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S-Plus for ArcView GIS User`s Guide

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1. Lid sida mel eh er Fide cor lt mpetial coc sidsiwid fc sgre etdebbicthoe Pidin neighbor Stecietic Ente seep liag Pree Spereikes JOU b pidr tor neighbor Spatial Corcelacion Latimsc BERLLECLO MiraN Sapling Cree Coros letica 0 22587 Tarisrss 0 0 Sua Error otras Marmol statistic 2 TLT Hoca p values 2 sided 0 004275 Bull Fepothesia Wo epacial somes latrini Dismsiity Gf Eh pesmutetion corcceletions i Hin irt Qu Midia Mimi 3rd gu Ee W Aiii 2 0070F 0 91510 0 01224 0 CNW D Sal PER praus D PLL Figure 4 36 Running two commands from the Script window against the null hypothesis of no spatial autocorrelation For more discussion of this see section 5 2 of the S SPATIALSTATS U ser s manual 6 Click the Save toolbar button fl to save the script in a file for later use or distribution 83 Chapter 4 Using S PLUS and S SPATIALSTATS ANALYZING SPATIAL DATA IN S PLus FOR ARCVIEW Spatial Statistics 86 Data Preparation 86 Defining Neighbor Relationships 89 Spatial Autocorrelation 91 Local Spatial Association 94 Spatial R egression 98 Bibliography 103 This chapter provides a detailed example of spatial data analysis in S PLUS In several stages you will see the unique way in which S PLUS and ArcView GIS work together If you are unfamiliar with S PLUS look at chapter 4 Using S PLUS and S SPATIALSTATS before continu
2. 36 Use this dialog to import an S PLUS data frame as a table in the current project The variables from the data frame can then be displayed in the View window if joined to an existing table For example you can plota residual or fitted value for each polygon in a map 1 2 Select a data frame from the list of S PLUS objects Select the columns of the S PLus data frame to import To select more than one column hold down SuitFt while clicking Specify a value to denote missing values in the imported table Instances of NA in the S PLus data frame will be converted to this value when imported to A rcV iew 4 Specify a name for the imported table 5 To join the fields in the imported table to the attribute table of a theme click the checkbox next to Join Imported Columns to Theme and choose a theme from the drop down list Specify the names for the common field in each table under M atch Records Based on Common Values Click OK The new table is added to the list of Tables in the current A rcV iew Project window SPULE Diim io ha Daa Frama Lia Ear Cound F dom bepested Coura Te Theres te foc tore Match Feecordt Bared on Conon akat in impeded Cohan Theves d Fiii Faecal a fpa OF cares Hee Figure 3 4 The mport Table From S PLUS dialog TheS PLUS Menu Import Point Use this menu item to convert an S PLUS data frame into a point theme Theme from and add it to the ArcView View
3. 102 Bibliography BIBLIOGRAPHY Anselin L 1994 Local indicators of spatial association LISA Research Paper 9331 Regional Research Institute West Virginia U ni versity Morgantown WV Bao S and Henry M S 1996 Heterogeneity issues in local measure ments of spatial association G eographical Systems 1996 3 1 13 Cressie N and Chan N H 1989 Spatial modeling of regional vari ables Journal of American Statistical Association 84 393 401 Cressie N A C 1993 Statistics for Spatial Data Wiley New York 103 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView 104 INDEX Numerics 2D plot palette 63 66 3D plot palette 67 A Add Indicator Field dialog 39 analysis of variance 71 building a model 71 fitted values 73 generating plots 73 residuals 73 saving results 72 viewing printed output 73 Analysis of V ariance Fixed Effects dialog 72 Atlanta Census tracts data 9 30 B brush and spin dialog 22 C clearing selection and graphics in ArcView 43 Color Classification dialog 40 conditioning mode in S PLus 21 conditioning on a field 19 D data frame removing a column 74 sorting on a field 58 Data window 69 data windows in S PLus 13 Execute S PLUS Commands dialog 45 executing S PLUS commandsin A rcV iew 44 Export Data to S PLus dialog 35 exporting attribute table 70 S PLUS histogram to ArcView 15 theme data to S PLUS 34 F Fixed Effects A nalysis o
4. Choose Properties from the View menu and change the map units and the distance units to decimal degrees and miles respectively 2 Specify a distance threshold C hoose Spatial Neighbors from the Spatial Statistics menu Enter 30 next to Distance the dialog indicates that units of miles are expected T siad Metghhaia fd tho fer Comtoalating Hegia mgr e puia C oiif Dede e i i i i i L a Certence Barri Mathods Daima a a Emidio Criei O iade wimi JAUH Righter Dber Hrer Heca nmga J of Cmmi Hei Figure 5 2 Calculating spatial naghbor weights in ArcView 3 Create spatial neighbors C lick the Centroid to Centroid button We assume that the county seats and the county centroids are in close proximity in this exercise Verify that Ncco neighbor is under S PLUS Neighbor Name and click OK An S PLUS object of classspatial neighbor is created Now we can proceed to compute spatial correlation measures and model the spatial structure of sudden infant death rate given other covariates Spatial Statistics Spatial Autocorrelation We need to check whether the process of sudden infant deaths is spa tially autocorrelated If so then spatial models are indeed needed to analyze these data 1 Open the dialog Choose Spatial Autocorrelation from the Spatial Statistics menu Select sidsarc under S PLUS Data Frames 2 Specify variables Under Columns click sid and then births Corresponding entries a
5. The O bject Browser works in a way similar to the Browser from the Window enut biing i forwaed Windows Explorer In the left hand pane click the plus sign next to the data frame icon to expand the list In the list below it is Census tracts 12 Exercise 1 Exploring Demographic D ata 12 Look at the data in a Data window Double click the Census tracts icon to open a Data window as shown in figure 2 4 It contains the 477 records exported from the Census tracts attribute table ry 23 ri 26 at Fc mS inc Oe L Med inc Per papine Prt mala Palema TET iag 4 F 40 35 4 4 5 amp T o Figure 2 4 The exported data in an S PLus data frame Data windows in S PLUS are similar to table windows in ArcView See chapter 4 Using S PLUS and S SPATIALSTATS for an overview and chapter 4 of the S PLus U se s Guide for complete details on what you can do in the S PLUS Data window Make Histograms Comparing Percentages of Infants Barplots such as those available in ArcView are ideal for categorical data with relatively few categories Such data sometimes arise from grouping numeric data into intervals H istograms on the other hand are ideal for numeric data that take on a continuous range of values For example the percentages of infants aged 0 to 4 years in each of the Atlanta Census tracts data are well suited to visualization with a histogram because the percentages vary over a continuous range of values He
6. and group the newly selected records by writing to the same field and using the string South as the Group ID If you export the resulting field to S PLUS it will result in a categorical variable a factor with two levels Add Indicator Field TheS PLUS Menu Similar to Group Selected Records the Add Indicator Field dialog adds a numeric field that records which records are selected This is useful after selecting a subset from the attribute table of the active theme An indicator field can be added to the attribute table for labeling the selected subset of records This field can then be used in S PLUS to sub set corresponding variables or asa dummy variable in linear regression models or other statistical analyses Before opening the dialogs select some features in a theme Some tools for this include the query dialog custom Avenue scripts or the selection tool If no features were selected all records will be included in the selection To group the records into numerous categories repeatedly make a new selection then call the dialog 1 To create a new field check the corresponding button and specify a name for the indicator variable Specify a Join Field so that the new field can be joined to the active theme s attribute table 2 To write the indicator values to an existing numeric field check the corresponding button and choose a field from the drop down list For selected records choose whether to replace current
7. bess upha SFIS wine bain Ba CS Fae Dee e 2 CE Ee a ed NE Las Spada Aniana Epad Eapro Figure 3 13 The Spatial Statistics menu This dialog is designed to construct spatial weight objects for spatial sta tistics and modeling The concept of a spatial weight is important in spatial statistics and spatial modeling M any criteria have been sug gested for constructing various forms of spatial weights and different weighting schemes may significantly affect the results of a spatial analy SiS In S PLUS and S SPATIALSTATS there is an object structure called spatial neighbor for managing spatial weights S PLUS also provides aread neighbor function to read geographical neighbor information from a text file However the user must construct the text file contain ing the spatial neighbor information This can be time consuming for a study region having many spatial units S PLUS for ArcView provides an easy tool for constructing spatial neighbors spatial weights objects The spatial weights are calculated based upon the geo locational information included in ArcView shape files The Spatial Neighbors dialog allows the user to select among sev eral options for calculation of the spatial weights First Order Neighbor Weights This option constructs a spatial weight matrix based solely on the adjacency of spatial units polygons The element x i j of the resulting weight matrix The Spatial Statistics M enu Tipini
8. The dialog shown in figure 2 3 appears Engel Date to SPOS Diets fo E apace Jin Fai lM 477 of 0D Pee Selai bor pa E aptaki Theres tercureacth Pare Cortech Pt Leedi Fiii M ms Doned Cuma n Daken Mira ha Coaches Coka H mra kr T Cantina T Pieke Cikin Fiag PLUS Ohens TIF Fames of Dia Paara ic Creada Emring SFLU Obyects Mung aisar Lorem lo HEE Figure 2 3 The Export Data to S PLUS dialog This dialog allows you to save an ArcView table as an S PLUS data frame An S PLUS data frame is a table of data which can have numeric character and other kinds of data in its fields The dialog reports that only 477 of 482 records are selected for export as desired 11 Chapter 2 Quick Start Tutorial The glisa function is cre 8 Name the new data frame By default the name of the S PLUS a Wee that data frame to be created is based on the ArcView theme name ae ne es There is no risk of overwriting the ArcView table since the S PLUS data frame is saved in a different directory Keep the name that is displayed below Name of Data Frame to Create or change it to another name Scroll through the list below Existing S PLUS Objects to see all the objects in the S PLUS working directory If you are using S PLUS for the first time this working directory has the name _Data and contains only the objects Last value andglisa S PLus names must start If you have already been using S PLUS there may be several wit
9. The plots appear on pages of a Graph sheet The plot of fitted values against residuals shows a relatively homogeneous scatter of residuals across fitted values There are a few slightly outlying values the three most extreme are labeled by row number The plot of the residuals against normal quantiles does not indicate any marked departure from the assumption that the residuals are normally distributed The plots suggest that the results of the Analysis of Variance can be trusted 9 View the printed results The printed output appears in a Report window The F statistic of 6 645 on 8 and 42 degrees of freedom yields a p value of 000014 this indicates a significant difference in the mean values of M edianrent between subregions Now you will prepare the results of the Analysis of Variance for import into ArcView Keep in mind that the rows of the US States data and state anova res data frames correspond 10 Work with the saved results Open the data frames state anova res and U S States Highlight the column State name in US States click in the rows of data and drag over an empty column in state anova res as shown in figure 4 29 This copies that column into the state anova res data frame Copy the 73 Chapter 4 Using S PLUS and S SPATIALSTATS ae fapmle Bedigerent Iob ragian dace TS Scares 28 actim oT Tema Sob cegian Best duels Su J Squares GOES BISS8 Beg af Fresia a az Bestchiml cherdacd citoi TU 03
10. and Spin dialog Hold down Ctrl while selecting the fields in order to make a multiple selection 8 Explore the 3D data interactively Click the arrow buttons in the upper right of the Spin window to rotate the scatterplot of Avg inc Pct 0 4yrs and Pctfemale You can see the 3 dimensional features of the plot 22 Exercise 2 Finding R dationships B ewen D enographic Variables 9 Sweep a selection of the data Drag the pointer across any of the plots and the points which it covers are highlighted in all plots and in the list of data points in the lower right Since the box next to Persistence is checked the points remain highlighted after the pointer passes over them To leave the Brush and Spin windows click the Q uit button ale z Bati Ame Help T Beteed a 9 E Sale a A m JAWGUNC zj Help an E Pepino r Labels E Big Polis He Figure 2 15 S PLUS Brush and Spin windows 10 Print a view of the interactive plot To print a snapshot of the interactive Brush and Spin windows it is necessary to copy the screen image to the clipboard and then save the image using an image editing program Press the Print Screen button on your keyboard to copy the screen image Then open M icrosoft Paint or M icrosoft PowerPoint and paste into a blank document Save the file You can then import it into an ArcView layout 23 Chapter 2 Quick Start Tutorial EXERCISE 3 GEOGRAPHIC CLUSTERING OF LINEAR REGR
11. and is placed on the left side of the formula and the explanatory factor Sub region is placed on the right side see figure 4 24 win Subrat Hoer eat E Saw Model Objet F Dra frar eth Wing Visi Sup Ba aver Forais famia Fadar n UU Crea Formula CE creat te Figure 4 24 The Moda page of the Fixed Effects Analysis of Variance dialog 6 Save relevant results Click the Results tab of the dialog Select the printed results Short O utput and Type Sums of Squares Save the resulting fitted values and residuals in a data frame called state anova res see figure 4 25 Medd Daime en Pt Printed Patent Tred A Hay Fe Sat ha Saeain ae E Typed Sure of 9 qe E Fated esd T Tyre fof fous F Fekah l Ertreated Laitan 7 Beare E oei kar ke Fistor l Bismi D iede CE w Figure 4 25 Results page of the Fixed E ffects Analysis of Variance dia log 72 W hat isS PLUS 7 Create diagnostic plots Click the Plot tab of the dialog Specify the Residuals vs Fit and Residuals Normal QQ plots Click OK Feed Elle Ansy af Variance Alle Model Daim Aen Pa Phi Tories FP Resid i Fa T ik Fani M Sgr dbo Aeka vr Fi l iick fugi l Repre wt Fa Runia of Esirera Poor 2 kiar ip Fo Placidusk Horai 0 fi I Feabh Eora Pama Aika Plt T Phot Pia Fiadh l rki r r F l DE Cancel ipp k omei Hee Figure 4 26 Plot page of the Fixed E ffects Analysis of Variance dialog 8 View the plotted results
12. ere is how to perform such a check for the Atlanta census tract demo graphic data 6 Clean the data Select the 25th field Avg_inc a field of interest Choose Statistics from the Field menu This displays summary statistics in a pop up window Notice that the minimum value of the average income is 99 which does not make sense The numerical value 99 has been used to denote missing data Now you need to find out how many such values there are in the table To do this quickly first choose Sort Ascending from the Field menu with the field Avg_inc still selected The top portion of the table now appears as in figure 2 2 The first four rows of the table have entries of 99 in all fields Evidently no data was available for these census tracts The fifth row is rather suspicious because it has many zero values From the sixth row on the data look reasonable Select rows 6 through 482 as follows First select the first 5 rows by clicking each of them while holding down the shift key Then click the Switch Selection button on the ArcView toolbar You are now ready to export the cleaned data to S PLUS Exercise 1 Exploring Demographic D ata Figure 2 2 The attribute table of the C ensus tracts theme after sorting on the Avg_inc fidd Export the Cleaned Attribute Table to S PLus 7 Open the Export dialog Click the title bar of the Atlanta view to make it active Now choose Export Data to S PLUS from the S PLUS menu
