1、Introduction to Spatial Data Analysis in the Social Sciences,RSOC597A: Special Topics in Methods/StatisticsKathy Brasier Penn State University June 14, 2005,Session Objectives,Understand why spatial data analysis is important Identify types of questions for which SDA is relevant Gain basic knowledge
2、 of the concepts, statistics, and methods of SDA Identify some important issues and decision points within SDA Learn about some resources for doing spatial data analysis (software, web sites, books, etc.) Avoid getting lost in equations!,Why Do Spatial Analysis?,“Everything is related to everything
3、else, but closer things more so.” (attributed to Tobler),Examples,Is your educational level likely to be similar to your neighbors? Are farm practices likely to be similar on neighboring farms? Are housing values likely to be similar in nearby developments? Do nearby neighborhoods have similar burgl
4、ary rates?,County Homicide Rates 1990,What Is Spatial Data?,4 main types event data, spatially continuous data, zonal data, spatial interaction data Most frequently used in social sciences is zonal data Data aggregated to a set of areal units (counties, MSAs, census blocks, ZIP codes, watersheds, et
5、c.) Variables measured over the set of units Examples: Census, REIS, County and City Databook, etc.,What is Spatial Data Analysis?,“The analysis of data on some process operating in space, where methods are sought to describe or explain the behavior of this process and its possible relationship to o
6、ther spatial phenomena.”Bailey and Gatrell (1995:7)Objective of spatial data analysis: to understand the spatial arrangement of variable values, detect patterns, and examine relationships among variables,Why Do Spatial Data Analysis?,To learn more about what youre studying To avoid specification pro
7、blems (missing variables, measurement error) To ensure satisfaction of statistical assumptionsTo be cool! To go crazy! To learn more about statistics than you ever wanted or thought possible! To learn the limitations of statistics,Theoretical Reasons for Spatial Analysis,It tells us something more a
8、bout what were studying Is there an unmeasured process that affects the phenomenon? Does this process manifest itself in space? Examples: interaction processes, diffusion, historical or ethnic legacy, programmatic effects,Statistical Reasons for Spatial Analysis,Violation of regression assumptions U
9、nits of analysis might not be independent Parameter estimates are inefficient Estimated error variance is downwardly biased, which inflates the observed R2 valuesIf spatial effects are present, and you dont account for them, your model is not accurate!,Examples of Research Using SDA,Epidemiology (en
10、vironmental exposure research) Criminology (crime patterns) Education (neighborhood effects on attainment) Diffusion/adoption (technologies) Social movements (trade unions, demonstrations) Market analysis (housing and land price variation) Spillover effects (economic spillovers of universities) Regi
11、onal studies (regional income variation & inequality) Demography (segregation patterns) Political science (election studies),BREAK!,When do you need to do SDA?,Is there a theoretical reason to suspect differences across space? Differences in phenomena (variable values) Differences in relationships b
12、etween phenomena (covariances) Are you using data with spatial referent? If yes to both, it is a good idea to at least explore any potential spatial effects Exploration will tell you more about the subject youre studying,Spatial Independence,Null hypothesis (H0) Any event has an equal probability of
13、 occurring at any position in the region Position of any event is independent of the position of any otherImplicit assumption of much work in social sciences,Spatial Effects,Test Hypothesis (H1) Probability of an event occurring not equal for each location within region Position of any one event dep
14、endent on position of any other eventMethods and statistics of SDA test this hypothesis If supported, can tell us more about what were studying; can improve our models If not supported, we know that we have satisfied assumptions,First Order Spatial Effects,Non-uniform distribution of observations ov
15、er space Large-scale variation in mean across the spatial units Values of the variables are not independent of their spatial location Results from interaction of unique characteristics of the units and their spatial location Ex: magnets and iron filings (Bailey & Gatrell) Referred to as spatial hete
16、rogeneity,Causes of Spatial Heterogeneity,Patterns of social interaction that create unique characteristics of spatial units Spatial regimes: legacies of regional core-periphery relationships = differences between units (pop, econ dvpt, etc.) Differences in physical features of spatial units Size of
17、 counties Combination: Differences in topography of units = different patterns of economic development (extractive industries),County Homicide Rates 1990,First order effects?,Second Order Spatial Effects,Localized covariation among means (or other statistics) within the region Tendency for means to
18、follow each other in space Results in clusters of similar values Ex: magnets and iron filings (Bailey & Gatrell) Referred to as spatial dependence (spatial autocorrelation),Causes of Spatial Dependence,Underlying socio-economic process has led to clustered distribution of variable values Grouping pr
19、ocesses grouping of similar people in localized areas Spatial interaction processes people near each other more likely to interact, share Diffusion processes Neighbors learn from each other Dispersal processes People move, but tend to be short distances, take their knowledge with them Spatial hierar
20、chies Economic influences that bind people together Mis-match of process and spatial units Counties vs retail trade zones Census block groups vs neighborhood networks,County Homicide Rates 1990,Second order effects?,So now that Ive convinced you that spatial data analysis is an important considerati
21、on.,What Do We Do About It?,Goals of SDA,To identify spatial effects and their causes To appropriately measure spatial effects To incorporate spatial effects into modelsTo improve our knowledge of the process and how it occurs over spaceAll of these goals require both theory and methods,Exploratory
