Spatial Analysis

What is Spatial Analysis?

    1. A geographical analysis which seeks to explain patterns of human behavior and their spatial expression in terms of mathematics and geometry
    1. The study of “regularities in the spatial distribution of economic activity, populations, land use, and other dimensions of human activity”

Location is Key

  • A hugely important determinant of the quality and characteristics of something - an event, a building - is the location
  • Being able to identify and analyze characteristics of different locations is a foundational use of GIS and spatial analysis methodologies

Euclidean Distance Buffer

  • Straight-line distance; buffer at certain radius from point;
  • Ring buffer draws a series of buffers at increasing distances around given features
  • Next step in analysis is often to then count how many “things” occur within buffer

Overlay

  • Overlay is the layering of data on top of each other in a GIS to analyze multiple aspects of the same location
  • It is a fundamental use of a GIS
  • There are many different ways to use overlay:
    • Intersect
    • union
    • Subtract

“Crisp” Criteria

  • Overlay assumes clarity and crispness of criteria
    • Boundaries are definite
    • Levels of suitability are clear
  • Note in the example that all criteria have specific, crisp definitions and cutoffs

Fuzzy logic and fuzzy membership sets

  • Fuzzy logic recognizes that criteria are often not clear or are ill-defined
  • Instead of clear criteria definitions and cut-offs, fuzzy logic assumes that a set of suitable choices exists and asks, “What is the likelihood that particular data value is within that suitable set?”
  • A fuzzy set replaces original data values with likelihood values. from 0-1

Spatial Patterns:Points Pattern

Spatial Patterns of Data

  • Example: A grid of POINT data
  • These could have attribute values we are interested in
    • House prices
    • Traffic accident counts
    • Pollen accounts
  • We could be interested in identifying patterns in the event occurrences themselves – the locations (point pattern analysis)
  • Or We could be interested in identifying pattern is the values – the ATTRIBUTES (spatial autocorrelation)

Identify Points Clustered or Not By Sampling Grid

  • Normally (ie under randomness) you would expect
    • some empty cells
    • many with about the mean number of points
    • few cells with many points
  • Uniform: most have about the average number of points
  • Clustered: many empty cells and with many points

Deviation Variance
Uniform small small
Clustered large large

Kernel Estimation

  • Kernel estimation uses a kernel function (there are many to choose from) which draws the curve of a mathematical function over each point, and assigns weights to other events found within the search radius based on nearness to the point - thus according to where it sits along the function
  • Values for each event within the point’s search radius are summed to give the estimated intensity at the point
  • There are better for tackling the areal problem than standard density measure

Average Nearest Neighbor

  • A distance-based measure of clustering
  • Steps: 1. Measure distance from one point to closest neighboring point 2. repeat for all points; sum distance then divide by number of points

Spatial Patterns: Spatial Autocorrelation

Interpreting Spatial Autocorrelation

  • Null hypothesis is complete spatial randomness

  • Positive spatial autocorrelation: Neighbor locations are more likely to have similar values

  • Negative spatial autocorrelation: Neighbor locations are more likely to have dissimilar values

    Hotspot map is relative value.

Spatial Modeling

What is Spatial Model

  • A spatial model is
    • a representation
    • of a real process operating on the Earth’s surface
    • a design process conceived of by a human

Relationship to theory

  • A Theory
    • an abstraction of some phenomena
  • A model
    • simplification of reality which takes the theoretical abstractions and puts it into a from that we can manipulate
    • simulation is often used to characterize this process of implementation

Representation Models and Process Models

  • Distinction:
    • A representation model is template for data, a framework into which specific details of relevant aspects of the Earth’s surface can be fitted. It is a statement about how the world looks.
    • Process models are expressions of how world is believed to work.They are expressions of process.
  • Two key requirements of spatial process models:
    • There is variation across the space being manipulated by the model
    • The results of modeling change when locations of objects change

Methods for Process Models

  • Analytical: use mathematical analysis to arrive at explicit equations representing the behavior of the system
  • Simulation: used to derive the behavior of the system when it is too complex to be modeled via analytical approach

Species Distribution Models

  • Utilizes known species occurrence and environmental variables to predict occurrence of species over larger area

  • AUC(Area Under the Curve) (or ROC): used as the measure if a model is a good model. If it fits the data well;

  • Percent Contribution :measure how important each variable is

  • Permutation Importance: how important the order of adding variables to the model runs

Spatial Regression

  • Spatial regression models incorporate the relative location of dependent and independent variables in a regression model to identify the different relationships across space

System Dynamic Models

  • Processes that are influenced by space and that influence/modify the space

Spatial Predictive Modeling

  • Attempts to describe constraints and influences on where events occur by spatially correlating occurrences with these factors that represent constraints;
  • A process for analyzing events through a spatial filter in order to make predictions for event to occur

Spatial Dynamic Models

  • Uses identical simple components(cells) to exhibit complex behavior
  • Each cell has it state s(i,t) at site i and time t
  • Rules for exchanges between sites can also be defined

Agent-Based Models

  • An agent represents an independent entity with a set of attributes
  • Three characteristics separate the agents apart from the cells:
    • Autonomy
    • Interaction activity
    • Reactivity