##### AM-67 - Space-scale algorithms

- Describe how space-scale algorithms can, or should, be used

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.

- Describe how space-scale algorithms can, or should, be used

- 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

- 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

- 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

- 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

- 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

- 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

- 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

## AM-84 - Simulation modeling