13.2 General Considerations and Issues in the Spatial Analysis of EA Data
189
(e.g., commodity, gene flow, disturbance) is taken
up by a fixed population; (2) exchange and transfer (e.g., income transfer, flow of nutrients); (3) interactions, in which events at one location influence and are influenced by events at other locations
(e.g., pricing patterns across retail sites reflecting
underlying competitive interactions among retailers, distribution of individuals of different species
as a function of interspecific competition); and (4)
dispersal or spread (e.g., migration of human and
animal populations, seed dispersal). Diffusion and
spread are differentiated by Raining (1990); diffusion is defined as the dispersal of an attribute
through a fixed population, whereas spread refers
to the dispersal of the population itself. These
processes are often included in models of spatial
distribution (e.g., Raining, 1990, in the social sciences; Pearson and Gardner, 1997, Tilman and
Kareiva, 1997, in ecology; see also Chapter 18).
13.2.2 Issues in Spatial Data Analysis
Analytical Issues
Analytical issues encountered in spatial analysis of
EA data fall into three broad categories (Table
13.1): (1) sampling, (2) numerical summary and
characterization of the spatial properties of the data,
and (3) analysis of multivariate data sets. The first
analytical issue, the design of spatial sampling
schemes to fit the goals of an EA (see Chapter 1),
is an important consideration, whether with existing or de novo data (see Chapter 7), including accuracy assessment of remotely sensed data (see
Chapter 10). The second analytical issue includes
TABLE 13.1. Analytical and practical issues in the
spatial analysis of ecological assessment data.
Analytical issues
Spatial sampling
Numerical summary and characterization of the spatial
properties of map data
Analysis of multivariate data sets
Practical issues
Conceptual models and inference frameworks for spatial
data
Modeling spatial variation
Statistical modeling of spatial data and:
Dependency in spatial data
Spatial heterogeneity
Spatial distribution of data points and boundary effects
Assessing model fit
Distributions
Extreme data values
Model sensitivity to the areal system
Size-variance relationships in homogeneous aggregates
the numerical description of the spatial properties
of map data. EAs often use maps as a basis for evaluation and scenario planning (see Chapters 3, 22,
and 24); therefore, it is important to study the spatial arrangement of map values and to devise summary measures that characterize spatial patterns
and their properties at different scales (e.g., Burrough, 1995).
For example, characterization of map data provides the basis for (1) constructing additional
smoothed and interpolated maps (Webster, 1985);
(2) defining the spatial attributes of models, such
as the spatial variation in precipitation in hydrological models (e.g., TOPMODEL in RHESSYS;
see Chapter 18) or in fire regimes in vegetation
models (e.g., LANDIS; see Chapter 18); (3) comparing different maps; and (4) comparing map surfaces at different points in time. The third analytical issue stems from the fact that the issues
addressed in an EA (see Chapter 1) generally require the analysis of data describing two or more
variables in a region. Multivariate analysis of spatial data includes measures of association between
variables and regression models such as higherorder trend surface analysis (Casetti and Jones,
1987; Anselin, 1988; Raining, 1990).
Practical Issues in Spatial Data Analysis
There are three broad categories of practical issues
in the analysis of spatial data for EAs (Table 13.1):
choosing conceptual models and inference frameworks, modeling spatial variation as a function of
attribute properties, and analyzing spatially referenced point and area data. The choice of an inference framework for the analysis of spatial data is
a fundamental issue, because the assumptions of
classical inference theory (i.e., that the data are the
outcome of some well-defined experiment) and its
implications (e.g., the stationarity assumption; see
Section 13.3.1) may not apply to EA spatial data.
Exploration of alternatives to classical theories of
inference is an active field of research and includes
the Bayesian approach (Leamer, 1978), which allows an explicit mixing of prior information with
current data, and tests based on data randomization
(e.g., bootstrapping, permutation tests; see Diaconis, 1985; Manly, 1997), among others.