13. for the addition of the loess fit The loess fit shows little nonlinearity and does not fit the points in the upper left of the plot To make a tighter fit right click the plotted points and choose Smooth Sort from the menu which appears 19 Chapter 2 Quick Start Tutorial 207 z 5000 30000 55000 80000 105000 130000 155000 Avg inc Figure 2 11 Atlanta census tract Average income versus Percent Popu lation 0 to 4 Years with a loess curve fit displayed Next to Span enter 0 1 and click OK The plot shown in figure 2 12 appears 30 7 20 7 Pct 0 4yrs T T T T T T T 5000 30000 55000 80000 105000 130000 155000 Avg inc Figure 2 12 Atlanta census tract Average income versus Percent Popu lation 0 to 4 Years with a loess curve using a span of 0 1 20 Exercise 2 Finding R dationships B ewen D enographic Variables How does this relationship depend upon Pct female To explore this you will use Pct female as a conditioning field to divide the records into several classes and then display the relationships in all the different classes in a single S PLUS Trellis plot 4 Turn on conditioning mode First turn on the conditioning mode for graphics by depressing the Set Conditioning M ode toolbar button 4 Be sure that the number of modes seen just beside is E 5 Select the fields Ctrl click Avg inc Pct 0 4yrs and Pct female in this order 6 Create the plot Click the Loess butt
14. information on the S PLUS user interface Choose Q uestions and Answers for a discussion of some com mon difficulties and their solutions The Visual Demo item launches an online demo to help users familiarize themselves with common tasks in S PLUS The S PLuS User s Guide the S PLUS Programmer s Guide and the S PLUS Guide to Statistics can all be accessed in electronic form from the S PLUS Help menu In both ArcView and S Plus you can access context sensitive help by clicking the Help button in any dialog or by clicking the context sensitive H elp button h in the main toolbar W hen working in the S PLUS Commands window typehel p at the S PLUS prompt or press F1 to open the S PLUS online help system To display the index of S SPATIALSTATS help files use the S SPATIALSTATS Help item in the ArcView Help menu This manual follows these typographic conventions and references The italic font is used for emphasis and also for the names of S PLUS manuals The bold font is used for filenames Thetypewriter fontis used for S PLUS commands and output Displayed S PLUS commands follow the S PLUS prompt gt Commands that require more than one line of input are displayed with the S PLUS continuation prompt Key names appear in capitalized form For example the shift key appears as Shift When more than one key must be pressed simultaneously the two key names will appear with a plus sign between them For exam
15. palette Click the Scatter Plot M atrix button The plot in figure 2 11 appears in a Graph sheet Several of the plots show features outside the main cluster of points The plot of Average Income versus Percentage 0 to 4 Years shows a negative association and other plots show a small number of census tracts with extreme values of Percentage Female Exercise 2 Finding R dationships B tween D enographic Variables es a es oe ce ee Sees Se Avg inc Pct female Pct 0 4yrs Figure 2 10 A scatterplot matrix showing several pairwise relation ships Find the Relationship Between Average Income and Percentage 0 to 4 Years Conditioned on Percentage Females You can discover detailed relationships between several fields by condi tioning on one of the fields This means looking at the relationship between two fields on various subsets of the data set The subsets are determined by the values of a third field in much the same way that you use a Classification field to specify a graduated color legend in Arc View 3 Create a scatter plot with a loess curve fit For example first make a scatterplot of Avg inc versus Pct 0 4yrs with a loess nonlinear curve fit Ctl click Avg inc and then Pct 0 4yrs in the O bject browser and click the Loess button on the Plots 2D palette The plot shown in figure 2 11 appears The scatterplot is the same as that in the lower left panel of figure 2 10 except
16. see fes negative Red in the Command box Go again to the Field list and select res positive Select the color Blue You will see 29 Chapter 2 Quick Start Tutorial d prt bii reun AEREI 1 oe Se TFN a aru Mizar oe Err AT Gra 46654 1 Sere Hi SL ani ODS Sane IAR a ee an T S19 1 ab06S 174 Meio She Pao TSE PSF aha T 1N SSPE 13001 BESSA el a 7 BS Cae 4608 Sen 11 be 061011 Bedi ES Ana ST Bd PSST Bod Ze Sm Figure 2 21 Census tracts attribute table showing new fields fres negative Red fres positive Blue in the Command box Under Chart Properties specify Bar Chart and change the scale factor to 0 75 Click OK 10 The result shown in figure 2 22 below gives a clear visual indication of where the large positive model errors are clustered and where the large negative model errors are clustered E ania E arni Figure 2 22 Atlanta census tracts showing spatial bar charts for both positive and negative linear model residuals 30 USING S PLus FOR ARCVIEW GIS Overview Running S PLUS for ArcV iew The S PLUS Menu Export Data to S PLUS Import Table from S PLUS Import Point Theme from S PLUS Group Selected R ecords Add Indicator Field Color Classification Spatial Bar Pie Chart Import Graph from S PLUS Clear Selection and Graphics Linear Regression Execute S PLUS Commands The Spatial Statistics Menu Spatial N eighbors Spatial Autocorrelation Local Spatial Ass
17. select the fields Avg_inc Pct_male Avg_age from the first column in that order This generates the formula Avg_inc Pct_male Avg_age indicating that Avg_inc is the response to be modeled as a function of Pct_male and Avg_age Specify Tract as the Join Field if it is not already set Finally ensure that Display File after Computation is checked and click OK Caution Avoid the tempta tion to believe the t statis tics and p values Reliable values for these quanti ties are given by a spatial linear regression model Exercise 3 Geographic Clustering of Linear Regression Modding Errors 2 Lier Reya ron fim Taed Cire kra iha Sconce Mri Selechen a Napan Herec Thora Fide JPU Date Free oreari bees Grippa Tract Crap ago Tyri Brag ne Pot raser aoe Select Aghir Hof ead F Thews Fields CE E Fie Cole Shaved Farir Eure AUS O beeen ik Tuten Fapt ASCH Caa heda ini f Mapori Bpa e E ingsi Disa Fises pan Tab F Dipp Fie dhe Ciri E Joa ty Dusa T hersey Take io P Figure 2 16 The Linear Regression dialog The fields selected will be exported to S PLus for analysis creating the Census tracts lm data frame in S PLUS Once done results of the linear regression such as coefficient values t statistics and p values are displayed a window Upon closing this window the dialog closes The resulting Linear Fits and Residuals are imported to a new table Linear Regression Analysis of Census tracts lm and
18. statistics are estimated for each row of your data and can be associated with their global counterparts and used to estimate the contribution of the individual statistics to the corre sponding global statistics A value is returned for each sampling unit record thus the output can be visualized in the View window as another attribute of the corre sponding theme 1 Select one variable for analysis from fields in the attribute table of the current theme and columns in S PLus data frames in the S PLUS data directory You can also type directly in the Variables for Analysis box Caution If the data does not come from ArcView the join may not be possi ble The Spatial Statistics Menu Choose a spatial neighbor object in the current S PLUS workspace The spatial neighbor object must be consistent with the selected variable it must be associated with the same spatial region of study Use the dialog for spatial neighbors to generate such an object for the current theme If desired specify a vector of weights from the list of columns of the currently selected data frame or theme Choose between M oran s or Geary s c correlation indices Specify a name for the S PLUS object which is created when the correlation routine is run Check whether the results should be imported as a table into ArcView Check whether the imported table should be joined to the current theme s attribute table If so a join field
19. then joined to the Attributes of Census tracts table See figure 2 17 25 Chapter 2 Quick Start Tutorial D Cers isoh im tel Hoad Fie Edi prm Hee eee lisar Regression Fit es Call Lai bormule Ceram tracta t isldt rg inz Ceres tr cta f i ld3Pct sala Cage tracis ieldting wae Residuals Hin 10 Hadian 40 Hax 5557 L254 1613 Gals Lira Gosliicissta Value Std Error E malus Esioltj Lint rcepi Sh42 0526 1U 41Ir 1121 0 3417 U oda TNE bracts FisldePot wale bg J507 156 7066 2 262 D edil IS bracts i ieldikTg tgs LOSE 7526 Lo 1338 E J57A 0 00 Remsdual standerd ecrcor 15500 on 474 degree of resica Huoltiple E Squared 0 04157 F statistic 16 81 on 2 and 474 decrees of frasica the p value is 2 25 007 Correlation of Coed i icient Carms fects fasldaPot eels Tei EPS Lie ldshwy b35 3 DODO E DDC aa 2 OOD eT lo dd 0000 i TT eT FT T i 2a 1150 TOn paT re el ST 22 10000 260000 EN ie PARE EnA Ea 2b ee rer ea Te 3 TI hoo 70 TH Tes os HE 25600 eae Ha E IE N Figure 2 17 Linear Regression M odel results and selected record set Color Classify the Census Tracts Using Residual Values 4 Prepare the view With the View window in focus click the Zoom to Full Extent button E on the ArcView toolbar Turn off the Highways theme but keep the Streets in downtown theme turned on to provide a visual indicator of the downtown census tracts From ArcV iew s S PLUS menu s
20. to see the various property dia logs available Exercise 1 Exploring Demographic D ata The number of classes and the class size for the above histogram has been computed using an automatic algorithm based on our 477 values of Pct 0 4yrs In this case 26 classes resulted 15 16 Change the title and axis label To add annotations clarifying the data being displayed first double click the X axis title and change it from the default AUTO to Percent of Census Tract Population Under 4 Years Old and then from the Insert menu select Titles Main and enter Infant Distribution in Atlanta Census Tracts to set the main title Change the number of classes To change the number of classes first click one of the histogram bars You clicked in the right place if a green handle appears below the first histogram bar Right click on the histogram and choose Options from the context menu to bring up the Histogram Density property dialog Change the entry beside Number of Bars from Auto to 50 and click OK The histogram is redrawn with 50 bars instead of 26 which shows finer detail lg lh ili zb l bi bb ibb 120 iib ili iki Wo j F ioniza Trat Fep t THH iren c Figure 2 7 Histogram of the percentages of children aged 0 to 4 years in the selected Atlanta census tracts using 50 classes Import an S PLUS Histogram into an ArcView Layout T Import the graph Switch back to ArcView by selecting it from the
21. 20 D os a eo i ji ngi z al 5 00 UE a BSR BS Figure 4 7 The output from the Summary Statistics dialog dialog Highlighted text in the Report Window can be copied to the clipboard and pasted into another program You can even paste the text into an ArcView layout 7 Trim the data using the Indicator field W hen analyzing the data below you will want to exclude the records which we have marked with 0 in the Indicator field Click again on the income data icon in the Object Browser and choose Subset from the Data menu The dialog should show income data next to Data Frame Select Avg inc Pct male and Avg age next to Columns in Subset To include those records for which Indicator is 1 enter Indicator 1 next to Subset Rows with Select D ata Frame as the Result type and enter income trim as the name of the new data frame next to Save As Click OK The Object Browser shows that the new data frame income trim has 477 records and 3 fields as expected Running Linear Regression 1 Find the data fields Expand the data frame icon in the left pane of the O bject Browser to show income trim In the right pane the three fields of income trim are listed W hat isS PLUS Dieta Fetus Ce Foxem m Reite E Datore Suban Heerreats rakaa nn 7 adC Coke iv tiba pr F gg fai o I Bhen Gita aio on cra r Figure 4 8 The Subset dialog daah Fid cipia Puget Lpi Figure 4 9 The Object B r
22. 553 Ertimsted affects may be cibelerrswd GE ne of iq Bean Jy F Valor FriFi Wb regim 8 OGLE JALA Bee 0 Lee Fecidmals 45 MELIS SMIT Te Figure 4 28 Printed output of the Analysis of Variance column Sub region from U S States into state anova res as well 11 Are the fitted values reasonable Highlight the Sub region column in state anova res and click the Sort Ascending toolbar button 1 Scroll down the data frame and notice that the fitted values are the same within each subregion as expected see figure 4 30 Highlight the Sub region column once more and click the Remove Column toolbar button i to remove the column from state anova res 74 W hat isS PLUS Subregion State abbr Fo Faih WA IBAI Mn HiT Fa Heng ME 1z2 Wehien MO Bau Whiten SD ea hain vay 35 ENGen Mi gy Figure 4 29 U sing drag and drop to copy the State name column from U S States into state anova res if tate aroee ree 1 2 fit residuals State ne T 35 00 5 DoheViscansin 2A 3300 35 00indaw a EET Lois 236 32600 43 00iinois Rial 325 00 17 hoMichgan B ae 241 75 R 25M entucky 7 RETR 1 Tennessee G B42 Misv5 12 75 Albena eas 2178 26 7 SMississippig ri Figure 4 30 Using the additional column Sub region to verify results from Analysis of Variance Bring the results into ArcView for visualization 12 M ove to ArcView now and choose Import Table from S PLUS in the S P
23. ArcView GIS THE HELP SYSTEM S PLus for W hile working in ArcView you can access on line help with the func ArcView Help tionality in the S PLus and Spatial Statistics dialogs S PLus for Displays an on line copy of this manual ArcView User s Manual S Plus Language This is a comprehensive reference to over 2 000 S PLUS functions and Reference built in data sets S PLus Spatial Displays help for theS SPATIALSTATS module Statistics Help About S PLus for Provides information about the current version of the extension and the ArcView location of the S SpatialStats module if installed USING S PLus AND S SPATIALSTATS What is S PLus 56 O bject Browser 56 Graph Sheets 65 Data Windows 69 What is S SPATIALSTATS 79 Types of ArcV iew Data and S SPATIALSTATS 79 Analysis in S SPATIALSTATS 79 Script Window and Commands W indow 81 When you use S PLUS for ArcView you have full access to the analyti cal and visualization tools of S PLUS one of the most comprehensive programs available for exploring and analyzing data The optional S SPATIALSTATS module extends S PLUS for modeling spatially corre lated data With S PLUS for ArcView you can use S PLUS to analyze data from ArcView attribute tables Tables may be exported to S PLUS and analy sis results later joined in ArcView to the original theme attribute table Themes can have features with different geometric shapes The main shapes that can be analyzed using S SPATIALSTATS ar
