Spatial analysis is static, spanning one point in time or an average through time. It leads you to search for patterns that may guide future hypothesis generation.
Spatial modeling will occur in multiple stages, perhaps across different points in time. In this case, you are trying to replicate real-world decision with implications for policy or environmental decisions. Output may not simply be a map, but an animation, a statistical artifact, or some other more abstract output.
Solution envelopes range of possible solutions. Term used to describe how specific a model is to particular outcomes.
Step threshold: simple binary weight used to discriminate spatial data (slope < 5 degrees)
Linear thresholds: weight function that linearly decreases the parameter in question as a function of distance or time (frog habittat less and less likely the further you get from the stream).
Gaussian thresholds: weight function that forms a U-shape, where paramater begins at a minimum, rises to a maximum some distance from the origin, and decays back towards minimum.
Static models represent a system in a single point in time. While similar to analysis, their more complex architecture justifies representation in a GIS system as a model.
Individual models: models that try to represent each independent element of a system. Common type of individual model is called an agent based model (ABM).
Aggregate models: aggregate elements of a system into some larger components when simulating individual elements would be too challenging.
Cellular models: represent the model space as a raster, each cell having a number of states that are changed at each iteration of the model by the execution of rules.
Cartographic models: specialized raster models that symbolically represent operations using map algebra.
Calibration: operation that examines historical data (or data outside system of interest), to determine which paramaters to use in model and their values.
Cross-validation: post-model test of model validity. A subset of original calibration data is held back from initial calibration, and then used to evaluate whether results are reliable.
Sensitivity tests: Individual tuning of pramater value to see how sensitive a model is to the value of a particular paramater. If changing paramater 5% produces model outputs that are < 5% different, model is said to be robust.