here we will look at the map movie command. There are two ways to view the movie, cumulative or single. Cumulative is recommended. Map > Map Movie > Cumulative. This opens a select variable dialog box. c) Select CPR and press OK and watch the movie. (don t use Map Movie if your project has many units of analysis as it can take a long time to watch the movie). Task 11. Explore Options in more detail with reference to Moran s I scatterplot. The functions under the Space Menu such as Moran and LISA statistics can only be invoked if a spatial weights file has been created. After specifying a spatial weights matrix a window opens with a statistical graph or map. The Options menu controls several settings for specific graphs and statistical analyses. The options available are specific to the graph type present in the program window. We have yet to discussed the Moran scatterplot but it is worth noting that additional options are available if a univariate or multivariate Moran graph is in the program window (e.g., randomization and permutations and envelop slopes). For a quick illustration follow these commands: a) Edit > Select Variable > 1st Variable (and select infant mortality rate IMR). b) Map > Quantile > 4 > OK. (A quantile map will appear) c) Space > Univariate Moran (then select appropriate weights file earlier we created the file GDANEPW1.GAL) d) Click on OK. (A Moran scatterplot will appear and will need to be resized). 19

20 This shows the spatial lag of the variable on the vertical axis and the original variable on the horizontal axis (based on queen s contiguity). The variables are standardized and the graph is divided in to four quadrants: high-high (upper right) and low-low (lower left) for positive spatial autocorrelation; and high-low (lower right) and low-high (upper left) for negative spatial autocorrelation. The slope of the regression line is Moran s I. e) To compute a reference distribution to assess the significance of a Moran s I spatial autocorrelation statistic, with the Moran scatterplot window active choose Options > Randomization > 499 permutations This sets the number of permutations to be used in the computation of a reference distribution to assess the significance of a Moran s I spatial autocorrelation statistic and then generates a randomization histogram for a reference distribution, with the observed Moran s I shown as a yellow bar and a pseudo-significance level or p-value. Also listed on the graph are the Moran s I, the theoretical mean for Moran s I, and both the mean and standard deviation for the reference distribution. 20

f) In the randomization graph one can re-run to generate another set of simulated values. In this example below the focus was on the infant mortality rate (IMR).

21 f) In the randomization graph one can re-run to generate another set of simulated values. In this example below the focus was on the infant mortality rate (IMR). We see from the map a seemingly clustered pattern with higher IMR found in the Far West and Mid West Development Regions and lower rates generally in the Kathmandu Valley and the southern border in the Eastern half of the country. This clustering of high values (and of low values) is confirmed by the Moran scatterplot and randomization histogram. g) Close (delete) the scatterplot by clicking on the. h) Close the Randomization histogram. i) Reset the map to the basic Nepal default by using the command Map > Reset j) Maximize the Map window by clicking on the. That concludes the brief tour of GeoDa. The next section discusses in more detail some of the different map types that can be generated as well as the global and local measures of spatial autocorrelation. 21

22 4. Mapping and Spatial Autocorrelation Exercises The examples in this section are illustrative only. If you complete these exercises in the time available the last page includes some additional suggested spatial data explorations using this data set (or alternatively you could load some of the sample data sets that come with GeoDa (e.g., Columbus Crime and SIDS in NC data files they should be available in a directory called something like C:\Program Files\GeoDa\Sample Data the exact path will depend on the local installation). Back to Nepal Task 12. Explore the different mapping options in GeoDa. All maps are invoked from the Map menu. The most commonly used choropleth maps are the quantile map and the standard deviational map. The exercise assumes the shape file and data GDANEPAL.SHP has been loaded in to GeoDa and that Edit > Select Variable > 1st Variable does not have a check mark specifying a default variable. We will map the Total Fertility Rate (or TFR). a) Use Edit > Select Variable > 1st Variable, select TFR91. The variable TRF91 can be found at the bottom of the variable listing. With the settings above click on OK. Now lets map total fertility rate (variable TRF91) using quantiles first. In a quantile map, the data are sorted and grouped in categories with near equal numbers of observations (or quantiles). Note that it is not possible to resolve ties and allocate observations with the same value to different groupings. 22

SHP) then move and resize maps so they can both be seen or use Windows > Tile Horizontal).

23 b) Map > Quantile (invokes the dialog box to specify the number of quantiles the default is 4). c) Click OK generates the quantile map. Lets create a new map based on standard deviations. d) Use Edit > New Map (select GDANEPAL.SHP) then move and resize maps so they can both be seen or use Windows > Tile Horizontal). e) A standard deviational map groups observations according to where their values fall on a standardized range, expressed as standard deviational units away from the mean. Use the command Map > Std Dev. This creates a standard deviational map. Because TFR91 is set as the default the appropriate map is generated (the top map in the figure below) 23

f) Note, a histogram of TRF91 reveals the range of data values is from a low of 3.06 to 5.77 and the standard deviation map legend reports many data values more than 2 SD from the mean of 4.86.

