********************************
PEP 0001 Spatial Dynamics Module
********************************

========  =================================
Author    Serge Rey <sjsrey@gmail.com>,
          Xinyue Ye <xinyue.ye@gmail.com>
Status    Approved 1.0
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.