24. Avg age Ctrl click Avg age and then residuals in the C ensus data folder Depress the 2D Plots button Si if it is not already depressed to open the 2D Plot Palette In the 2D Plot Palette click the Scatterplot button Ej A Graph sheet opens showing a scatterplot of residuals against Avg age as seen in figure 4 12 From this plot it is seen that the residuals increase with increasing values of Avg age When linear regression is valid the scatter of the residuals is relatively homogeneous along each independent variable 63 Chapter 4 Using S PLUS and S SPATIALSTATS Figure 4 12 Plot of residuals against Avg age 4 Transform Avg inc To remedy the problem seen above you can try replacing the Avg inc by a transformation of it which grows more slowly A common choice is to take the logarithm of the data Click income trim in the left pane of the O bject Browser and choose Transform from the Data menu The Transform dialog appears Enter Log avg inc as the new column name Notice Avg inc in the Variable box Select log10 in the list next to Function and click Add The S PLUS expression is automatically filled in as seen in figure 4 13 Click OK Figure 4 13 The Transform dialog 5 Perform another linear regression Click Log avg inc then Ctrl click Avg age and Pct male in the right pane of the Object Browser O pen the Linear Regression dialog 6 Save the results of the fit M ove to the Results page Check the b
25. E Filesi pues ibe Ditas it Vion Files ip duds plu Dee Froga Fi usii Library tosllis i Deta Fesgram File VWLlibterpi lelurter Date Feagia Pile ap Libr arpi ti Dara Progresa Pilari oplusAt y Libr erp agai Dera ti Pcogcmm Fi Up lua Libr erpi Leditdete i Tita VWoogea Filas yap 95 libi arpi emi Deta C hi cogrea Filesi eplueis Library Matrix Dat Figure 5 1 The Commands window 3 Bring the data into S PLus To bring the data into S PLUS open the file AVH O M E Samples SArcView sids q in S PLUS where AVHOME refers to the directory in which ArcView is installed This is typically c esri av_gis30 arcview as we assume here Enter the following command in the Commands window and hit Enter gt source c esri av_gis30 arcview samples sarcview sids q This adds the data frame sids to your S PLUS working directory You can check that you have now two versions of the sids data frame by running gt find sids 1 C Program Files splus45 users minardi _ Data 2 C Program Files splus45 module spatial _ Data The output indicates that there are two copies of the si ds data frame The first one listed in the default S PLUS working directory was loaded by the previous command It will be used in our analysis Remove or rename the first version the one that was just sourced in when you want to follow the examples in the S SPATIALSTATS Use s Manual otherwise you may encounter erro
26. ESSION MODELING ERRORS Caution Use ordinary least squares linear regression with spatial data only as an explor atory tool To make cor rect conclusions about spatially correlated data use spatial linear regres sion available from the Spatial Statistics menu in ArcView when the S SPA TIALSTATS module for S Plus has been installed In these exercises you will fit a simple linear regression model for pre dicting average income based on average age and percentage male for each of the Atlanta census tracts You will visualize the model errors or residuals for each census tract using both color classification and spatial bar charts The exercise follows these steps e Fit a Linear Least Squares Regression M odel e Color Classify the Census Tracts According to Residuals Values Add a Spatial Barchart Based on Residuals e Improve the Barchart by Creating and Using Positive and Negative Residuals Fit a Least Squares Linear Regression Model 24 1 Select the data Follow steps 1 through 6 of Exercise 1 This selects all but 5 rows of the census tract data 2 Display Linear Regression Dialog Select the Atlanta view and ensure the Census tracts theme is selected to enable the items in ArcView s S PLUS menu Select Linear Regression from the menu and accept the warning dialog indicating that the Linear Regression will be computed only on the 477 selected records 3 Specify the model In the resulting dialog figure 2 16
27. Fed Codes Omiin Senta Es Fit Cheat ine 5 PLUG Giph Dai akitii red Ge agati Lee hpa Execute 5 PLUS Cofis Figure 3 2 TheS PLUS menu Select Export Data to S PLUS to export selected fields and records into a new S PLUS table called a data frame This dialog can also be used to add centroid information to the attribute table To export data follow these steps 1 Choose a theme from the drop down list under Exportable Themes Select the fields to be exported from the A rcV iew attribute table associated with the chosen theme These fields will be exported into the data frame To select more than one field hold down the SHIFT key while clicking If the data is to be imported back into ArcView and joined to an existing table you must specify a field to be used as a Join Field The field specified must have all non duplicate values A check for record uniqueness is performed at selection time Specific geographical information of spatial observations is often required when conducting a spatial analysis The x and y coordinates for a point coverage or the centroids of a polygonal coverage are typically useful in spatial analysis To create centroid columns in the exported data frame check the TheS PLUS Menu box under Polygon Centroids or Point Coordinates and specify names for the x and y coordinate columns such as Latitude and Longitude for instance You must specify a Join Field when centroid coordin
28. LUS menu Import the state anova res data frame Specify Join Imported Columns to Theme and select U S States as the theme to join from the dropdown box 75 Chapter 4 Using S PLUS and S SPATIALSTATS 13 Match records based on common values in Select State_name as the Imported Column and the same as the Theme s Field Click OK see figure 4 31 bnp Fable Fre SPS BPLLES Obini iy largui Lala Fura tate aL Cirit Faplce bitang Wai w h F impri lbet r Hew Tabie fens grea G dembepoted Cote Ta Thee iste a Match Records Bisai an Conor Yuen in inspected Cabaret Themes Rej Etats saree ik Canca ha Figure 4 31 U sing the Import Table from S PLus dialogin ArcView to bring the results from the Analysis of Varianceinto ArcView 14 View the results To view the results of the Analysis of Variance in the Continental United States view you may use the Color Classification dialog from the S PLUS menu in ArcView Select US States as the active them and Residuals last column as the field or column to classify upon Click OK see figure 4 32 To change color scale you may double click the US States theme name in the table of contents of the view The states in the view are lightly shaded where median rent is relatively low for the subregion and heavily shaded where median rent is relatively high for the subregion see figure 4 33 One feature seems unusual in this view the cluster of very lightl
29. MathSoft S PLUS FOR ARCVIEW GIS USER S GUIDE Version 1 01 July 1998 Data Analysis Products Division M athSoft Inc Seattle Washington Proprietary Notice Copyright Notice Trademarks Acknowledgment M athSoft Inc owns both this software program and its documentation Both the program and documentation are copyrighted with all rights reserved by M athSoft No part of this publication may be produced transmitted transcribed stored in a retrieval system or translated into any language in any form without the written permission of M athSoft Inc See the License Agreement and Limited Warranty for complete infor mation The correct bibliographical reference for this document is as follows S PLUS for ArcView GIS User s Guide Data Analysis Products Divi sion M athSoft Seattle WA Copyright 1987 1998 M athSoft Inc All rights reserved M athSoft Inc 101 M ain Street Cambridge MA 02142 USA Printed in the United States of A merica S PLUS is a registered trademark and STATSERVER S SDK S SPATIALSTATS S DOX StWAVELETS and AXUM are trademarks of M athSoft Inc S and New S are trademarks of Lucent Technologies Inc ArcView GIS and ARC INFO are registered trademarks of Environmental Systems R esearch Institute Inc Intel is a registered trademark and 486 SX and Pentium are trademarks of Intel Corporation Microsoft Windows MS DOS and Excel are registered trademarks and Windo
30. Project to navigate to and then open the ESRI AV_G1S30 AV Tutor ArcView qstart apr project Start the S PLus for ArcView extension With the qstart apr window in focus select the Extension dialog from the File menu In the dialog check the S PLUS for ArcView GIS item in the list of available extensions When O K is pressed to confirm your selection the extension will load If S PLUS is already running the extension connects to S PLUS otherwise S PLUS will be started which may take a minute or two Open the Atlanta view Once the extension has loaded the window titled qstart apr will display several views Select the Atlanta view and then press the O pen button in the window Open a theme table Click on the Census tracts theme to enable most tools and many menu items Click the Open Theme Table button on the ArcView toolbar The attribute table of the Census tracts theme opens This table has 482 records and 47 fields with one record per census tract The fields of this table are demographic attributes such as average income median income population in 1990 and average age Chapter 2 Quick Start Tutorial Alinman of Cane hate Figure 2 1 The attribute table of the C ensus Tracts theme Compute Summary Statistics in ArcView and Prepare Data for Export 10 Before exporting your table to S PLUS to create graphs it is a good idea to check for anomalous data which should not used in making graphs H
31. R egression Bibliography Index WELCOME Installation What You Can Do with S PLUS for ArcView Tips on Learning S PLUS for ArcView Typographic Conventions Technical Support NuUBWN Welcome to S PLUS for ArcView GIS This software package combines desktop GIS and mapping with powerful statistical and graphing tools for visualizing exploring and analyzing spatially referenced data S PLUS for ArcView consists of e ArcView GIS e S PLUS e S PLUS for ArcView extension e S SPATIALSTATS add on module optional Chapter 1 Wdcome S PLUS for ArcView connects ArcView with the S PLUS data analysis software through a number of menu driven dialogs You will work with S PLUS for ArcView through ArcView s S PLUS and Spatial Statistics menus shown below Pi Ed ee a ireke Hep LT Jl 2 SPS ther Acie OS Die felt y ier m jun Pee ims jie E mam Ae in SMES Sm Gaai Line Beaton Figure 1 1 TheS PLUS and Spatial Statistics menus in ArcView This manual explains how to use S PLUS for ArcView and gives a brief introduction to both S PLUS and S SPATIALSTATS T his chapter covers how to install S PLUS for ArcView e what you can do with S PLUS for ArcView how to learn S PLUS for ArcView Installation S PLUS for ArcView requires S PLUS Version 4 5 or later To install the S PLUS software refer to the instructions that come with the software It is a good idea to turn off other applications in particular vir
32. S workspace The spatial neighbor object must be consistent with the selected variables it must be associated with the same spatial region of study This is usually generated using the dialog described above Use the slider bar to specify the number of permutations used in the M onte Carlo distribution of the correlation index Choose between M oran s or Geary s c correlation indices Specify a name for the S PLUS object which is created when the autocorrelation routine is run A summary report of the routine will be saved in a text file Specify a name for the report file and indicate whether if should be opened immediately after running the regression After reviewing the summary information as displayed be sure to close the opened file so that the dialog will close 49 Chapter 3 Using S PLus for ArcView GIS Local Spatial Association 50 Select Columns ha dhe Source Meat Theta Fetch PUL Dhol Fiar Eras Bi ieii Carte Dirinon of Coada Indes Hiasi of Pemain 1000 Sneed Ramir Sieg Dara iri a bd Daa inant cna Fe Depia Fly sis Capii Figure 3 15 The Spatial Autocorrelation dialog This dialog uses S SPATIALSTATS to estimate generalized versions of the local M oran and the local Geary indicators of spatial association The local M oran index helps identification of spatial agglomerative pat terns The local Geary index helps to identify spatial patterns of similar ity and dissimilarity These local
33. TATS e what types of analysis are available in S SPATIALSTATS The Commands and Script windows in S PLUS give you access to the full power of over 2 000 S PLUS functions Use the Commands window to quickly run commands singly Use the Script window to run and edit several commands at a time and to save sets of commands as scripts for future use or distribution to others Here are a few simple examples using the SID S data 1 Open the Commands window by depressing the Commands Window toolbar button 3al 2 If it is installed the S SPATIALSTATS module is automatically loaded when S PLus for ArcView starts up When you run S PLUS without running ArcView you must load S SPATIALSTATS module Do this by entering the following command in the Commands window gt module spatial You can check that the S SPATIALSTATS module is loaded by entering 81 Chapter 4 Using S PLUS and S SPATIALSTATS 82 gt search and checking that the S SPATIALSTATS data directory is in the second position in the list of S PLUS databases as seen in figure 4 35 To rerun a previous command press the U p arrow until it reappears r IKT gt ammrch PCL SCi hiite Filesi oglu ass bus elmer disi Pore 3 TE Propam Filesi pd ede pera y pany 11 TC Peogemm Filesi yop dues jpg Pence 4 WCU Peapod Res Pie bad 5 Cr Foogrem Filesi jap duds a 08 TC iFeogeme Fa lewi yep duds yaY 17 TCP i Eege Fables aplasia f ga C
34. Thesa Tiaki SALS ia Fii TET a Sad Fecuits Saree S PLUG Dii ia Hendra FP Mispa Data Fiane i a Tabii E jebate tirara ari E Janis Due Thasa T iie D epin Fin atte Cepia E T Figure 5 9 Spatial linear regression on the SIDS data 5 Fit the spatial model Click OK This creates a data frame with residuals and fitted values named Ncco slm Chapter 5 Analyzing Spatial Data in S PLus for ArcView The spatial linear regession output begins as follows Spatial Linear Regression Fit Call sl m formula sids arc sid ft sids arc nwbirths ft cov family SAR spatial arglist list neighbor Ncco neighbor Residuals Mi n 1Q Median 3Q Max 2 036 0 568 0 02794 0 4586 2 69 Coefficients Value Std Error t value Pr gt t Intercept 1 5428 0 2211 6 9766 0 0000 sids arc nwbirths ft 0 0420 0 0062 6 7371 0 0000 Residual standard error 0 792143 on 97 degrees of freedom Variance Covariance Matrix of Coefficients Intercept sids arc nwbirths ft Intercept 0 048901832 0 001126093289 sids arc nwbirths ft 0 001260933 0 00003884459 Correlation of Coefficient Estimates Intercept sids arc nwbirths ft Intercept 1 00000 0 91488 sids arc nwbirths ft 0 91488 1 00000 rho 0 02318 Iterations 4 Gradient norm 4 472e 7 Log likelihood 206 1 Convergence RELATIVE FUNCTION CONVERGENCE Both coefficients appear highly significant and the covariate indeed explains some of the variability i
35. US and imported into ArcView Specify an alternate name for the graphics file to be created if so desired Choose a layout into which to place the plot Click OK TheS PLUS Menu PLUS Geaph ka inept SALIS pih To lapri Gough Sheat 051 Pepe GSF Fie U asd For Torii Ble a Femi Er E o Fpa Ta Lopni i ymaa j or Ewreal palp Figure 3 10 The Import Graph from S PLUS dialog Clear Selection and Graphics Linear Regression Choose this item after drawing the Spatial Charts on the spatial units in the View window It resets the picture to its state before the charts were added When a table is selected this menu item will clear the selection in the same way as the Clear Selection toolbar button Use this menu item to fit a linear regression model based on variables selected from the attribute table for the active theme or from S PLUS data frames 1 Build a formula from fields in the current theme and columns in S PLUS data frames in the S PLUS data directory Click a theme field or data frame column to add it to the formula The first selection made is used as the response variable You cannot type directly in the formula field 2 If desired choose a vector of weights from among the columns of the currently selected data frame or theme The default is to fit a model without regard to weights 3 An S PLUS data frame containing fitted and residual values will be saved after the regression runs Specify