22、Spatial Data Analysis,Start with questions about your theory and data: Are there likely to be spatial processes at work (diffusion, interaction, etc.)? Do your data units match the process? (Messner et al. reading)Visually and statistically explore your data Run basic descriptive statistics Map vari
23、ables Look for patterns, outliers Look for spatial effects (large-scale variation, localized clusters),Gini Index 1989,How to Measure Space?,Need to define space in order to measure its effectsTraditional ways (regional dummy variables, distance measures, etc.) Neighborhood structure Weights matrix
24、n x n matrix, where:0 = not neighbor1 = neighbor,Weights Matrix,Neighbors can be defined as: Boundaries: Adjacent units (rook or queen) Those units sharing some minimum/maximum proportion of common boundary Centroids If centroids are within some specified distance If unit is one of k nearest neighbo
25、rs defined by centroid distance Others? Decision to use one over another somewhat arbitrary Simpler is generally better Closer is generally better Rely on theory, your knowledge, and the ESDA to guide you,Weights Matrix Example,Simple Contiguity (rook) Matrix,Sample Region and Units,Statistical Test
26、s for Spatial Dependence (Autocorrelation),Univariate Global Morans I Indicates presence and degree of spatial autocorrelation among variable values across spatial unitsWhere z is a vector of variable values expressed as deviations from the mean Where W is the weights matrixExpected value of I conve
27、rgences on 0 when n is large; can do significance tests Large positive = strong clustering of similar values Large negative = strong clustering of dissimilar values,Global Morans I and Moran Scatterplot,Assesses relationship between the variable value for unit of origin (x axis) against the average
28、of the values its neighbors (y axis),Local Indicators of Spatial Autocorrelation (LISA),Local Morans I Decomposes global measure into each units contribution Identifies the local hotspots, areas which contribute disproportionately to global Morans I,LISA Cluster Maps,Homicide Rate 1990,Gini Index 19
29、89,Additional Suggestions for ESDA,Identify outliers and hotspots both statistically and visually Try taking outlier units out of analysis and see what happens (does Morans I change?) Explore changes in spatial patterns over time Compare two (or more) regions Split your sample by a variable of inter
30、est Try different weights matrices Play around with different covariates get into your data!,BREAK!,Regression Modeling and SDA,Use theory and ESDA findings to craft your model Procedure: Run OLS model Assess diagnostics If diagnostics indicate no spatial autocorrelation (or other violations of regr
31、ession assumptions), OLS model is fine If diagnostics indicate spatial autocorrelation present, need to consider ways to measure and incorporate spatial structure,OLS Diagnostics,Diagnostics of OLS model will indicate type of spatial effects If either present, need to identify likely source Remedies
32、 Spatial heterogeneity (Koenker-Bassett test) Include covariate which accounts for heterogeneity? Split region? Spatial autocorrelation (Lagrange Multiplier tests) Identify missing variables? Explore effects of spatially-lagged independent variables? Use appropriate spatial regression model?,Spatial
33、 Regression Models,ESDA and OLS diagnostics tell you that there is spatial autocorrelation Identify the source (LM tests will help) Regression residuals (LM-Error) Mis-match of process and spatial units = systematic errors, correlated across spatial units Dependent variable (LM-Lag) Underlying socio
34、-economic process has led to clustered distribution of variable values = influence of neighboring values on unit values Spatial autocorrelation in both,Spatial Autocorrelation in Residuals = Spatial Error Model,y = X + = W + is the vector of error terms, spatially weighted (W); is the coefficient; a
35、nd is the vector of uncorrelated, homoskedastic errors Incorporates spatial effects through error term,Spatial Autocorrelation in Dep. Variable = Spatial Lag Model,y = Wy + X + y is the vector of the dependent variable, spatially weighted (W); is the coefficientIncorporates spatial effects by includ
36、ing a spatially lagged dependent variable as an additional predictor,Spatial Lag Example,Spatial lag = sum of spatially-weighted values of neighboring cells= 1/3(7) + 1/3(5) + 1/3(4)= 5.3,Sample Region and Units,Example: Change in Farm Numbers 1982-1992,RQ: How do changes in agricultural structure a
37、ffect the rates of farm loss during the Farm Crisis? Hypothesized spatial effect: spatial dependence through clustering of similar types of farms,Farm Structure Example: Morans I Statistics,Farm Structure Example: LISA Maps,Farm Structure Example: OLS Regression & Diagnostics,Farm Structure Example:
38、 Spatial Error Spatial Lag Regression,Practical Issues with SDA,Scale of observations vs scale of process Time as a factor in analysis (no natural order) Definition of proximity Edge/boundary effects Modifiable area unit problem Complexity of topography Assumptions related to sample of attributes,Ho
39、w in the Heck Do I Actually Do This?,Existing statistical software packages (SPSS, SAS) Have trouble with weights matrix, so need to bring in by hand Some routines exist, but limited Comprehensive software packages S+ Spatialstats Linear spatial regression; weights construction Not transparent; no d
40、iagnostics; not compatible with ArcView 8.2 Spatial Toolbox (LeSage) Matlab routines Linear spatial regression; weights construction; Bayesian estimation; spatial probit/tobit models,Software Packages (2),SpaceStat Linear spatial regression; weights construction; diagnostics; multiple options Outdat
41、ed architecture and interface; not supported by Anselin; not compatible with ArcView 8.2 GeoDa driven by command language Both shareware, downloadable Little support, other than network of those using software Anselins working on PySpace, software to have greater breadth of options, diagnostics, mod
42、els, and estimation procedures,Additional Resources,Handout has resources listed (web, articles, etc.) Geographic Information Analysis group within PRI CSISS, SAL If interested, consider joining Openspace listserve AERS faculty,Assignment,Details in handout Article choices Use those with * Due Date June 19 (Mon.) by 4:30 pm (email preferred) I will email you comments/grades by June 22 (Thur.) Re-writes due June 26 (Mon.) by 4:30 pm (email preferred)Questions?,