24 f) Note, a histogram of TRF91 reveals the range of data values is from a low of 3.06 to 5.77 and the standard deviation map legend reports many data values more than 2 SD from the mean of (Use Explore > Histogram) g) We will now look at outlier maps in GeoDa. Two map types are available: Box map and Percentile Map. Create two new map windows. Edit > New Map (select GDANEPAL.SHP) do this twice then resize the maps using Windows > Tile Horizontal). h) Then click on one of the new Map title bar to make active and select Map > Box Map This creates a box map, which is a special case of a quartile map where outliers (if present) are shaded differently. There are six legend categories: four base categories one for each quartile and one for extremely low values and one for extremely high values. In the TFR91 map there are three lower outliers where the TFR is low (two in Kathmandu Valley area (Kathmandu and Lalitpur) and the district of Manan on the northern border in the West Development Region. i) Then click on one of the fourth Map title bar to make active and select Map > Percentile This creates another special case of the quantile map. The categories are grouped to accentuate the extreme values. Specifically, six legend categories are created, corresponding to < 1%,!% to 10%, 10-50%, 50-90%, 90-99%, and > 99%. If all four maps of TFR91 are visible your screen should look like 24

25 j) Close THREE of the maps and any graphs that may be open by clicking on the respective boxes. Leave one map window visible. k) Reset the map to the basic Nepal default by using the command Map > Reset Task 13. Further explorations with global spatial autocorrelation univariate Moran. Now back to calculating and displaying Moran s I. The global spatial autocorrelation analysis requires that both a variable be specified (Edit > Select Variable) as well as a spatial weights file (use Tools > Weights > Create if this file does not exist). GeoDa can be used to look at a univariate Moran scatterplots as well as bivariate (multivariate) Moran scatterplots. Lets look at the Gender Empowerment Measure (GEM) remember defaults. a) Change the default variable to GEM using Edit > Select Variable > 1st Variable. 25

26 b) In the dialog box select the variable of interest (GEM) by scrolling up/down the 1 st variable Y listing. Click OK. c) To create a quantile map of GEM use Map > Quantile > 4 > OK d) Space > Univariate Moran (this opens up a dialog box prompting for the name of the weights file). Browse for the weights file as necessary and then click on OK. As GEM is the default the resultant Moran Scatterplot is QII QI QIII QIV Moran s I provides an indication of the relationship between a vector of observed values, y, and a weighted average of values that neighbor, or are contiguous to, y. The latter are often referred to as the spatial lag of y, and is expressed as Wy, where W stands for the spatial weights matrix. The calculated value of Moran s I is the slope coefficient of a regression of Wy on y. The scatterplot of individual components of Moran s I, measured in standard deviations, permits the visualization of the contributions that each observation makes to the calculated statistics. 26

27 The four quadrants represent the four types of spatial association that exist: Quadrant I - high values of y surrounded by similarly high values; Quadrant II - low values of y surrounded by dissimilarly high values; Quadrant III low values of y surrounded by similarly low values; Quadrant IV high values of y surrounded by dissimilarly low values. Quadrant I and III contribute to positive spatial autocorrelation, while Quadrant II and IV contribute to negative spatial autocorrelation. Influential observations can be identified for their contributions, or leverage, by means of the two-sigma rule, or those observations falling more than two standard deviations from the origin e) There are a number of options for Moran scatterplots. First, there is the option to exclude selected data points. To select some districts in the scatterplot (e.g., outliers), Left click and then drag to make a rectangle. f) Use Options > Exclude Selected When the excluded selection is active, the selection of observations in the graph(s) will result in the recalculation of Moran s I for a layout without the selected observations. The new regression line is shown in brown. g) With the Map window active and the SHIFT KEY pressed down click on the three districts within the Kathmandu Valley (or see h on page 19 for Zoom In assistance). For GEM excluding the three districts in the Kathmandu Valley generates the following Moran scatterplot with a slightly higher Moran s I. h) It is possible to select data elements and or dynamically brush the Moran scatterplot. To make a rectangle dynamic press CTRL (control), click and drag, then release. The box will flash and then become active and can be moved around the graph. 27

With the Map window active, districts can be selected using Options > Selection Shape > Point. Move the cursor over a district to be selected and then click.

28 i) Alternatively, one can use the map (or other graph window) to make selections that can be excluded on the scatterplot. For example, the example below excludes those districts in the East Development Region (see Data Dictionary Document for definitions of Development Regions). With the Map window active, districts can be selected using Options > Selection Shape > Point. Move the cursor over a district to be selected and then click. To select multiple districts hold the SHIFT-key down when selecting districts. j) As in the earlier example of Moran s I with the Moran scatterplot active choose Options > Randomization > 499 permutations This generates a randomization histogram for a reference distribution, with the observed Moran s I shown as a yellow bar and a pseudo-significance level or p-value. Also listed on the graph are the Moran s I, the theoretical mean for Moran s I, and both the mean and standard deviation for the reference distribution. 28

k) Close the Randomization histogram. l) The envelop slope option visualizes the range of autocorrelation statistics that can be obtained in spatially random simulated data sets.