36. Windows Task Bar Then with the Atlanta view open and selected use ArcView s S PLUS menu to open the Import S PLUS Graph dialog If you do not have an existing layout you 15 Chapter 2 Quick Start Tutorial will be asked whether to create one Specify Yes The resulting dialog shown in figure 2 8 allows selection from a number of plots open in S PLUS the file and format used to store the graphic and the destination layout in ArcView Since the defaults suffice simply click the OK button to actually import the graph from S PLUS PLUS Geaph te inept SALIS pih To lapt Gough Sheat 051 Pepe GSF Fe tend Fer Toeris Fl cog ben EFS Femi er EFS Fpa Ta Lapat i ymaa zj D Ewreal biaip Figure 2 8 The mport Graph From S PLUS dialog 18 Display and format the graph Display the imported graph by selecting Layouts in the qstart apr project window in ArcView then selecting the newly created Layoutl and pressing the Open button Detailed graph features may not display in the layout but will print fine See figure 2 9 19 Closing the extension When you are done using the extension go to the project window qstart apr in this example so it has focus and then under the File menu select the Extensions dialog and uncheck the S PLUS for ArcView GIS extension As for all ArcView extensions if you close and save the project while an extension is active that extension will automatically be loaded the next
37. age and Pct male Data Windows An S PLUs Data window is similar to a spreadsheet but is column ori ented rather than cell oriented You will use Data windows in S PLUS to 69 Chapter 4 Using S PLUS and S SPATIALSTATS browse edit and transform data The following exercise illustrates a number of common tasks with Data windows In the exercise you will also see how to perform an analysis of variance in S PLUS and bring the results back into ArcView Export Data to S PLuS 1 In ArcView open the usa apr project You can find the usa apr project in the esridata directory Open the Continental United States view and click the U S States theme in the table of contents 2 Export the attribute table Choose Export Data to S PLUS from the S PLUS menu and export the theme table to an S PLUS data frame called U S States 3 Select State name as the Join Field From the dropdown box with field names select one to be used for future joins say Emai Date te GPL Data ne Eaa Joan Feed S1 ar Mamai Setcted ka Dapoi Lor Polep Cisi of Pearl Caii O m Dmm ir Tokar Hams ka H Ceis Cakar hsa fre Y Coire Y D Fraea Cohan Foseating S PLUS Diese Piara of Dads Frame io Create Eara PLUS Die iu ts Ming Vatu Cor m to HA eet ne r Figure 4 21 Exporting the U S States theme table to S PLUS State_name Click OK The U S States data frame is now visible in the O bject Browser The data frame state now
38. al region of study It can be generated using the Spatial Neighbors dialog described earlier Select one of the following three types of the spatial regression model for the analysis CAR or Conditional Autoregressive SAR or Simultaneous Autoregressive and MA or Moving Average An S PLUS data frame object will be saved after the regression runs with fitted and residuals values from the regression Specify a name for this object and indicate whether it should be imported into ArcView and joined to the active theme If a join is requested then a Join field must be entered Indicate whether to include Moran s test on the estimated residuals A summary report of the routine will be saved in a text file Specify a name for the report file and indicate whether if should be opened immediately after running the regression After reviewing the opened file close it to complete the operation The Spatial Statistics Menu Select Coia ican Diha Sraa let Saeco o Meco Humer Thare Fook SPU Dais Pirar Erron kat Poo_qenath Desr hei P Care e O Dew Bpis paren a EPLUE Spatial hii D iiyn BF Taran a rga O Crims AF o birang fang Seed Fosan Seve PU Obed a y Papen S78 Cereus acii dri E ii rist Wt al Ba lirga Data Firea di i Tabie F incheie Howi Tari E iomh Leari harar Tabia F Dispis Fis sie Coni aia STe O E o ca a Figure 3 17 The Spatial Regression dialog 53 Chapter 3 Using S PLus for
39. ame and Ncco names by clicking their icons in the S PLUS Object Browser Select the column Name in 95 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView Ncco names and by clicking in one of its rows drag it to an empty column in Ncco lisa geary s data window see figure 5 6 we ee l Tea ob ea Figure 5 6 Using drag and drop to copy the Name column from N cco names into N cco local geary 96 Spatial Statistics 6 Visualize the results Choose Import Table from S PLUS from the S PLUS menu Enter Ncco lisa geary next to S PLUS Data Frame Fill in the dialog as shown in figure 5 7 below Figure 5 7 Import Table From S PLUS S PLUS Object to Import Data Frame Ncco lisa geary z Columns Replace Missing Values With 999 Import Object s New Table Neco lisageay V Join Imported Columns To Theme J Neco shp x Match Records Based on Comon Values in Imported Column Theme s Field Name z OK Cance Help Importing local spatial association results into ArcView 97 Chapter 5 Analyzing Spatial Data in S PLus for ArcView Spatial Regression You can now use the Color Classification dialog to display the Local Geary s c statistics Figure 5 8 Color classification of thelocal correlation coefficient In the resulting color classification agglomerations of both low and high values are apparent This is characteristic of Geary s c statisti
40. aname for this object and indicate whether you would like to import it as a table and join it to the current theme for further exploration in A rcV iew 4 A summary report of the regression will be saved in a text file Specify a name for the report file and indicate whether if should be opened immediately after running the regression After 43 Chapter 3 Using S PLus for ArcView GIS reviewing the summary information as displayed make sure to close the displayed file to complete the operation and close the dialog Tesi Dokar inna pis ces Foi Saai ip Repor Meramec taa Fai S PLUS Data Farar es Corer Model Franek Fuge F o Sard eget H et Fergus O Tere Fick Fma asi a Daire Coun Carved Harz See LFLL Diea Ae D Anat En ii Tarau ancir ira e gers baaa irid FF kg gts Fuse a a Tahe F iia Ciaran Tines Toii niei ma Fe Dopey Fi ote Copan ec el Figure 3 11 The Linear Regression dialog The OK button remains disabled until a formula with two variables at least has been selected and a join field in the case of a requested join Execute S PLus This menu item provides easy access to S PLUS commands from Arc Commands View Use this to run analytical routines or perform simple operations without having to invoke the S PLUS user interface 1 Refer to the S PLUS O bjects list for the names of existing objects in the S PLUS data directory Choose an object class such as data frame to view only that type of o
41. appears in a Data window Figure 4 23 shows the imported data frame 70 W hat isS PLUS Ubi Hrann E e rE i aff dies i Figure 4 22 The newly imported U S States data frame Perform an Analysis of Variance Analysis of variance is used to determine whether the average values of a continuous field like average income vary between categories of a discrete field like state H ere we analyze the effect of geographical sub region on the median rent in a state 4 Build a model Begin by highlighting the fields of interest in the data frame U S States First click the field M edianrent then C trl click the field Sub region J US Staten ag 40 ai er 43 Dener oce Rerterocc Medanval Reha Units Idet Units 1 1171580 00 70065100 GOO sAa027277100 ARDAN A 205e99 00 1088400 Saena r 3752300 B43 a 227689 aao sai amaan 1175 ee 157 00 PA SoA ee a00 1023 5 17116100 674730 miad 5A Bee 1454400 5120500 12319700 621 T 1a Lo fae Se Pe cee JATAN EN anal Figure 4 23 Highlighting columns in U S States 5 View the model formula Choose the Fixed Effects Analysis of Variance dialog from the Statistics menu The model page is showing when it appears The U S States data frame is already chosen and the formula field reflects the currently highlighted columns the first chosen field M edianrent is taken as the 71 Chapter 4 Using S PLUS and S SPATIALSTATS response variable
42. ates are requested 5 Specify a name for the S PLUS data frame to be created By default a unique name is suggested 6 Check whether the resulting columns in the S PLUS data frames should preserve the same formatting width and precision as in the theme s attribute table Choosing this option will increase the time needed to export the data considerably 7 If there are missing value codes such as 999 in the data enter these values below Missing Values Convert to NA Separate multiple values with a comma Surround strings with double quotes These will be converted to the special NA Not Available value when the data is transferred to S PLUS The selected fields and records are extracted from the shape files and are transferred into S PLUS as an S PLUS data frame with the specified name Disa ns Epal joa Fela IA TAB Paccad Sobecka Trat E ipaa abis Theres Paie pan wi JUL Tj Fen Ceh o Podi Codai Feii E Cer Omn Coun Coker Hine ka X Cikin Dokar Flee Peat r Coanda Y FE Prises Coka Firean EFE Diese Fiara od Dais Frans ia Geste Emra amp PLUS Dear Peyami pogulsten mi A Ming aba Erman io HA Figure 3 3 The Export Data to S PLUS dialog 35 Chapter 3 Using S PLus for ArcView GIS Import Table from S PLUS Joining two tables causes them to be temporarily merged Joining the imported table to an existing table requires one field from each table with corre sponding values for each record to be joined
43. atial data on which they act e Geostatistical data or random field data e Lattice data e Spatial point patterns 79 Chapter 4 Using S PLUS and S SPATIALSTATS The assignment is not meant to be exclusive since many of the func tions can be used on different types of spatial data For example spatial regression modeling is typically used for lattice data but it can be used on geostatistical data Likewise it is possible to perform geostatistical type analyses such as variogram estimation on lattice data In ArcView point themes represent geostatistical and point pattern data while polygons represent lattice data For analyzing geostatistical data S SPATIALSTATS includes tools to perform the following e Estimate and visualize standard or robust omnidirectional or directional variograms e Model empirical variograms fit theoretical variogram models to empirical data e Perform ordinary kriging to obtain point estimates for unsampled locations and kriging prediction variances e Perform universal kriging to model large scale trends while calculating predictions For the analysis of lattice data S SPATIALSTATS includes functions to perform the following e Find nearest neighbors or groups of neighbors based on distance or common boundaries e Calculate and test for spatial autocorrelation using the M oran and Geary correlation coefficients e Perform spatial regression modeling using conditional autoregressive simul
44. bject W hen a data frame is selected its columns are displayed to the right Use the buttons below the O bjects list to browse copy rename or delete an S PLUS object in the S PLUS data directory before issuing any command TheS PLUS Menu 3 Compose an S PLUS command in the top field Press Enter or click on the Run button to issue the command If you do more work in the dialog after entering the command click first on the command line and then press Enter to issue the command The output appears in the S PLUS Output window 4 Use the checkboxes below the command line to paste a copy of each command either to the clipboard or to the S PLUS output window in the dialog J Execute PLS Conwereds Xh Gir reed LG ete OH Oe Align Moon Pagu Bla WG 1 459 2599 SRE iii Dai Bee T Pegs Pike ghee rere Daly Oar a z Dinka Frana Gokanwrer Figure 3 12 The Execute S PLUS Commands dialog 45 Chapter 3 Using S PLus for ArcView GIS THE SPATIAL STATISTICS MENU Spatial Neighbors For users who have access to the S SPATIALSTATS module of S PLUS S PLUS for ArcV iew takes advantage of the ease of identification of geo referenced data in ArcView S PLUS for ArcV iew facilitates the compu tation of spatial neighbor relationships used in the computation of spa tial autocorrelation spatial regression and other spatial statistics As with the S PLUS menu a view must be in focus to have access to this menu Bis Eat Yew
45. c when used in this context It detects clusters of positively correlated values high values surrounded by high values and low values surrounded by low values If you run the Local Spatial Association using the transformed variable sid ft sqrt births the color classification does not pick out such striking patterns of local agglomeration The transformed variable behaves more like a stationary process as expected given our results using the global statistic To model the rate of SIDS as it is standardized by the Freeman Tukey transformation use spatial linear regression 98 1 Open the Spatial Linear Regression dialog Choose Spatial Linear Regression from the Spatial Statistics menu 2 Specify a response variable Select sids arc below S PLUS Data Frames and click sid ft in the list under Columns This will be used as the response in the formula Spatial Statistics 3 Specify a covariate To specify a covariate click nwbirths ft in the list under Columns This field the number of non white births also standardized with the Freeman Tukey transforma tion 4 Choose a covariance model Under Covariance Family choose the simultaneous autoregressive covariance model SAR For more details about this model and for a caveat on correcting the covariance using weights if CAR is desired see section 5 3 of the S SPATIALSTATS U ser s M anual Spatial Limia Nogai pikaj Sci umer bom Eih parce Fra Select a Raper Murai
46. column of data and then click the Sort Ascending button 4 Generate summary statistics for the income data fields Click the income data data sheet to make it active Open the Summary Statistics dialog in the Data Summaries submenu of the Statistics menu The income data data frame will already be selected as shown in figure 4 6 W hat isS PLUS if meone dala 1 2 a 4 Agin Petmale Avgage indicator 00 aang d d AREE qo el CL i 99 00 30 00 25 00 oO oa 19 0 900 100 5000 aa 00 3500 00 EP 4414 Shad Aa Figure 4 5 Theincomedata data frame sorted by Indicator F Himba of Ae F Hanba of Mang Aosa M ma raps Hunar a rw FF id Druin Birta of aira io Hamari Vaks a P Tots Guan Rank F lurai Gategoncel tansi F Pimi Fenis PE p Figure 4 6 The Summary Statistics dialog Next to Variables choose Avg inc Pct male and Avg age Next to Grouping Variables choose Indicator M ake some choices of statistics to calculate Be sure that the Print Results box is checked Click OK 6 View the results The results are displayed in a Report Window as seen in figure 4 7 To format output in the report window just highlight the text right click and choose Font to open the Font 59 Chapter 4 Using S PLUS and S SPATIALSTATS fer sta ant tncome dece HI J b SEBES Bead Boooooooo ys ee f HD fa Gi T 1 del Gath 21 DELP FI ED 33 0 5 0 Cad i Cel Gath Block m gi i
47. e polygons and points Analysis is not presently available for themes which represent arcs or other ARC INFO feature classes This chapter illustrates a variety of typical tasks that the S PLUS for Arc View user will perform in S PLUS and S SPATIALSTATS when analyzing GIS data Starting with data in ArcView you will perform an analysis in S PLUS and bring numeric and graphical results back into S PLUS 55 Chapter 4 Using S PLUS and S SPATIALSTATS WHAT IS S PLus Object Browser If the Object Browser but ton is already depressed and the Object Browser is not visible choose Object Browser in the Window menu to bring the Object Browser into view 56 This section describes several elements of the S PLUS user interface that you will use when running S PLUS for ArcView Object Browser e Data Editor Graph sheets e Command window and Script files The exercises which follow lead you through the basic operations of S PLUS For more detailed and comprehensive information refer to the S PLus U se s Guide The S PLUS environment is object oriented in that all items are distinct editable objects This includes not only data objects and functions but also graph objects and interface objects such as menus dialogs tool bars and toolbar buttons The O bject Browser is a simple and powerful interface through which to work with S PLUS objects It operates in a way similar to the Windows Explorer The exercises below illustra
