PEP 0001 Spatial Dynamics Module

Author	Serge Rey <sjsrey@gmail.com>, Xinyue Ye <xinyue.ye@gmail.com>
Status	Draft
Created	18-Jan-2010
Updated	09-Feb-2010

Abstract

With the increasing availability of spatial longitudinal data sets there is an growing demand for exploratory methods that integrate both the spatial and temporal dimensions of the data. The spatial dynamics module combines a number of previously developed and to-be-developed classes for the analysis of spatial dynamics. It will include classes for the following statistics for spatial dynamics, Markov, spatial Markov, rank mobility, spatial rank mobility, space-time LISA.

Motivation

Rather than having each of the spatial dynamics as separate modules in PySAL, it makes sense to move them all within the same module. This would facilitate common signatures for constructors and similar forms of data structures for space-time analysis (and generation of results).

The module would implement some of the ideas for extending LISA statistics to a dynamic context ([Anselin2000] [ReyJanikas2006]), and recent work developing empirics and summary measures for comparative space time analysis ([ReyYe2010]).

Reference Implementation

We suggest adding the module pysal.spatialdynamics which in turn would encompass the following modules:

• rank mobility rank concordance (relative mobility or internal mixing) Kendall’s index
• spatial rank mobility add a spatial dimension into rank mobility investigate the extent to which the relative mobility is spatially dependent use various types of spatial weight matrix
• Markov empirical transition probability matrix (mobility across class) Shorrock’s index
• Spatial Markov adds a spatial dimension (regional conditioning) into classic Markov models a trace statistic from a modified Markov transition matrix investigate the extent to which the inter-class mobility are spatially dependent
• Space-Time LISA extends LISA measures to integrate the time dimension combined with cg (computational geometry) module to develop comparative measurements

References

[Anselin2000]

Anselin, Luc (2000) Computing environments for spatial data analysis. Journal of Geographical Systems 2: 201-220

[ReyJanikas2006]

Rey, S.J. and M.V. Janikas (2006) STARS: Space-Time Analysis of Regional Systems, Geographical Analysis 38: 67-86.

[ReyYe2010]

Rey, S.J. and X. Ye (2010) Comparative spatial dyanmics of regional systems. In Paez, A. et al. (eds) Progress in Spatial Analysis: Methods and Applications. Springer: Berlin, 441-463.