Question

Describe fixed point and point pattern spatial data. What is being measured in each type of approach? What are first and second order effects? What is positive and negative spatial correlation? To be completely spatially random provide two requirements that must be met.

Answer 1

Point is the term used for an arbitrary location
>Event is the term used for an observation
> Mapped point pattern: all relevant events in a study
area R have been recorded
>Sampled point pattern: events are recorded from a
sample of different areas within a region.

Three general patterns
>Random - any point is equally likely to occur at any location
and the position of any point is not affected by the position of
any other point
> Uniform - every point is as far from all of its neighbors as
possible
>Clustered - many points are concentrated close together, and
large areas that contain very few, if any, points.

Spatial data is used as an all-encompassing term that includes general-purpose data sets such as digital cartographic data, remotely sensed images, and census-tract descriptions, as well as more specialized data sets such as seismic profiles, distribution of relics in an archaeological site, or migration statistics. Taken literally, spatial data could refer to any piece of information related to a location from stars in the heavens to tumors in the human body.

The concept of 1st order effects and 2nd order effects is an important one. It underlies the basic principles of spatial data.It’s important to note that it is seldom feasible to separate out the two effects when analyzing point patterns, thus the importance of relying on a priori knowledge of the phenomena being investigated before drawing any conclusions from the analyses results.

Spatial autocorrelation measures how much close objects are in comparison with other close objects. Moran’s I can be classified as positive, negative and no spatial auto-correlation.

• Positive spatial autocorrelation is when similar values cluster together in a map.
• Negative spatial autocorrelation is when dissimilar values cluster together in a map.

In the completely spatially randomness, suppose now that n points are each located randomly in region R . Then
the second key assumption of spatial randomness is that the locations of these points have
no influence on one another. Hence if for each 1,.., i n  , the Bernoulli variable, ( ) Xi C ,
now denotes the event that point i is located in region C , then under spatial randomness
the random variables { ( ) : 1,.., } Xi Ci n  are assumed to be statistically independent for
each region C . This together with the Spatial Laplace Principle above defines the
fundamental hypothesis of complete spatial randomness (CSR), which we shall usually
refer to as the CSR Hypothesis.