48. elect Clear Selection and Graphics to unselect the various census tracts 5 Color classify the Census tracts Select Color Classification from the S PLUS menu In the dialog that appears click the Theme button and for the Census tracts theme select the last numerical column Last_res M ove the Color Classes slider to 8 and click OK The Census tracts now appear color coded with the legend indicating coding according to the value of the residuals in the linear regression model 26 Exercise 3 Geographic Clustering of Linear Regression Modding Errors Figure 2 18 Atlanta census tracts after color classification by residuals Some geographic patterns are now clear The most positive residuals model errors tend to cluster in groups to the north of the downtown area and in a few areas to the south of downtown The most negative residuals tend to cluster in the downtown and the region just to the south and west of downtown and in groups near the boundary of the region In other words the simple linear regression model which predicts aver age income with average age and percent male has errors whose values are geographically clustered or correlated The clustering may suggest how to improve the simple linear predictive model by adding other predictor variables Add a Spatial Barchart Based on Residuals 6 Remove the color classification Change the color classification in the previous step to a Single Symbol Legend type wit
49. ercises illustrate concretely how you can extend your analysis and visualization with S PLUSfor ArcView The exercises are designed so you can work along with them on your computer The next chapter Using S PLus for ArView GIS gives detailed descriptions of the functionality in the S PLus and Spatial Sta tistics menus in ArcView You may want to skim chapter 3 at first reading to take just a brief look at the A rcV iew interface to S PLUS This chapter will be a helpful reference later on when you face specific tasks You ll want to work in S PLUS to create graphs of your multi dimensional GIS data and to calculate summary statistics or fit models based on geographical data Go to chapter 4 Using S PLUS and S SPATIALSTATS for a look at the S PLUS environ ment and for an overview of how to work in S PLUS and its S SPATIALSTATS module In chapter 5 you will see in more how to use the S SPATIAL STATS module in S PLUS to analyze spatial data e When running S PLus for ArcView choose S PLUS Language Reference in the Help menu to open the S PLUS online help system In the help index you can access help files for over 2000 S PLUS functions Choose S PLus for ArcView Help for information on any of the items under the S PLUS and Spatial Statistics menus in Arc View This manual can also be accessed in electronic format from the Help menu Typographic Conventions e When running S PLus choose Using S PLUs in the Help menu for
50. esired for additional bars or slices Choose between bar chart and pie chart and specify a scale factor for the chart Specifying a number less than 1 makes a smaller chart specifying a number greater than 1 makes a larger chart Click OK to generate the chart Use the Clear Selection and Graphics choice from the S PLUS menu to remove the plots from the current view 41 Chapter 3 Using S PLus for ArcView GIS Import Graph from S PLUs 42 Fiar Takens duro Fiski ga ht DE paire There Fa Erh Coren Sabri a Coker La Feis 1S unary kal eth H aed Chena Popii Scala facia ry F flee Chet oe T CE eee ae Figure 3 9 The Spatial Bar Pie Chart dialog To transfer a graph created in another application into ArcView you would normally export the graph as a file in one of the file formats sup ported by ArcView open a layout in ArcView draw a picture frame on the display and place the graphics file in the picture frame The Import Graph From S PLUS dialog automates this procedure If no layout currently exists you are first prompted to create a new one Graphs in S PLUS are placed on Graph Sheets which can contain multi ple pages 1 Select an S PLUS Graph Sheet from the drop down menu Plot names cannot contain spaces If the Graph Sheet has more than one page select the desired page from the list Choose a format for the graphics file with which the plot will be exported from S PL
51. f V ariance dialog 72 G Geary statistic 49 50 gl isa function 12 Graph sheet 14 62 65 graphs importing from S PLUS 42 Group Selected Records dialog 38 groupng records 37 H histogram 66 changing the number of bars 66 customizing 66 histograms in S PLUS 13 15 105 Index 106 Import Point Theme dialog 37 Import Table From S PLUS dialog 36 importing data from S PLUS 36 graphs from S PLUS 42 point theme from S PLUS 37 table from S PLUS 75 indicator field 24 installing 2 over S PLUS 4 0 2 interactive brush and spin plot printing 23 interactive brush and spin plots 22 L legend editor 26 linear regression 60 64 generating plots from 65 generating plots with 62 model in ArcV iew 43 plot of a three dimensional fit 67 residuals 63 saving results 62 saving results of 64 specifying a model 61 versus spatial linear regression 25 viewing the results of 62 visualizing the fitin three dimensions 67 Linear Regression dialog 24 44 62 local spatial association 50 Local Spatial Association dialog 51 M menu S PLUS 34 model errors see linear regression residuals M oran statistic 49 50 0 Object Browser 12 56 displaying object details 57 filtering with 12 57 folders in 63 opening 56 right pane property dialog 57 viewing a data frame 58 viewing classes 57 viewing data frames with 13 viewing databases 57 R Report window 59 62 73 formatting 59 residuals see linear regression residua
52. fy a field for analysis Select sids arc below S PLUS Data Frames and the Column sid Specify a neighbor object Select Ncco neighbor as the Spatial Neighbor object that depicts the neighborhood structure in the data and select Geary s c statistic as the local measure of association to be used Run local spatial association C lick OK This creates an S PLUS object named N cco lisa geary Since these data did not come from ArcView you cannot automatically join the results to the active theme ncco shp You need to add acolumn with the county names to the results and then import the resulting table and join based on these names Spatial Statistics Local Spatial Association Select One Column from Either Source Numeric Theme Fields S PLUS Data Frames Area sids arc a Pop1990 ca Pop1996 easing Pop1390 northing ql Pop30_sqmi A TFF births Variable for Analysis only one sids arc sid Clear 5 PLUS Neighbor Object Local Correlation Index Neco neighbor X z Moran s Weights C Geary sc None x Saved Results SPLUS Object Nocolsa tStC CS IV Import Resulting Data Frame as a Table J Join to Current Theme s Table Join Field z Figure 5 5 Computing a local indicator of spatial association 5 Prepare resulting data frame for import to ArcView To add the Name column to the data frame N cco lisa geary open up this data fr
53. h a symbol having white foreground 7 Create spatial barcharts Click the View window to make it active and choose Spatial Bar Pie Chart from the S PLUS menu In the dialog that appears select C ensus tracts in the list below Theme and select Last_res as the Field Then select Blue 27 Chapter 2 Quick Start Tutorial below For Each Column Select a Color At this point Last_res Blue appears in the Command box Under Chart Properties specify Bar Chart and change the scale factor default value to 0 75 Click OK The result shown in figure 2 19 gives a good indication of the location of the model errors having largest magnitude and gives a similar sense of clustering of large model errors Barcharts provide a better visual comparison of the relative size of model errors than our color classification did _ Figure 2 19 The Atlanta Census tracts with Spatial bar charts Improve the Spatial Barchart Using Positive and Negative Residuals 28 8 Identify positive and negative residuals To visualize more readily the residuals we will classify them by sign You will now add two fields to the Census tracts theme one containing only the positive valued residuals with zeros elsewhere and one containing only the negative valued residuals with zeros elsewhere Begin by selecting Tables on the qstart apr project window Double click on Attributes of Census tracts to open this table From the Table menu select Start Edi
54. h a letter and can con additional objects in your working directory By default the Puce E Undce dialog displays a data frame name that does not exists in scores in particular are S PLUS If you specify an existing object s name a warning not permitted dialog will confirm your choice Join fields are used by the 9 Select a Join Field Next select Tract from the list of fields in the Picea Redd Join Field combo box This identifies a field containing unique joined displayed together values for each record and is helpful if you ever need to re with to the theme s origi import the data or analysis results from S PLUS back into nal attribute table ArcView Click OK to export the Census tracts demographic data to S PLUS Locate the Table in S PLus 10 Look in the Export dialog O pen the Export to S PLUS dialog again and scroll down the list below Existing S PLUS Objects In the list you will see the name of the data frame just created When you loaded the S PLUS for ArcView extension S PLUS was started automatically Move to S PLUS now by selecting it from the Task Bar You can confirm that the data frame Census tracts matches the selection in the Census tracts attribute table in ArcView If the Object Browser but 11 Look in the Object Browser If an S PLUS Object Browser ton is depressed and the am Object Browser is not visi window is not open depress the O bject Browser button S on ble choose Object the toolbar
55. he S PLUS Object Browser move to the right pane and ctrl click the fields Pct male Avg age and Log avg inc in this order 2 Open the 3D Plots palette Depress the 3D Plots toolbar button Ea The 3D Plots palette opens 3 Generate the plot of the linear fit Click the 3D Regression Scatter button a A three dimensional scatter plot is generated along with a gridded plane representing the Linear Regression fit 4 Rotate the plot To view the fit from another angle rotate the three dimensional plot Click any white space within the plotting area Five handles four round and one triangular will appear To rotate about the vertical axis drag one of the round 67 Chapter 4 Using S PLUS and S SPATIALSTATS MO o 4 ee H a Sitas Figure 4 17 Histogram with 24 bars and a title Figure 4 18 G raph sheet showing the three dimensional fit and the 3D Plots palette handles To rotate into the graph sheet drag the triangular handle A different view with handles visible is shown in W hat isS PLUS figure 4 19 Figure 4 19 A rotated view of the three dimensional fit 5 Create a spline plot To see a nonlinear fit of the same data click the Surface Spline button g in the 3D Plots palette The spline plot brings out features which are not evident from the three dimensional scatterplot This is shown in figure 4 20 Figure 4 20 Spline plot showing a nonlinear fit of Log avg inc by Avg
56. he linear regression you will see a Report Window with printed results and a two page Graph Sheet as shown in figure 4 11 From the output in the Report Window it seems that both Pct male and Avg age are related to Avg inc in a linear fashion H owever the W hat isS PLUS ti Linear Bode te Calli Jecboreile ij ine Fel aale Mite dete infemr LELE na LiTE am pit Hin lj M iar J Hax ISiT LLIA 1632 Jik Let CombPi ciente Value nd Errar T value Fe Soci i Trirercegei Sidhe MHI7 ELI 5417 D Seed Pt al Sh 2682 LES Tee ETT 0 ia Wed gL ape IDIJE 1538 L 1918 12378 0 BD Begiduel etendacd accor 17510 on 414 degrese af freeads Buolripie F lquered O ORE Featatastiol La an 2 aad od degrees of freee the pal Figure 4 11 Results of the linear regression normal quantile quantile plot indicates that the residuals do not follow a normal distribution They have a long tail on the high side Based on this the results of this linear regression are suspect 2 Make a folder to group data of interest Click the Object Browser window to make it active Right click in the left pane and choose Insert Folder from the context menu Type Census data for the name of the folder Click the income trim icon in the left pane then drag Avg age and Pct male into the Census data folder Click the income res icon in the left pane and drag residuals into the Census data folder 3 Plot the residuals against
57. ialog If you chose to display functions you ll that notice the glisa function appears under the function icon This function is currently placed there when S PLUS for A rcV iew is installed 3 Makesure the relevant information about the displayed objects is given Right click in the right pane and choose Right Pane from the context menu Another property dialog appears Click the radio button next to List Details In order to see the names of the selected classes make sure that the D ata Class box is checked It will also be useful to check the Dimensions box 57 Chapter 4 Using S PLUS and S SPATIALSTATS 58 iter r Leice Iera F Seadoo l Eea C Lb beer F fis Gi Fr Lit Details P iia T Daa Hada E bemimi Pope Sire c T Gate E3 J Camel aere omen Figure 4 3 The Right Pane property dialog for the O bject B row se Click OK to apply these selections and close the dialog Browse your data The O bject Browser now shows data which has been exported from ArcView in Exercise 3 of chapter 2 Expand the data frame icon in the left pane and click the data frame income data Its four fields are displayed as in figure 4 4 In the Dimensions column you see that each field has length 482 as expected a Diei Beer Figure 4 4 Theincomedata data frame Double click the income data icon to open the table of data in the S PLus data editor To sort on the Indicator field for example click anywhere in the Indicator
58. ibo Files jap duds A Depa 3 TE i Peogemm Files ep lus Library tosllisi i Deca f 1 TE iif eogi Fe splus di Libr erpi elute Data FIL i grak Fil ap By Libr arp api Cena fiz e imp i i 11 70 Lope La CAPE Piles ap 15 C45 Feogeem Filesi opie f I al Figure 4 35 The Commands window 3 To open a Script window to manage a short analysis click the New toolbar button Select Script File from the New dialog and click OK A new Script window opens In chapter 5 you work with data on SIDS rates in 100 counties in North Carolina The first two commands in the top pane of the Script window in figure 4 36 create the SIDS data frame in S PLUS and identify the location of the built in spatial neighbor object si ds neighbor The next two commands calculate an estimate of Spatial Correlation You may highlight those commands and click the Run button or press F10 to run them The output appears in the bottom pane of the Script window as seen in figure 4 36 Click the Run button again to rerun the lines Some of the output is not identical because random permutations are performed in generating the sample autocorrelation Similarly your quantiles of permutations correlations and the corresponding p value may not match that in figure 4 36 Both the Moran statistic and the permutation test give evidence W hat is StSPATIALSTATS Anei i pogam Tens eC ak ae Oy ar ai ag ee ee ai a g
