Spatial Analysis: An Overview of Methods for Space-Time Analysis of Stocks and Transaction Flows

Stuart H. Sweeney

Department of GeographyUniversity of California, Santa Barbara

February 2004

Globalization in the World-System: Mapping Change over Time, UC Riverside

Overview

• Motivation

• Spatial dependence, spatial heterogeneity, and time

• Exploratory Spatial Data Analysis

• Spatial-Interaction (SI) modeling concepts

• Exploratory methods for transaction data

• Invitation for demonstrations

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

1

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

2

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

3

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

(M8590 -M7580)>0

Motivation

• Interested in space-time dependence

- stock (variable on a map)

- flows (interactions on a map)

• Visual, exploratory, and modeling approaches

(M8590 -M7580)<0

• Spatial dependence: yi=f(yj), i=1,..,n and i=j

- frame dependence (MAUP)

- spatial process

• Spatial heterogeneity: yi = xi $i + ei

- specification issue

• W matrix

y* = Wy

y = DWy + e

y = DWy + X$ + e

Spatial dependence, spatial heterogeneity, and time

t=1

t=2

t=T

• EDA- “discover” potentially interesting patterns

• ESDA- explicable spatial patterns in distribution, outliers, regimes (heterogeneity)

- tool for discover and specification

• ESDA + dynamic = GeoDA- linking, brushing, animations... and much more.

Exploratory Spatial Data Analysis (ESDA GeoDA)

• GeoDA features- local and global Moran’s I and Multivariate Moran’s I

- parallel coordinate plots

- scatterplot matrices

- conditional plots

- map movies

- basic GIS functionality

- !! directly reads ArcView shape files !!

• GeoDA Demonstration

Exploratory Spatial Data Analysis (ESDA GeoDA) Exploratory Spatial Data Analysis (ESDA GeoDA)

• Complexity of ODT interactions

• Information use in traditional modeling approaches

• Regions: spatial regularities

• Epochs: temporal regularities

• Ideally link regionalization, flow visualization, model fitting, and evaluation.

Spatial-Interaction (SI) modeling concepts

t=1t=2

t=T

data = {nij}

n11 n12 .......................... n1Jn21 n22 .......................... n2J. . . .. . . .. . . .. . . .

nI1 nI2 .......................... nIJ

orig

ins

destinations

OD O

D

X{ik}

X{jk}

parameter/information sets

one-way: O, D, Xtwo-way: OD, proxy

Spatial-Interaction (SI) modeling concepts (cont.)

OD O

D

X{ik}

X{jk}

parameter/information sets

one-way: O, D, Xtwo-way: OD, proxy

multiplicative models

nij = τ τiO

τiD 1^

nij = nij = τ τiO

τiD

τijOD ^

constrained model:

nij = τ τiO

τiD

τijOD ~

where subset of τijOD are not

equal to 1

~

Spatial-Interaction (SI) modeling concepts (cont.)

Regionalization- subsystem- typology- prior knowledge

Parameter Constraint

Model estimation and fit (LR)

Visualization- observed- fitted- errors

Spatial-Interaction (SI) modeling concepts (cont.)

Flow Mapper Software Flow Mapper Software

Flow Mapper Software Flow Mapper Software

Instant tea exports, 2000

Bulk tea exports, 2000

Flow Mapper Software Flow Mapper Software

Flow Mapper Software Flow Mapper Software