29 k) Close the Randomization histogram. l) The envelop slope option visualizes the range of autocorrelation statistics that can be obtained in spatially random simulated data sets. Specifically this option plots the lower 5 th percentile and the upper 95 th percentile of the reference distribution as a slope of dashed lines in the Moran scatterplot. Use Options > Envelop Slopes. This generates This is shown for GEM illustrating the degree of extremeness of the observed statistic. n) Close the Moran Scatterplot graph by clicking on. o) Reset the map to the basic Nepal default by using the command Map > Reset p) Deselect the districts on the map by clicking once inside the map window but outside of the Nepal shape. 29

30 Task 14. Further explorations with global spatial autocorrelation bivariate Moran. In this example we will explore (the relationship between Gender Development Index (GDI) and per capita income (PCNRS). a) Select two variables using Edit > Select Variable b) In the dialog box select the variables of interest, GDI by scrolling down the 1 st variable Y listing, and PCNRS by scrolling down the 2nd variable X listing. Notice that the box select variables as default is checked. Then click OK. c) Space > Multivariate Moran. This opens up a dialog box prompting for the name of the weights file. d) Browse for the weights file as necessary and then click on OK. 30

The resultant Moran Scatterplot is This scatterplot shows the spatial lag of the first variable (PCNRS) on the vertical axis and the second variable (GDI) on the horizontal axis.

31 The resultant Moran Scatterplot is This scatterplot shows the spatial lag of the first variable (PCNRS) on the vertical axis and the second variable (GDI) on the horizontal axis. Both variables are standardized. The slope of the regression line shows the degree of linear association between GDI and the values for PCNRS at neighboring locations (as defined by the spatial weights file). e) Inference is based on randomization. Options > Randomization > 499 permutations f) Close the Moran Scatterplot graph by clicking on. 31

32 The following is not to be done. Anselin suggests combining univariate and bivariate Moran scatterplots to produce a scatterplot matrix. This matrix provides an overview of the spatial patterning of each variable with itself as well as with the spatial lags of the other variables. Thus one can generate something like the following This can be contrasted against the usual non-spatial correlation matrix 32

33 Task 15. Further explorations with local spatial autocorrelation. The local spatial autocorrelation analysis is based on the Local Moran LISA (Local Indicators of Spatial Association) statistics. This computes a measure of spatial association for each individual location. The LISA statistics requires that both a variable(s) be specified (Edit > Select Variable) as well as a spatial weights file (see Tools > Weights > Create if this file does not exist). GeoDa can be used to look at a univariate LISA statistics as well as bivariate (multivariate) LISA statistics. As we did with the global Moran s I lets look at the Gender Empowerment Measure (GEM). a) Change the default variable to GEM using Edit > Select Variable > 1st Variable. b) In the dialog box select the variable of interest (GEM) by scrolling up/down the 1 st variable Y listing. c) Click OK. d) Univariate LISA statistics are invoked by Space > Univariate LISA. This generates four graphs see below. It is recommended that you use the Window > Tile Vertical command to arrange the graphs. The lower right corner is the Moran Scatterplot for GEM The two maps on the left show the locations with significant LISA statistics. The bottom map is the Moran Significance Map that differentiates by significance level (see legend). The top map is the LISA Map that shows the significant locations (for p = 0.05) by type of association with surrounding neighbors (districts). Notice that the four colors match the four quadrants of the Moran Scatterplot. The box plot in the upper right shows the distribution of the individual LISA statistics. 33

This will require you to select data points by holding down the SHIFT KEY and draging to create a selection rectangle

34 f) In the screen capture below the highest LISA values in the box-plot (above hinge) are selected. With the box plot active, select those districts that score high on GEM. This will require you to select data points by holding down the SHIFT KEY and draging to create a selection rectangle (or with the SHIFT KEY held down click on each data point). The LISA principle can be applied to a bivariate measure of local spatial autocorrelation using Explore > Multivariate LISA. 34

35 The Regress Menu is a new suite of tools available in Geoda 0.95i that allows the user to run classical OLS, spatial lag, and spatial error regression models. This will be the subject of another lab exercise. Selected tasks to think about on your own a) Use Tools > Weights > Create to construct higher order contiguity weights files (i.e., second, third, fourth and fifth order spatial lags weight files). Then calculate Moran s I based on each weight file for demographic variables such as LE (life expectancy), AL (Adult literacy), CPR (Contraceptive Prevalence Rate), TFR91, (Total Fertility Rate). b) Use Tools > Weights > Create to construct a first order contiguity weights file based on Rook Contiguity and compare results for Moran s I for selected variables when Queen Contiguity criterion were used. c) Generate bivariate Moran for Female Literacy (ALF) and Male Literacy (ALM) I encourage you to download the latest GeoDa User s Guide (2005) available from (under Spatial Tools). 35

OPEN GEODA WORKSHOP / CRASH COURSE FACILITATED BY M. KOLAK

OPEN GEODA WORKSHOP / CRASH COURSE FACILITATED BY M. KOLAK WHAT IS GEODA? Software program that serves as an introduction to spatial data analysis Free Open Source Source code is available under GNU license