59. in S PLUS as a data frame with one factor column Turn this factor column into a character vector of the county names with the following command Notice that S PLUS object names are case sensitive gt ncco names lt as character Ncco names 1 The county names for the sids data frame are the row names of the data frame You can get those as follows gt sids names lt row names si ds A quick test shows that the counties are sorted differently in each vector even though they both contain the same strings You should compare these 10 values to the first 10 rows of the correspond ing table in ArcView Spatial Statistics gt all sids names ncco names 1 F gt all sort sids names sort ncco names 1 T Reorder SIDS data frame accordingly The rows of the sids and ncco names data frames must be joined on the names of the counties To this end you want to find out the order of the names in ncco names and reorder the sids data frame accordingly The S PLUS function mat ch returns a vector of the positions of si ds names in ncco names Once we have these positions re ordering si ds aSsids arc will yield the desired result a data frame with the same ordering as ncco names hence the same ordering of the records in ArcView gt ind lt match ncco names sids names gt sids names ind 1 10 1 Ashe Alleghany Surry 4 Currituck Northampton Hertford 7 Camden Gates Wa
60. ing here Chapter 4 describes the basics of effective data management and analysis in S PLUS Data coming from a GIS package has an inherent spatial component that is of central interest to the data analyst In this chapter spatially ori ented data is used in an example which requires the optional S SPA TIALSTATS module to S PLUS Using these sample data you will see how to e perform exploratory data analysis using the Commands window e define neighbor relationships for use in spatial analysis e calculate spatial autocorrelation and local association measures perform spatial regression 85 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView SPATIAL STATISTICS This exercise uses data provided with the S SPATIALSTATS module complemented with data from ArcView The data framesids contains rates of death from Sudden Infant Death Syndrome SIDS for the years 1974 1978 Cressie and Chan 1989 for each of the one hundred counties in the state of North Carolina Exploratory analysis of this data can be found in Chapter 3 of the S SPATIALSTATS User s Manual Chapter 5 of that manual describes sev eral approaches to the analysis of these data In this section we will use the same data to illustrate the spatial analysis tools available in S PLUS for ArcView Data Preparation If the Commands Window button is depressed and the Commands Window is not visible choose Com mands in the Window menu to bring it forward Cautio
61. lly not valid In exercise 3 of chapter 2 for exam ple we saw demographic data from the Atlanta census tracts that are highly correlated in space In spatial analysis this spatial structure is incorporated into the statistical model The S SPATIALSTATS module extends the functionality of S PLUS with such tools for modeling data having spatial dependencies Types of ArcView Data and S SPpATIALSTATS S PLUS for ArcView works with spatial data stored in ArcView Themes can have features with different geometric shapes the main shapes that can be analyzed using S SPATIALSTATS are polygons and points Anal ysis is not presently available for themes which represent arcs or other ARC INFO feature classes Points can be exported to S PLUS for ArcView and analyzed in S SPA TIALSTATS as point patterns if you are interested in detecting specific patterns in the locations themselves With S SPATIALSTATS tools you typically explore whether the points are randomly distributed in space or whether they follow specific patterns Polygons are the focus of the Spatial Statistics menu in S PLUS for Arc View Attributes of polygonal features are called lattice data in S SPA TIALSTATS The neighbor structure among these features is integrated into the models in the S SPATIALSTATS module and in the Spatial Sta tistics menu items Analysis in S SPATIALSTATS The S SPATIALSTATS functions can be separated along the lines of the three broad categories of sp
62. ls Rotate 67 running S PLUS for ArcV iew 32 S scatter plot 63 matrix 18 three dimensional 22 with loess curve fit 19 scatter plot matrix 18 spatial autocorrelation 49 Spatial Autocorrelation dialog 49 spatial bar chart 41 Spatial Bar Pie Chart dialog 41 spatial barchart 27 28 spatial linear regression 52 building a model formula 52 Spatial Linear Regression dialog 52 spatial neighbor object 51 spatial neighbors 46 49 Spatial N eighbors dialog 46 spatial pie chart 41 spatial statistics menu 46 module 46 spatial statistics menu 2 46 spatial weights 46 49 adjusted neighbor 47 border to border distance 48 centroid to centroid distance 48 distance units 48 first order neighbor 46 higher order neighbor 48 spline plot 69 S Plus for ArcV iew running 32 tips on learning 4 5 S PLUS menu 2 34 Subset dialog 60 subsetting the rows of a data frame 60 summary statistics generating 58 Summary Statistics dialog 58 sweeping data in a plot 23 T technical support 6 Transform dialog 64 transforming a field 64 typographic conventions 5 Index U U S States data 42 V viewing statistical output 59 W weighting data 24 weights specifying in a linear regression model 43 107 Index 108
63. must be specified Tki Dine Dokar Pion Eih Grik Piara T haas Fiii PLUS Data Fanar 5 et Carman icir oe El Po Srp Mop gtr laj j ri bu breja krda ees Co Der F PLUS Meighbw Dbjeot Local Donnin Index Coreen bach regen M Musil 1i W oar 6 Howes Brad Pande SPUS b t Cnh a F imped ening Cinta Freee m a Table F donto Dani Thra Tabia kin Fid Tar a ik Cancel Fale Figure 3 16 The Local Spatial Association dialog 51 Chapter 3 Using S PLus for ArcView GIS Spatial Linear Regression Specific formulae for the covariance matrices corre sponding to these models can be found in the help file for the S SPATIALSTATS function sim 52 This dialog fits a spatial regression model to selected variables It looks at both large scale changes in mean due to spatial location or other explanatory variables and small scale variation due to interactions with neighbors 1 Build a model formula from fields in the attribute table of the current theme and columns in S PLus data frames The variables must be consistent with each other they must be associated with the same region of study The first variable selected will be used as the response variable You cannot type directly into the M odel Formula box Choose a spatial neighbor object in the current S PLUS workspace The spatial neighbor object must be consistent with the variables in the model formula it must be associated with the same spati
64. n Some typograph ical errors existed in the original data distributed with S SPATIALSTATS Ver sion 1 1 Use the data set described here for reli able results 86 Open the Commands window in S PLus O pen the Commands window by depressing the Commands Window toolbar button 3al For information on the Commands window refer to the Script Window and Commands Window section in chapter 4 In what follows commands are indicated next to the default S PLUS prompt gt Parts of commands which exceed the length of a line are preceded by the default S PLUS continuation prompt When working along with the examples type only the command and not the prompts Load the S SPATIALSTATS module if available This is not needed in all the examples in this section If it is installed the S SPATIALSTATS module is automatically loaded when S PLUS for ArcView starts up When you run S PLUS without running ArcView you must load S SPATIALSTATS module Do this by entering the following command in the Commands window gt module spatial You can check that the S SPATIALSTATS module is loaded by entering gt search and checking that the S SPATIALSTATS data directory is in the second position in the list of S PLUS databases as seen in figure 5 1 Spatial Statistics AS ULE Le Pe KiF moma Fi Vea majai apa Darna Frogrmm Fi iyapa i Ponctia i1iPEogi Fi i gE Pie bo iiron Fil mi Ba Fumio C iFcogom Fi hop us jah Dateer SEP EO
65. n the data 6 Diagnose using residuals The residuals from the fit are imported into ArcView and joined to the original table This join is performed as in the example using the Local Spatial 100 Spatial Statistics Association results Add the name column to the resulting data frame Ncco slm then use Import Table from S PLUS to import and join the results in ArcView 7 Visualize in ArcView Color classification of the residuals seen in figure 5 10 does not show any striking patterns of spatial autocorrelation left over Figure 5 10 Color classification of counties by residuals of the spatial linear regression 8 Assess leftover spatial corelation The model output contains also Moran s index of spatial autocorrelation for the model residuals For the model we just fitted these are as follows Spatial Correlation Estimate Statistic moran Sampling free Correlation 0 001165 Variance 0 003835 Std Error 0 06192 Normal statistic 0 1443 Normal p value 2 sided 0 8853 Null Hypothesis No spatial autocorrelation 101 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView Summary of the permutation correlations Min lst Qu Median Mean 3rd Qu Max 0 1899 0 05413 0 0176 0 01114 0 03174 0 1805 permutation p value 0 409 From these results we may conclude that the model accounts for most of the spatial autocorrelation in the data since the residual correlation is not significant
66. nds directly In addition if you have the optional S SPATIALSTATS module installed you can create neighbor objects also known as spatial weight matrices e calculate global Spatial Autocorrelation or localized Local Spatial Association measures of spatial autocorrelation e estimate spatial regression models Running To run S PLUS for ArcView follow these simple steps S PLus for 1 Start ArcView on your computer ArcView 2 From the File menu select Extension 32 Overview 3 Choose S PLUS for ArcView GIS from the list of available extensions 4 Click OK S PLus and Spatial Statistics menu items appear in the main menu bar as in figure 3 1 indicating that S PLUS for ArcView is active Note that most menu items are only enabled fie Pma PUL Speke Sisko yikes jja a e Figure 3 1 S PLUS and Spatial Statistics appear in the main menu if a view document is in focus and has a theme selected which is based on a shape file 33 Chapter 3 Using S PLus for ArcView GIS THE S PLus MENU Export Data to S PLUS Use the S PLUS menu to exchange data with S PLUS to place bar charts or pie charts on a view or to use S PLUS to analyze theme data You can execute single S PLUS commands on theme data or use S PLUS to per form analysis and visualization of theme data Fie Ed ieee Ihre eA Warder Hels tL r T Esa Dita te S PLUS ipot bbe fore SPL inpoi Pami Theres fore SPLA Grag Pasi eid reece
67. ociation Spatial Linear Regression The Help System S PLUS for ArcV iew Help S PLUS for ArcV iew User s M anual S PLUS Language R eference S PLUS Spatial Statistics H elp About S PLUS for ArcV iew 31 Chapter 3 Using S PLus for ArcView GIS OVERVIEW S PLUS for ArcView GIS an extension to ESRI s ArcView GIS pro gram allows users to access the powerful statistical capabilities of M ath Soft s S PLUS program S PLUS for ArcView does more than provide a convenient mechanism for moving data and graphics between the two programs It brings the vast analytical and graphical functionality of S PLUS into ArcView Further S PLUS for ArcView is fully integrated with the optional S PLUS Spatial Statistics module W hen that module is installed with S PLUS ArcView users have direct access to a variety of sophisticated spatial statistical analysis and visualization tools Use S PLUS for ArcView to e export selected records and fields from ArcView tables to S PLUS data frame objects e import S PLUS data sets to ArcView tables or point themes record row selections by storing character or numeric values in anew or existing field color classify a theme based on data from S PLUS or ArcView create graphic bar or pie charts relating data on a per polygon basis e import S PLUS graph to an ArcView layout e clear graphics and selections calculate linear regression fits and residuals for selected records e execute S PLUS comma
68. on B which now carries a horizontal bar to indicate that conditioning mode is on The plot shown in figure 2 13 appears 30000 80000 130000 Pct 0 4yrs 30000 80000 130000 Avg inc Figure 2 13 Trellis plot showing the rdationships bewen Average Income and Percentage Population 0 to 4 Years in 4 groups of census tracts The groups are classified by Percentage F emale 21 Chapter 2 Quick Start Tutorial This Trellis display clearly reveals relationships which are not easily seen otherwise e For census tracts with the highest percentage of females there is the strongest negative association of average income and percentage 0 to 4 year olds e Virtually all the census tracts with a high percentage of 0 to 4 year olds fall among those which have over 53 2 percent females e There is somewhat greater variation in the percentages of 0 to 4 year olds among those census tracts whose populations are unbalanced with respect to gender Visualize Average Income Percentage 0 to 4 Years and Percentage Females To explore these data interactively S PLUS provides a graph window with tools for rotating a 3 dimensional scatterplot and selecting subsets of data simultaneously in several scatterplots 7 Select the fields Choose Brush and Spin from the Graph menu The Brush and Spin dialog prompts you for a data frame and some of its fields as seen in figure 2 14 Pet Se Pci Sika Figure 2 14 The Brush
69. on of study If a data frame is selected then it must have been exported from ArcView with a Join Field from the active theme 2 After selecting the theme or data frame its fields columns will be displayed Select one field from the list of fields 3 Specify the number of quantiles or classes by using the slider The range is from 1 to 25 4 Click OK The selected variable is displayed in a map in the View window The color scale is automatically determined by the requested number of classes 5 A legend shows the corresponding ranges of values for each color class These ranges can be edited individually to create classes that are differently sized The labels can also be edited Double click the legend to open the legend editor TheS PLUS Menu Select Coin madis Coke Conky the che lhara Coa Charme i EE a Eel Figure 3 8 The Color Classification dialog Spatial Bar Pie This function plots a bar or pie chart using data from fields in the cur Chart rent theme or in any theme with the same number of records as the active theme that is with data associated with the same region of study 1 Build a plotting command from fields in the selected theme and colors for the corresponding bar or pie slice Select a theme and a field The field name appears in the command line Select a color with which to plot the attribute selected above You can also type directly in the command field Repeat steps 1 and 2 as d
70. ormal statistic 1 962 Normal p value 2 sided 0 04982 Null Hypothesis No spatial autocorrelation 92 Spatial Statistics Summary of the permutation correlations Min Ist Qu Median Mean 3rd Qu Max 0 1593 0 05445 0 02006 0 01077 0 02765 0 2433 permutation p value 0 034 The values for the Moran measure for spatial autocorrelation are rather high The p value for the significance of this coefficient is low enough that we can assume that there is enough spatial autocorrelation in the data to warrant the fitting of spatial models One more run of the spatial autocorrelation dialog this time to compute Geary s c statistic confirms this conclusion Geary s coefficient should lie between 0 and 1 You can also compute the spatial correlation of arbitrary S PLUS expressions For example following the reasoning in section 5 2 of the S SPATIALSTATS U se s Manual a transformation of SID rate is needed to achieve constant variance in the variable of interest This transformation is determined by the square root of the number of births times the Freeman Tukey square root of the rates contained in sids arc sid ft Enter this transformation in the dialog below Variables for Analysis wabia Pod Arena rec dod H el och ajhai Figure 5 4 Entering an expression as a variable for analysis This yields the following result Spatial Autocorrelation Analysis for sids arc sid ft sqrt sids arc births Spatial C
