##### 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 in regular font and linked directly to their original entries (published in 2006; these contain __only__ Learning Objectives). Entries that have been **updated and expanded are in bold. **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