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-81 - Adaptive agents
  • Describe different approaches to represent the effects of agent adaptation in the context of a specific agent-based model
  • Explain the effects of agent adaptation in the context of a specific agent-based model 
AM-79 - Agent-based models
  • Compare and contrast agent-based models and cellular automata as approaches for modeling spatial processes
  • Describe how agent-based models use object-oriented programming constructs of inheritance and encapsulation to represent the behavior of heterogeneous and interactive and adaptive actors
  • Describe how multiple, different types of agents in a given system behave and interact with each other and their environment
  • Generate multiple, different types of agents in a given system
  • Describe how multiple parameters (e.g., number of agents, variability of agents, random number seeds for different series of random events or choices during each simulation) can be set within an agent-based model to change the model behavior
  • Explain how agent behaviors can be used to represent the effects actors have on each other and on their environment
  • Design simple experiments with an agent-based model
  • Design and implement a simple agent-based model using appropriate commercial or open source development tools
  • Conduct simple experiments with an agent-based model, analyze results, and evaluate their statistical significance with respect to degrees of freedom, sensitivity analyses, and uncertainty in the model
  • Describe how measurements on various inputs and outputs of a model can be used to describe model behavior and to relate model outcomes to various initial conditions
  • Describe how various parameters in an agent-based model can be modified to evaluate the range of behaviors possible with a model specification
  • Determine if an agent-based model has been run enough times with enough different random number seeds for rigorous inference of its results
AM-02 - Analytical approaches
  • Compare and contrast spatial statistical analysis, spatial data analysis, and spatial modeling
  • Compare and contrast the methods of analyzing aggregate data as opposed to methods of analyzing a set of individual observations
  • Define the terms spatial analysis, spatial modeling, geostatistics, spatial econometrics, spatial statistics, qualitative analysis, map algebra, and network analysis
  • Differentiate between geostatistics and spatial statistics
  • Discuss situations when it is desirable to adopt a spatial approach to the analysis of data
  • Explain what is added to spatial analysis to make it spatio-temporal analysis
  • Explain what is special (i.e., difficult) about geospatial data analysis and why some traditional statistical analysis techniques are not suited to geographic problems
  • Outline the sequence of tasks required to complete the analytical process for a given spatial problem
  • Compare and contrast spatial statistics and map algebra as two very different kinds of data analysis
AM-11 - Analyzing multidimensional attributes
  • Relate plots of multidimensional attribute data to geography by equating similarity in data space with proximity in geographical space
  • Conduct a simple hierarchical cluster analysis to classify area objects into statistically similar regions
  • Perform multidimensional scaling (MDS) and principal components analysis (PCA) to reduce the number of coordinates, or dimensionality, of a problem
  • Produce plots in several data dimensions using a data matrix of attributes
  • Assemble a data matrix of attributes
AM-62 - Approaches to point, line, and area generalization
  • Describe the basic forms of generalization used in applications in addition to cartography (e.g., selection, simplification)
  • Explain why areal generalization is more difficult than line simplification
  • Explain the logic of the Douglas-Poiker line simplification algorithm
  • Explain the pitfalls of using data generalized for small scale display in a large scale application
  • Design an experiment that allows one to evaluate the effect of traditional approaches of cartographic generalization on the quality of digital data sets created from analog originals
  • Evaluate various line simplification algorithms by their usefulness in different applications
  • Discuss the possible effects on topological integrity of generalizing data sets
AM-25 - Bayesian methods
  • Define “prior and posterior distributions” and “Markov-Chain Monte Carlo”
  • Explain how the Bayesian perspective is a unified framework from which to view uncertainty
  • Compare and contrast Bayesian methods and classical “frequentist” statistical methods
AM-03 - Buffers
  • Compare and contrast raster and vector definitions of buffers
  • Outline circumstances in which buffering around an object is useful in analysis
  • Explain why a buffer is a contour on a distance surface
AM-15 - Calculating surface derivatives
  • List the likely sources of error in slope and aspect maps derived from digital elevation models (DEMs) and state the circumstances under which these can be very severe
  • Outline how higher order derivatives of height can be interpreted
  • Explain how slope and aspect can be represented as the vector field given by the first derivative of height
  • Explain why the properties of spatial continuity are characteristic of spatial surfaces
  • Explain why zero slopes are indicative of surface specific points such as peaks, pits, and passes, and list the conditions necessary for each
  • Design an algorithm that calculates slope and aspect from a triangulated irregular network (TIN) model
  • Outline a number of different methods for calculating slope from a DEM
AM-12 - Cartographic modeling
  • Describe the difference between prescriptive and descriptive cartographic models
  • Develop a flowchart of a cartographic model for a site suitability problem
  • Discuss the origins of cartographic modeling with reference to the work of Ian McHarg
AM-69 - Cellular Automata

Cellular automata (CA) are simple models that can simulate complex processes in both space and time. A CA consists of six defining components: a framework, cells, a neighborhood, rules, initial conditions, and an update sequence. CA models are simple, nominally deterministic yet capable of showing phase changes and emergence, map easily onto the data structures used in geographic information systems, and are easy to implement and understand. This has contributed to their popularity for applications such as measuring land use changes and monitoring disease spread, among many others.