71. orrelation Estimate Statistic moran Sampling free Correlation 0 2237 Variance 0 003835 Std Error 0 06192 Normal statistic 3 776 Normal p value 2 sided 1 595e 4 93 Chapter 5 Analyzing Spatial Null Data in S PLUS for ArcView Hypothesis No spatial autocorrelation Summary of the permutation correlations Min Ist Qu Median Mean 3rd Qu Max 0 1625 0 0522 0 006393 0 006191 0 03386 0 2558 permutation p value 0 001 This is consistent with that in the S SPATIALSTATS U se s M anual and indicative of high spatial autocorrelation for the transformed variable The expected value of Moran s is 1 n 1 which in this case is about 1 99 so a value of 0 2237 rejects the null hypothesis of no spatial autocorrelation Local Spatial Association Testing the hypothesis of no autocorrelation using the global statistics of the last section assumes stationarity of variance through space This is not likely to be the case for most variables of interest and for the SI D rates in particular An approach that does not require the assumption of global stationarity is provided by Local Indicators of Spatial A ssocia tion or LISA Anselin 1994 Bao and Henry 1996 S PLUS for Arc View provides an interface to LISA computations and display 1 Open the Local Spatial Association dialog To compute this indicator for the SIDS data choose Local Spatial Association from the Spatial Statistics menu Speci
72. ow ser showing income data and income trim 2 Specify a Linear Regression model Ctrl click the fields Avg inc Pct male and Avg age in that order 61 Chapter 4 Using S PLUS and S SPATIALSTATS 62 3 Open the Linear Regression dialog seen in figure 4 10 It is in Lena Amperse dafiura f egia ubmsi Rewer Save Modal Dber F rgd fisar eth Mining Vista Sad da un Fraud Pamias Desa Formia Figure 4 10 The Linear Regression dialog the Regression submenu of the Statistics menu Next to Formula you see the formula which you have specified The first selected column Avg inc is the dependent variable Pct male and Avg age are the independent variables You may click the button Create Formula to build the formula using the variables in the data frame income trim Save the results of the fit M ove to the Results page Check the box next to Long Output under Printed Results Check the box next to Residuals and enter income res next to Save In under Saved Results Specify plots to be generated M ove to the Plot page Check the boxes next to Residuals vs Fit and Residuals Normal QQ These diagnostic plots help to determine whether the results of the linear regression on your particular data can be trusted Click OK to run the regression print the results save the fit and generate plots Using the results of Linear Regression 1 View the results of the linear regression A fter running t
73. ox next to Long Output Check the box next to Residuals and Graph Sheets W hat isS PLUS enter log income res next to Save In under Saved Results 7 Specify plots to be generated M ove to the Plot page Check the boxes next to Residuals vs Fit and Residuals Normal QQ 8 Click OK to run the regression print the results save the fit and generate plots The plots of Residuals vs Fit and the Residuals Normal QQ are much improved as shown in figure 4 14 The results of the linear regression are much more reliable Notice from the Report Window output however that the linear regression only explains about 4 5 of the variation in Avg inc Gi ia ia iT T Pie Parae g m Figure 4 14 Plot of Residuals against Fitted Values Residual standard error 0 1693 on 474 degrees of freedom Multiple R Squared 0 04543 F statistic 11 28 on 2 and 474 degrees of freedom the p value is 0 00001639 In S PLUS plots are placed in Graph sheets just as plots and charts are placed in ArcView layouts The general technique for editing a plot in an S PLUS Graph sheet is to right click on the region of interest open a property dialog and make the desired change to the plot The following exercise illustrates several typical ways to customize a plot and its Graph sheet For more details refer to the S PLUS U se s Guide Diagnosing the Residuals 1 Select the data Click the income res icon in the left pane of the O bject Browse
74. ple the key combination of Shift and F1 appears as Shift F 1 The arrow keys are useful for moving objects around the page They appear as U p Down Left and Right Chapter 1 Wdcome Technical Support H ere is how to contact S PLUS technical support North America voice 206 283 8802 x230 Monday through Friday 7 30 a m to 5 00 p m Pacific Time fax 206 283 6310 e mail support statsci com Europe Asia Australia Africa and South America voice 44 1276 452299 fax 44 1276 451224 e mail shelp mathsoft co uk QUICK START TUTORIAL Exercise 1 Exploring Demographic Data Display the Atlanta V iew Compute Summary Statistics in ArcV iew and Prepare Data for Export Export the Cleaned Attribute Table to S PLUS Locate the Table in S PLUS M ake H istograms C omparing Percentages of nfants Import an S PLUS Histogram into an ArcV iew Layout Exercise 2 Finding Relationships Between Demographic Variables Plot the Relationships Between T hree Fields Find the Relationship Between A verage Income and Percentage 0 to 4 Y ears Conditioned on Percentage Females Visualize A verage Income Percentage 0 to 4 Y ears and Percentage F emales Exercise 3 Geographic Clustering of Linear Regression Modeling Errors Fit a Least Squares Linear Regression M odel Color Classify the Census T racts U sing Residual V alues Add a Spatial Barchart Based on Residuals Improve the Spatial Barchart U sing Positive and N egative Residual
75. ppear under Variables for Analysis Sea Aue bat Bami Dokar ore Hibs Sote LLLE iaha fiear Tik irea Washes ioi russia CoE Chem S PLUS Hohia Dbm Lorriion r Hoon neghte F Moa r Bear c Mre Cade Dacian od Coaredaons Irae Hiie of Parar 1000 owed Ace durran Hepat PADIN JPU Object GGN BiiRccacc F Depi Ha ar Crencubaten m ee Figure 5 3 Estimating spatial autocorrdation 3 Specify a neighbor object Select N cco neighbor under S PLUS Neighbor O bject and click O K The output below is displayed in a text editor window The text file isin the directory indicated under Summary Report 91 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView Note You need to close Spatial Autocorrelation Analysis for sids arc sid the text editor window with the results before you P 7 Spatial Correlation Estimate can go back to ArcView Statistic moran Sampling free Correlation 0 1191 Variance 0 003835 Std Error 0 06192 Normal statistic 2 086 Normal p value 2 sided 0 03695 Null Hypothesis No spatial autocorrelation Summary of the permutation correlations Min Ist Qu Median Mean 3rd Qu Max 0 1523 0 05107 0 01888 0 01198 0 02312 0 2639 permutation p value 0 026 Spatial Autocorrelation Analysis for sids arc births t Spatial Correlation Estimate Statistic moran Sampling free Correlation 0 1114 Variance 0 003835 Std Error 0 06192 N
76. r move to the right pane and click the residuals field 65 Chapter 4 Using S PLUS and S SPATIALSTATS 2 Open the 2D Plots palette Depress the 2D Plots toolbar button kil The 2D Plots palette opens It may be open already if you followed the last exercise 3 Generate the histogram Click the Histogram button la in the 2D Plots palette The histogram is generated as shown in figure 4 15 Figure 4 15 Histogram of residuals 4 Customize the bars It would be nice to see the divisions between the bars more clearly Right click on the histogram bars You have clicked in the right spot if a green handle appears below the leftmost bar Choose Histogram Bars from the context menu Check the box next to Draw Bars and click OK Now borders are drawn around the histogram bars 5 Change the number of bars To better see the features of the histogram regenerate it with more classes Right click the histogram again and choose O ptions from the context menu Next to Number of Bars enter 24 W hat isS PLUS Figure 4 16 Histogram with borders around bars 6 Create a title Place a title on the histogram by choosing M ain from the Title submenu of the Insert menu A text box appears in the Graph sheet Type Histogram of Residuals and click in another area of the Graph sheet The result is shown in figure 4 17 Visualizing a Linear fit in 3 Dimensions 1 Select the model Click the income trim icon in the left pane of t
77. re is how to construct histograms in S PLUS using numeric data exported from ArcView 13 Select the data to plot Click the S PLUS Object Browser window to make it active Expand the data frame icon in the left hand pane if necessary by clicking the plus sign The Census tracts icon is displayed in the left pane click it In the right hand pane you will see icons with names corresponding to the fields of the attribute table of the Census tracts theme Select Pct 0 4yrs by clicking on it 13 Chapter 2 Quick Start Tutorial Figure 2 5 Selecting the Pct 0 4yrs column in a data frame using the Object B row ser 14 Create a histogram Depress the 2D Plots button Kil on the S PLUS toolbar to make the Plots2D palette appear Click the Histogram button l on this palette A graph sheet appears with the histogram shown in figure 2 6 The histogram is 10 PARES BPs ae Pes m ET Figure 2 6 Histogram of the percentages of infants aged 0 to 4 years in the sdected Atlanta census tracts essentially unimodal with a longer tail on the right We immediately notice some rather high values some census tracts report over 20 of the population being between 0 and 4 years old There is a cluster of census tracts for which the percentage of the population in this age range is under 2 14 S PLUS allows nearly every feature of a graph to be customized for technical presentation purposes Right click on various parts of the graph
78. roid to centroid distance criterion as follows The element x i j of the weight matrix X is 1 if the shortest distance between the centroid of poly gon j and the centroid of polygon i is less than the distance entered and 0 otherwise Spatial Autocorrelation Beware of islands in your spatial units when computing a spatial neigh bor Records for an island must be removed before computation The help file for the S SPATIALSTATS function spatial cor lists the exact formulae for these statis tics The Spatial Statistics M enu In each case the resulting weight matrix is automatically converted into an S PLUS object of classs patial neighbor Specify the name for this object after choosing the method for calculating neighbor weights If some aspect of your geographic data is spatially autocorrelated there may be a need for spatial modeling such as Spatial Regression To decide whether spatial modeling should be used perform a test for spa tial autocorrelation This dialog calculates two common measures of spatial autocorrelation the Geary and M oran statistics 1 Build a list of variables for analysis from fields in the attribute table of the current theme and columns in S PLUS data frames You can also type directly in the Variables for Analysis box The variables must be consistent with each other they must be associated with the same region of study Choose a spatial neighbor object in the current S PLU
79. rren 10 Stokes gt all sids names ind ncco names 1 T gt sids arc lt sids ind gt all row names sids arc ncco names 1 T Now we can proceed with our spatial analysis Note that this data frame can also be imported into ArcView as a point theme using its columns easting and northing as x and y coordinates to georeference them Defining Neighbor Relationships The analysis of polygonal attributes is complemented by knowledge of a neighborhood structure If measures for neighboring counties are known to be correlated we can address this dependence when model ing an attribute of interest by other attributes In the SIDS data two counties are considered neighbors if their county seats are within 30 miles of each other following the convention of Cressie 1993 89 Chapter 5 Analyzing Spatial Data in S PLus for ArcView Note The resulting weight matrix has a different number of neighbors than the one included with S SPATIALSTATS because proximities in the sids dataset are based on county seats not cen troids of the counties as we used Increasing the distance threshold yields a more comparable weight matrix but Nceco neighbor is adequate here 90 S PLUS for ArcView manages neighbor relationships by computing an S PLUS spatial neighbor object based on the ncco shp theme data M ake sure this is the active theme before proceeding 1 Set the map units M ove to ArcView Click the View window
80. rs as you go due to the dis crepancies in county names and the precedence of this first version over the one already in S SPATIALSTATS 87 Chapter 5 Analyzing Spatial Data in S PLUS for ArcView 88 The variables in the SI D S data frame are displayed as follows gt names sids 1 5 9 fd easting northing sid births nwhirths group sia tt nwbirths ft For more detail on each variable look at the help file for si ds gt hel p sids 4 Create an ArcView shapefile with county information M ove to ArcView Open the usa apr project You may find this in the c esri esridata directory parallel to your AVHOME directory Bring up the table of Attributes for the US Counties theme Using the Query Builder toolbar button the hammer tool select all counties such that the field State name equals North Carolina Click on the view with the US Counties theme and from the Theme menu select Convert to Shapefile to create a new shapefile with the data for North Carolina only Call the new file ncco shp This new shapefile will be added to the view s table of contents M ake it active by clicking on it and check marking it You may zoom the view in to this active theme Export the County names into S PLus 5 Choose Export Data to S PLUS from the ArcView menu Select Name below Exportable Fields Enter Ncco names under Name of Data Frame to Create Click OK Moveto S PLUS Ncco names appears
81. s 19 22 24 24 26 27 28 Chapter 2 Quick Start Tutorial The S PLUS scientific and statistical graphing capabilities provide a comprehensive complement to the basic charting capabilities in Arc View With the S PLUS graphing tools you will discover more valuable information in your ArcView data summarize it more effectively and produce presentation quality charts This chapter contains three detailed lessons on extending your work in ArcView with S PLUS for ArcView They are designed so that you can walk through each step along with the exercise In order to do the exer cises you will need to have installed S PLUS and S PLUS for ArcView on your system It is not necessary to have installed the S SPATIAL STATS module to do these exercises Exercise 1 Exploring Demographic D ata EXERCISE 1 EXPLORING DEMOGRAPHIC DATA In this exercise you will find out how to e Clean up the demographic data in the attribute table for the Atlanta census tracts e Export this clean version of the data to S PLUS Generate histograms for several of the fields for informative comparisons Generate scatterplots of pairs of fields with automatic linear and nonlinear curve fits e Import a graph back into an ArcView layout Display the Atlanta View 1 Start ArcView typically by selecting Program from the Start Button then navigating to ESRI and ArcView GIS Open the qstart apr project From the File menu use Open
82. s Heighheads Veber iia Candeadatrey Maghi W eeghtr P Fant Dmie T aiii Fay Die Hag Cees i i i i i Dictance Bare bahak oo a a specified distance units e TE FP E S PLUS tbaghba hed hiana Figure 3 14 The Spatial N aghbors dialog X is 1 if polygon j is adjacent to polygon i and is 0 otherwise The diagonal elements x i i of the spatial weight matrix X are all equal to 0 Adjusted First O rder Neighbor Weights In most cases polygons of a theme are irregularly shaped A polygon may be a short distance from a given polygon i without sharing a boundary with it The simple spatial neighbor criteria may fail to cap ture such a kind of significant spatial relationship In this method adjustments are made to the neighbor weights based on the spatial distance between neigh bors First a spatial weight is defined by using the simple firt order neighboring criteria Then an average centroid to centroid distance between the neigh boring polygons and polygon i is calculated A poly gon not among those defined as neighbors already will be admitted as a neighboring polygon if its spa tial distance centroid to centroid from the polygon i is less than this average distance The element x i j of the weight matrix X is 1 if polygon j is a neighbor of polygon i under the above criteria and is 0 otherwise 47 Chapter 3 Using S PLus for ArcView GIS Higher Order Neighbor Weights Distance Units This option con