The second practical issue, the choice of a model
of spatial variation, is influenced by the geographic
attributes of the data and the study region, which
constrain how data analysis proceeds. It is important to note that, whereas temporal and spatial data
share a number of similarities, they also differ in
189
(e.g., commodity, gene flow, disturbance) is taken
up by a fixed population; (2) exchange and transfer (e.g., income transfer, flow of nutrients); (3) interactions, in which events at one location influence and are influenced by events at other locations
(e.g., pricing patterns across retail sites reflecting
underlying competitive interactions among retailers, distribution of individuals of different species
as a function of interspecific competition); and (4)
dispersal or spread (e.g., migration of human and
animal populations, seed dispersal). Diffusion and
spread are differentiated by Raining (1990); diffusion is defined as the dispersal of an attribute
through a fixed population, whereas spread refers
to the dispersal of the population itself. These
processes are often included in models of spatial
distribution (e.g., Raining, 1990, in the social sciences; Pearson and Gardner, 1997, Tilman and
Kareiva, 1997, in ecology; see also Chapter 18).
13.2.2 Issues in Spatial Data Analysis
Analytical Issues
Analytical issues encountered in spatial analysis of
EA data fall into three broad categories (Table
13.1): (1) sampling, (2) numerical summary and
characterization of the spatial properties of the data,
and (3) analysis of multivariate data sets. The first
analytical issue, the design of spatial sampling
schemes to fit the goals of an EA (see Chapter 1),
is an important consideration, whether with existing or de novo data (see Chapter 7), including accuracy assessment of remotely sensed data (see
Chapter 10). The second analytical issue includes
TABLE 13.1. Analytical and practical issues in the
spatial analysis of ecological assessment data.
Analytical issues
Spatial sampling
Numerical summary and characterization of the spatial
properties of map data
Analysis of multivariate data sets
Practical issues
Conceptual models and inference frameworks for spatial
data
Modeling spatial variation
Statistical modeling of spatial data and:
Dependency in spatial data
Spatial heterogeneity
Spatial distribution of data points and boundary effects
Assessing model fit
Distributions
Extreme data values
Model sensitivity to the areal system
Size-variance relationships in homogeneous aggregates
the numerical description of the spatial properties
of map data. EAs often use maps as a basis for evaluation and scenario planning (see Chapters 3, 22,
and 24); therefore, it is important to study the spatial arrangement of map values and to devise summary measures that characterize spatial patterns
and their properties at different scales (e.g., Burrough, 1995).
For example, characterization of map data provides the basis for (1) constructing additional
smoothed and interpolated maps (Webster, 1985);
(2) defining the spatial attributes of models, such
as the spatial variation in precipitation in hydrological models (e.g., TOPMODEL in RHESSYS;
see Chapter 18) or in fire regimes in vegetation
models (e.g., LANDIS; see Chapter 18); (3) comparing different maps; and (4) comparing map surfaces at different points in time. The third analytical issue stems from the fact that the issues
addressed in an EA (see Chapter 1) generally require the analysis of data describing two or more
variables in a region. Multivariate analysis of spatial data includes measures of association between
variables and regression models such as higherorder trend surface analysis (Casetti and Jones,
1987; Anselin, 1988; Raining, 1990).
Practical Issues in Spatial Data Analysis
There are three broad categories of practical issues
in the analysis of spatial data for EAs (Table 13.1):
choosing conceptual models and inference frameworks, modeling spatial variation as a function of
attribute properties, and analyzing spatially referenced point and area data. The choice of an inference framework for the analysis of spatial data is
a fundamental issue, because the assumptions of
classical inference theory (i.e., that the data are the
outcome of some well-defined experiment) and its
implications (e.g., the stationarity assumption; see
Section 13.3.1) may not apply to EA spatial data.
Exploration of alternatives to classical theories of
inference is an active field of research and includes
the Bayesian approach (Leamer, 1978), which allows an explicit mixing of prior information with
current data, and tests based on data randomization
(e.g., bootstrapping, permutation tests; see Diaconis, 1985; Manly, 1997), among others.
The second practical issue, the choice of a model
of spatial variation, is influenced by the geographic
attributes of the data and the study region, which
constrain how data analysis proceeds. It is important to note that, whereas temporal and spatial data
share a number of similarities, they also differ in