more than just maps
Mar 21, 2016
more than just maps
A Toolkit for Spatial AnalysisGUI access to the most frequently used toolsArcToolbox – an expandable collection of
ready-to-use toolsModelBuilder – a visual programming
environmentPython – A FOSS scripting language
integrated with ArcGIS
Most analyses involve repeated use of common toolslike “Select by Attribute” (SQL)
We can also create a selection interactively•The selected river is highlighted•The associated rows in the attribute table
are also highlighted
Creating a Buffer allows identification of all objects that fall within a specified distance of a selected feature
Buffers allow further selection, i. e., all patients within 1000 meters of the river
ModelBuilder is a visual programming environment where data and tools can be dragged unto a blank slateto create a working program.•Models can be saved•Models can be exported as graphic documentation•Models can be exported as scripts for further
development
Models are an excellent way to write bug-free code fragments, which can then be assembled into larger scripts
Models and scripts can be called in Models and Scriptsand can be saved as tools in ArcToolbox
PYTHON is a modern Language that is well supported and easy tolearn.
Observed Values Predicted Values
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Ordinary Least Square (OLS)
Geographically Weighted Regression(GWR)
Regression analysis
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•Regression analysis allows you to:Regression analysis allows you to:– Model, examine, and explore spatial relationshipsModel, examine, and explore spatial relationships– Better understand the factors behind observed spatial patternsBetter understand the factors behind observed spatial patterns– Predict outcomes based on that understandingPredict outcomes based on that understanding
What’s the big deal?•Pattern analysis (without regression):
oAre there places where people persistently die young?
oWhere are test scores consistently high?oWhere are 911 emergency call hot spots?
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Why use regression?Understand key factors
What are the most important habitatcharacteristics for an endangered bird?
Predict unknown valuesHow much rainfall will occur in agiven location?
Test hypotheses“Broken Window” Theory: Is there apositive relationship between vandalismand residential burglary?
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ApplicationsEducation
Why are literacy rates so low inparticular regions?
Natural resource managementWhat are the key variables that
explain high forest fire frequency?Ecology
Which environments should beprotected, to encouragereintroduction of an endangeredspecies?
TransportationWhat demographic characteristics contribute to
high rates of public transportation usage?Many more…
Business, crime prevention, epidemiology,finances, public safety, public health
Regression analysis terms and concepts
Dependent variable (Y): What you are trying to model or predict (e.g., residential burglary).
Explanatory variables (X): Variables you believe cause or explain the dependent variable (e.g., income, vandalism, number of households).
Coefficients (β): Values, computed by the regression tool, reflecting the relationship between explanatory variables and the dependent variable.
Residuals (ε): The portion of the dependent variable that isn’t explained by the model; the model under- and over-predictions.
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Intercept 1.625506INCOME -0.000030VANDALISM 0.133712HOUSEHOLDS 0.012425LOWER CITY 0.136569
Regression model coefficientsCoefficient sign (+/-) and magnitude reflect each explanatory variable’s relationship to the dependent variable
The asterisk * indicatesthe explanatory variableis statistically significant
Building a global OLS regression model
Choose your dependent variable (Y).Identify potential explanatory variables (X).Explore those explanatory variables.Run OLS regression with different combinations
of explanatory variables, until you find a properly specified model.
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Adjusted R-Squared [2]: 0.37407Akaike’s Information Criterion (AIC) [2]: 5813.121
Why are people dyingyoung in South Dakota?
Do economic factors explain this spatial pattern?
Poverty rates explain 66% of the variation in the average age of death dependent variable: Adjusted R-Squared [2]: 0.659
However, significant spatial autocorrelation among model residuals indicates important explanatory variables are missing from the model.
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Build a multivariate regression modelBuild a multivariate regression model•Explore variable relationships using the scatterplot matrixExplore variable relationships using the scatterplot matrix•Consult theory and field expertsConsult theory and field experts•Look for spatial variablesLook for spatial variables•Run OLS (this is an iterative, often tedious, trial and error, Run OLS (this is an iterative, often tedious, trial and error,
process)process)
1 Coefficients have the expected sign.Coefficients have the expected sign.2 No redundancy among model explanatory variables.No redundancy among model explanatory variables.
4 Residuals are normally distributed.Residuals are normally distributed.5 Strong Adjusted R-Square value.Strong Adjusted R-Square value.6 Residuals are not spatially autocorrelated.Residuals are not spatially autocorrelated.
Online help is … helpful! Online help is … helpful!
Coefficient significanceLook for statistically significant explanatory variables.
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* Statistically significant at the 0.05 level.
MulticollinearityFind a set of explanatory variables that have low VIF values.
In a strong model, each explanatory variable gets at a different facet of the dependent variable.
What did one regression coefficient say to the other regression coefficient? …I’m partial to you!
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VIF--------------2.3512291.5564981.0512071.4003583.232363[1] Large VIF (> 7.5, for example) indicates explanatory variable redundancy.
Model performanceCompare models by looking for the lowest AIC value.As long as the dependent variable remains fixed, the AIC value for different OLS/GWR models are comparable
Look for a model with a high Adjusted R-Squared value.
Akaike’s Information Criterion (AIC) [2]: 524.9762Adjusted R-Squared [2]: 0.864823
[2] Measure of model fit/performance.
Model biasWhen the Jarque-Bera test is statistically significant:The model is biasedResults are not reliableOften indicates that a key variable is missing from the model
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[6] Significant p-value indicates residuals deviate from a normal distribution.
Jarque-Bera Statistic [6]: 4.207198 Prob(>chi-sq), (2) degrees of freedom: 0.122017
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Statistically significant clustering of under and over predictions.
Random spatial pattern of underand over predictions.
For each explanatory variable,GWR creates a coefficient surface
showing you where relationships are strongest.
Global vs. local regression modelsOLS
Global regression modelOne equation, calibrated using data from all featuresRelationships are fixed
GWRLocal regression modelOne equation for every feature, calibrated using data from nearby features
Relationships are allowed to vary across the study area
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Running GWRGWR is a local spatial regression modelModeled relationships are allowed to vary
GWR variables are the same as OLS, except:Do not include spatial regime (dummy) variables
Do not include variables with little value variation
Defining local
GWR constructs an equation foreach feature
Coefficients are estimated usingnearby feature values
GWR requires a definition for nearbyKernel type
Fixed: Nearby is determined by a fixeddistance band
Adaptive: Nearby is determined by a fixednumber of neighbors
Bandwidth method AIC or Cross Validation (CV): GWR will
find the optimal distance or optimalnumber of neighbors
Bandwidth parameter: User-provideddistance or user-provided number ofneighbors
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Interpreting GWR resultsCompare GWR R2 and AICvalues to OLS R2 and AIC values
The better model has a lower AICand a high R2.
Residual maps show modelunder- and over-predictions.They shouldn’t be clustered.
Coefficient maps show howmodeled relationships varyacross the study area.
Model predictions, residuals,standard errors, coefficients,and condition numbers arewritten to the output featureclass.
Check condition numbers: > 30 indicates a less reliable result
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Observed
Modeled
Predicted
Calibrate the GWR model using known values for the dependent variable and all of the explanatory variables.
Provide a feature class of prediction locations containing values for all of the explanatory variables.
GWR will create an output feature class with the computed predictions.