83. s include the query dialog custom Avenue scripts or the selection tool If no features were selected all records will be included in the selection To group the records into numerous categories repeatedly make a new selection then call the dialog 1 Use the radio buttons on the left to specify whether to create a new field or overwrite values of an existing field If you write to a new field you will need to specify a Join Field so that the new field can be joined to the active theme s attribute table If you write to an existing field only values in currently selected rows will be overwritten In this case you can choose either to keep or to clear values in non selected records The text at the top of the dialog indicates how many of the total records are currently selected Specify a character value a category name or group identifier to write to each of the records in the current selection Click OK D Urewp Selected eco Tere tdkads a h E Sekine enwi of TA Tinted Fisadi xaupil Fmi m we Gap i tp Bier Fii Eo jeFeifigead Fairies Dioup ID ip Elsie Epira Feed E Opin fed Meier Baked Feit D Chaar Am k Vaia on Pecos that we H oi Selected Diman W Eira rien by 28S heci Fiia 1 Head i Carca Hat Figure 3 6 The Group Selected R ecords dialog For example select counties on the North side of the state and group D those using the string North then reverse the selection
84. structs a spatial weight matrix of order n based on the spatial neighbor relationship between polygons Specify the order using the slider bar For spatial neighbors of order 1 the elementx i j of the resulting weight matrix X is 1 if polygon j is adjacent to polygon i and is 0 otherwise For spatial neighbor weights of order 2 the element x i j of the weight matrix is 1 if polygon j is adja cent to the first order neighbors of polygon i and is 0 otherwise More generally for spatial neighbor weights of order n the element x i j of the weight matrix X is 1 if polygon j is adjacent to the neighbors of order n 1 of polygon i and is 0 otherwise The diagonal elements x i i of the spatial weight matrix X are all equal to 0 The distance entered in the spatial neighbors dialog should be in terms of the distance units specified for the view see figure 3 14 T he distance units are spec ified in the ArcView properties dialog Specify this distance when using one of the methods below for calculating neighbor weights Border to Border Distance This option constructs a spatial weight matrix using a border to border distance criterion as follows The element x i j of the weight matrix X is 1 if the shortest distance between the boundary of polygon j and the boundary of polygon i is less than the dis tance entered and 0 otherwise Centroid to C entroid Distance This option constructs a spatial weight matrix using a cent
85. taneous autoregressive or moving average covariance structures For the analysis of point pattern data S SPATIALSTATS includes func tions to perform the following e Plot geometrically accurate point maps without spatial distortion e Explore complete spatial randomness using nearest neighbor methods e Estimate intensity using kernel loess and gaussian methods e Test second order stationarity using Ripley s K function 80 Script Window and Commands Window If the Commands Window button is depressed and the Commands Window is not visible choose Com mands in the Window menu to bring it forward W hat is S SPATIALSTATS S SPATIALSTATS also includes methods for simulating the three basic types of spatial data For a detailed example see chapter 5 Functions in the S SPATIALSTATS module are currently available only at the command line in S PLUS or in the Spatial Statistics menu in S PLUS for ArcView This section illustrates how to analyze your Arc View data with S SPATIALSTATS from the command line in S PLUS Turn to chapter 5 to see how to use the Spatial Statistics menu in S PLUS for ArcView Future releases of S SPATIALSTATS will have full functionality from the S PLUS user interface In this section you will learn how the S SPATIALSTATS module can be used for the analysis of your ArcView data This includes e how to use the Commands and Script windows in S PLUS for the analysis of spatial data using S SPATIALS
86. te a number of typical uses of the O bject Browser in an analysis of data from the Atlanta C ensus tracts Summarizing Census tracts data 1 Open the Object Browser by depressing the Object Browser button 5 Like the Windows Explorer it is a two paned window with collapsible and expandable icons in the left pane w Uhd Hran Hn Ie Ll record Gughchea N Seach D verte Figure 4 1 The Object Browse W hat isS PLUS 2 Make sure that the right kinds of objects are displayed in the Object Browser To do this right click in the left pane and choose Filtering from the context menu The O bject Browser property dialog appears Use this dialog to specify what is displayed in the O bject Browser Page Into titeeng B D Eaki Cath 7H jo E Cy berate rice Chama E She Se aiabana fiim METAR Las Elmar irere vot FF ipid Garej Deen E coe Figure 4 2 The Object Browser property dialog Next to Databases is a list of directory paths The top line should be among those selected this is where S PLUS for ArcView stores its exported data as S PLUS objects In the list next to Classes make sure that the data frame item is selected You may also want to select vectors and functions say but avoid choosing too many items in the list as it may slow down the performance of the Object Browser The same warning applies to the Databases list Click OK to apply your choices and close the d
87. time you load the project 16 Exercise 1 Exploring Demographic D ata Lael Pim Figure 2 9 An ArcView layout with an S PLUS graph shee 17 Chapter 2 Quick Start Tutorial EXERCISE 2 FINDING RELATIONSHIPS BETWEEN DEMOGRAPHIC VARIABLES In this exercise you ll look some more at the Atlanta census demo graphic data In particular you ll do the following with tools in S PLUs Visualize the relationships between three or more variables using pairwise scatterplots Visualize the relationships between three or more variables using interactive brush and spin plots Visualize the relationships between several variables using the unique Trellis graphics displays of conditional views of the data We will focus on the relationships between Average Income and Percentage 0 to 4 Years within groups of records classified by Percent Female This exercise takes up where Exercise 1 leaves off If you have not already walked through Exercise 1 perform steps 1 through 9 from that exercise now to create the data set that is used here Plot the Relationships Between Three Fields 18 1 Select the fields In the S PLUS O bject Browser click on the data frame Census tracts in the left hand pane Its fields will be shown in the right hand pane Then Ctrl click Avg inc Pct female and Pct 0 4yrs in that order All three fields will be selected Create a scatter plot matrix Depress the 2D Plots button taal to open the Plots 2D
88. ting then under the Edit menu bring up the Add Field dialog twice and create two new fields res positive and res negative as shown in figure 2 20 Exercise 3 Geographic Clustering of Linear Regression Modding Errors Foeta Dichrpt oe Figure 2 20 Fidd Definition dialogs in ArcView Select the positive residuals by opening the Query dialog by clicking on the Query Builder button E in sequence double click the Linear_residuals field the greater or equal E button and then 0 from the keyboard Finally select the New Set button to select just those records that meet this criteria and close the dialog To insert the positive residuals into the new res positive field click once on the field name at the top of the table and then bring up the Calculate dialog via the Field menu Then reverse the selection using the Switch Selection button E select the negative residuals field in the attribute table and use the calculate dialog again to insert the negative residuals into the res negative field W hen done the Attributes of Census tracts table should look like figure 2 21 9 Create bar charts Now you will make spatial barplots with red bars for negative residuals and blue bars for positive residuals Click the View window to make it active and choose Spatial Bar Pie Chart from the S PLUS menu In the dialog that appears select Census tracts under Theme and select res negative under Field Then select the color Red You will
89. us checkers while installing S PLUS To install the S PLUS for ArcView extension 1 Insert the CD ROM into your CD ROM drive 2 From the system Explorer double click on the setup bat file in the root of the CD ROM What You Can Do with S PLus for ArcView In ArcView you create maps which incorporate geographic data and summarize this data in a flexible visual environment With S PLUS for ArcView you can now penetrate your data with unprecedented power using the data analysis tools in S PLUS What is more you can graphi cally explore the geographic data using the cutting edge intuitive S PLUS graphing tools and integrate both graphics and analysis results into the ArcView layout Continental United States TEA Ailes kibamia pasia 198 Population Clic wee HO a TH S EN Pape at Figure 1 2 Simple linear regression output from S PLUS in an Arc View layout Chapter 1 Wdcome Tips on Learning S PLus for ArcView In S PLUS for ArcView you can access S PLUS directly from ArcView to analyze data in the attribute tables of themes Other tables may be exported to S PLUS and the results later joined in ArcView to theme attribute tables See the release notes for details on which data types are currently supported e This manual focuses in turn on S PLUS for ArcView S PLUS and S SPATIALSTATS A good place to start is in chapter 2 Quick Start Tutorial Starting with some typical data in ArcView the ex
90. values of this field with the indicator value or to add the indicator value to the current value For non selected records choose whether to clear or to keep the current values 3 Specify an integer value to write to each of the records in the current selection Click OK For example select counties where the level of a chemical has risen above some threshold and assign an indicator value of lto those records then once exported to S PLUS you might evaluate records above the threshold with those below 39 Chapter 3 Using S PLus for ArcView GIS There labas hat ig Esokenied Fisadi cl 2 Toad Repaid Indecad cr Feel D Welah Vigo iy ee eek froth aad haii ia i iania inicia Wink ty Ewig Heresy Piet inasa zl Diorio kar Saskiak Fea E C Aopei ira Dii thy a H eee bika iah E deji aa be ire Dia Diga ka Horria Aana C Dey Are Dii Vai a Fkh that a Hoe Sa F Reap Aung i Vsk in Pecani thai are Fini Saker bed linear Vado 7 findsge Wisa by AES eect Aco cell OF Caro Hele Figure 3 7 The Add Indicator Fidd dialog Color This menu item allows you to use color to categorize features in the Classification active theme by values in any numeric field For example you may color states based on their population levels 1 Select a theme or an S PLUS data frame from one of the two drop down boxes T he theme or data frame must have the same number of records as the active theme its data must be associated with the same regi
91. window The S PLUS data frame must SPLus contain X and Y coordinates as column variables These can have any names such as Longitude and Latitude The selected S PLUS data frame is imported into ArcView as anew table leper Pet Theme CCE PLL Dibya ba limped Daia Frama Laz Doura path H Candee F z Colum reth V Caa D ipet Ob Az Maes labi ard hara Plame rar Figure 3 5 The mport Point Theme F rom S PLUS dialog 1 Select an S PLUS data frame from the drop down list 2 Select the variables which contain the X and Y coordinates in the data frame These must be different columns 3 Specify a name for the new theme and its table 4 Click OK The added table is converted into a point theme and is shown in the ArcView View window Group Selected Use this dialog to create a new character field that records which Records records are selected Once one or more selections have been recorded the table can be exported to S PLUS and analyses done to spot trends for each of the groups selected Use the Group Records dialog when you wish to denote the selection with a character value and use the similar Add Indicator Field dialog when you wish to denote the selection with a numeric value These dia logs record the selection in either a new field created on the spot or in an existing field 37 Chapter 3 Using S PLus for ArcView GIS 38 Before opening the dialogs select some features in a theme Some tools for thi
92. ws NT is a trademark of M icrosoft Corporation Other brand and product names referred to are trademarks or registered trademarks of their respective owners M athSoft gratefully acknowledges the substantial support from NASA Earth Observations Commercialization Application Program EO CAP 93 contract NAS13 623 for our project entitled SpaceStat An Object Oriented Software Tool kit for Statistical Analysis of Spatial and Spatial Temporal Data We thank the Project Liaison Support personnel particularly Paul Maughan and Brett T ho masie for their support during the course of this project TABLE OF CONTENTS 1 Welcome 1 Installation 2 W hat Y ou Can Do with S PLus for ArcV iew 3 Tips on Learning S PLus for ArcV iew 4 Technical Support 6 2 Quick Start Tutorial Exercise 1 Exploring Demographic Data 9 Exercise 2 Finding Relationships Between Demographic Variables 18 Exercise 3 Geographic Clustering of Linear Regression Modeling Errors 24 3 Using S PLus for ArcView GIS 31 Overview 32 The S PLus Menu 34 The Spatial Statistics Menu 46 The Help System 54 4 Using S PLus and S SPATIALSTATS 55 What is S PLus 56 O bject Browser 56 Graph Sheets 65 D ata W indows 69 What is S SPATIALSTATS 79 Script Window and Commands W indow 81 Table of Contents 5 Analyzing Spatial Data in S PLUs for ArcView Spatial Statistics D ata Preparation Defining N eighbor Relationships Spatial A utocorrelation Local Spatial Association Spatial
93. y shaded states covering the Pacific Northwest In a given region one would expect some states with high median rent 76 W hat isS PLUS 9 elect Coirm urari is Coles Carri tha cies hera OR Thews tia O ooo C SPLN Disks Fane Saket aureas Cobre Colo Care 5 Figure 4 32 Using the Color Classification dialog to visualize the results from the Analysis of Variance performed in S PLUS Boe H gee af aps Aiea vf ai giens af 0 Diha i A ee WNE mag EEE RS Figure 4 33 A view of the U S States with a graduated color legend type States are classified by Residuals taken from the Analysis of Vari ancein S PLUS 77 Chapter 4 Using S PLUS and S SPATIALSTATS and some states with low median rent relative to the subregion as a whole A look at the attribute table reveals that the Pacific subregion which contains Washington State also contains Oregon California Alaska and Hawaii Choose Full Extent from the Zoom menu Now Alaska and H awaii are in view they appear to have relatively high median rent values compared to their subregional neighbors as expected see figure 4 34 Figure 4 34 An expanded view of the U S States with a graduated color legend type 78 W hat is StSPATIALSTATS WHAT IS S SPATIALSTATS Spatial structure is intrinsic to ArcView data With spatially oriented data the assumptions of independent observations used in statistical inference are typica

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