Analytics and Modeling

This knowledge area embodies a variety of data driven analytics, geocomputational methods, simulation and model driven approaches designed to study complex spatial-temporal problems, develop insights into characteristics of geospatial data sets, create and test geospatial process models, and construct knowledge of the behavior of geographically-explicit and dynamic processes and their patterns.

Topics in this Knowledge Area are listed thematically below. Existing topics are linked directly to either their original (2006) or revised entries; forthcoming, future topics are italicized. 

 

Basic Spatial Operations Advanced Spatial Analysis Surface Analysis
Buffers Identifying & designing analytical procedures Calculating surface derivatives
Overlay Point pattern analysis Interpolation methods
Neighborhoods Cluster analysis Intervisibility
Map algebra Exploratory data analysis (EDA) Cost surfaces
  Analyzing multi-dimensional attributes  
Spatial Modeling Multi-criteria evaluation Network Analysis
Cartographic modeling Weighting schemes Least-cost (shortest) path analysis 
Components of models Spatial interaction Flow modeling
Coupling scientific models with GIS The spatial weights matrix The Classic Transportation Problem
Mathematical models Spatial interaction Other classic network problems
Spatial process models Space-scale algorithms Modeling Accessibility
Using models to represent info & processes    
Workflow analysis and design Space-Time Analytics & Modeling Data Mining
  Computational movement analysis Data mining approaches
Data Manipulation Time geography Knowledge discovery
Approaches to point, line, area generalization   Pattern recognition
Coordinate transformations Spatial Statistics Geospatial data classification
Data conversion Global measures of spatial association Multi-layer feed-forward neural networks
Impacts of transformations Local measures of spatial association Rule learning
Raster resampling Spatial sampling for statistical analysis  
Vector-to-raster and raster-to-vector conversions Stochastic processes Spatial Simulation
  Outliers Simulation modeling
Analysis of Errors and Uncertainty  Bayesian methods Cellular Automata
Problems of currency, source, and scale Principles of semi-variogram construction Simulated annealing
Theory of error propagation Semi-variogram modeling Agent-based models
Propagation of error in geospatial modeling Kriging methods Adaptive agents
Fuzzy aggregation operators Principles of spatial econometrics Microsimulation & calibration of agent activities
  Spatial autoregressive models  
  Spatial filtering Spatial Optimization
  Kernels and density estimation Location-allocation modeling
  Spatial expansion & Geographically weighted regression Greedy heuristics
  Spatial distribution Interchange heuristics
  Mathematical models of uncertainty Genetic algorithms
  Non-linearity relationships and non-Gaussian distributions  
  Interchange with probability  

 

AM-84 - Simulation modeling
  • Conduct an experiment using simulation techniques from an activity perspective
  • Explain how a simulation from an activity perspective can be used in transportation
  • Discuss important computational laboratory tools for creating new models and visualizing model simulations and model outcomes
  • Discuss whether, when prior information is absent, repeatedly generating random synthetic datasets can be used to provide statistical significance
  • Discuss Monte Carlo simulation use in GIS&T
  • Discuss effective scientific use of supervisory genetic algorithms with agent-based simulation models
  • Describe how supervisory search and optimization methods can be used to analyze key characteristics of initial conditions and results and to optimize results based on systematic targeted search through the parameter and random seed spaces
AM-67 - Space-scale algorithms
  • Describe how space-scale algorithms can, or should, be used
AM-32 - Spatial autoregressive models
  • Explain Anselin’s typology of spatial autoregressive models
  • Demonstrate how the parameters of spatial auto-regressive models can be estimated using univariate and bivariate optimization algorithms for maximizing the likelihood function
  • Justify the choice of a particular spatial autoregressive model for a given application
  • Implement a maximum likelihood estimation procedure for determining key spatial econometric parameters
  • Apply spatial statistic software (e.g., GEODA) to create and estimate an autoregressive model
  • Conduct a spatial econometric analysis to test for spatial dependence in the residuals from least-squares models and spatial autoregressive models
AM-47 - Spatial distribution
  • Find spatial patterns in the distribution of geographic phenomena using geographic visualization and other techniques
  • Hypothesize the causes of a pattern in the spatial distribution of a phenomenon
  • Differentiate among distributions in space, time, and attribute
  • Identify influences of scale on the appearance of distributions
  • Employ techniques for visualizing, describing, and analyzing distributions in space, time, and attribute
  • Discuss the causal relationship between spatial processes and spatial patterns, including the possible problems in determining causality
AM-34 - Spatial expansion and geographically weighted regression
  • Perform an analysis using the geographically weighted regression technique
  • Discuss the appropriateness of GWR under various conditions
  • Describe the characteristics of the spatial expansion method
  • Explain the principles of geographically weighted regression
  • Compare and contrast GWR with universal kriging using moving neighborhoods
  • Explain how allowing the parameters of the model to vary with the spatial location of the sample data can be used to accommodate spatial heterogeneity
  • Analyze the number of degrees of freedom in GWR analyses and discuss any possible difficulties with the method based on your results
AM-33 - Spatial filtering
  • Identify modeling situations where spatial filtering might not be appropriate
  • Demonstrate how spatial autocorrelation can be “removed” by resampling
  • Explain how dissolving clusters of blocks with similar values may resolve the spatial correlation problem
  • Explain how the Getis and Tiefelsdorf-Griffith spatial filtering techniques incorporate spatial component variables into OLS regression analysis in order to remedy misspecification and the problem of spatially auto-correlated residuals
  • Explain how spatial correlation can result as a side effect of the spatial aggregation in a given dataset
  • Describe the relationship between factorial kriging and spatial filtering
AM-10 - Spatial interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences.  Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.
 

AM-14 - Spatial process models
  • Discuss the relationship between spatial processes and spatial patterns
  • Differentiate between deterministic and stochastic spatial process models
  • Describe a simple process model that would generate a given set of spatial patterns
AM-26 - Spatial sampling for statistical analysis
  • List and describe several spatial sampling schemes and evaluate each one for specific applications
  • Differentiate between model-based and design-based sampling schemes
  • Design a sampling scheme that will help detect when space-time clusters of events occur
  • Create spatial samples under a variety of requirements, such as coverage, randomness, and transects
  • Describe sampling schemes for accurately estimating the mean of a spatial data set
AM-20 - Stochastic processes
  • List the two basic assumptions of the purely random process
  • Exemplify non-stationarity involving first and second order effects
  • Differentiate between isotropic and anisotropic processes
  • Discuss the theory leading to the assumption of intrinsic stationarity
  • Outline the logic behind the derivation of long run expected outcomes of the independent random process using quadrat counts
  • Exemplify deterministic and spatial stochastic processes
  • Justify the stochastic process approach to spatial statistical analysis

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