GeospatIal Distribution DYnamics (GIDDY)¶

Giddy is an open-source python library for the analysis of dynamics of longitudinal spatial data. Originating from the spatial dynamics module in PySAL (Python Spatial Analysis Library), it is under active development for the inclusion of many newly proposed analytics that consider the role of space in the evolution of distributions over time and has several new features including inter- and intra-regional decomposition of mobility association and local measures of exchange mobility in addition to space-time LISA and spatial markov methods.

Rose diagram (directional LISAs)

Spatial Markov Chain

Neighbor Set Local Indicator of Mobility Association (LIMA)

Installation¶

From version 2.2.0, giddy supports python 3.6 and 3.7 only. Please make sure that you are operating in a python 3 environment.

Installing released version¶

giddy is available on the Python Package Index. Therefore, you can either install directly with pip from the command line:

pip install -U giddy

or download the source distribution (.tar.gz) and decompress it to your selected destination. Open a command shell and navigate to the decompressed folder. Type:

pip install .

You may also install the latest stable giddy via conda-forge channel by running:

$ conda install --channel conda-forge giddy

Installing development version¶

Potentially, you might want to use the newest features in the development version of giddy on github - pysal/giddy while have not been incorporated in the Pypi released version. You can achieve that by installing pysal/giddy by running the following from a command shell:

pip install git+https://github.com/pysal/giddy.git

You can also fork the pysal/giddy repo and create a local clone of your fork. By making changes to your local clone and submitting a pull request to pysal/giddy, you can contribute to the giddy development.

API reference¶

Markov Methods¶

`giddy.markov.Markov`(class_ids[, classes])	Classic Markov transition matrices.
`giddy.markov.Spatial_Markov`(y, w[, k, m, …])	Markov transitions conditioned on the value of the spatial lag.
`giddy.markov.LISA_Markov`(y, w[, …])	Markov for Local Indicators of Spatial Association
`giddy.markov.FullRank_Markov`(y)	Full Rank Markov in which ranks are considered as Markov states rather than quantiles or other discretized classes.
`giddy.markov.GeoRank_Markov`(y)	Geographic Rank Markov.
`giddy.markov.kullback`(F)	Kullback information based test of Markov Homogeneity.
`giddy.markov.prais`(pmat)	Prais conditional mobility measure.
`giddy.markov.homogeneity`(transition_matrices)	Test for homogeneity of Markov transition probabilities across regimes.
`giddy.markov.sojourn_time`(p)	Calculate sojourn time based on a given transition probability matrix.
`giddy.ergodic.steady_state`(P)	Calculates the steady state probability vector for a regular Markov transition matrix P.
`giddy.ergodic.fmpt`(P)	Calculates the matrix of first mean passage times for an ergodic transition probability matrix.
`giddy.ergodic.var_fmpt`(P)	Variances of first mean passage times for an ergodic transition probability matrix.

Directional LISA¶

giddy.directional.Rose(Y, w[, k])

Rose diagram based inference for directional LISAs.

Economic Mobility Indices¶

giddy.mobility.markov_mobility(p[, measure, ini])

Markov-based mobility index.

Exchange Mobility Methods¶

`giddy.rank.Theta`(y, regime[, permutations])	Regime mobility measure.
`giddy.rank.Tau`(x, y)	Kendall’s Tau is based on a comparison of the number of pairs of n observations that have concordant ranks between two variables.
`giddy.rank.SpatialTau`(x, y, w[, permutations])	Spatial version of Kendall’s rank correlation statistic.
`giddy.rank.Tau_Local`(x, y)	Local version of the classic Tau.
`giddy.rank.Tau_Local_Neighbor`(x, y, w[, …])	Neighbor set LIMA.
`giddy.rank.Tau_Local_Neighborhood`(x, y, w[, …])	Neighborhood set LIMA.
`giddy.rank.Tau_Regional`(x, y, regime[, …])	Inter and intraregional decomposition of the classic Tau.

References¶

BB03: Frank Bickenbach and Eckhardt Bode. Evaluating the Markov property in studies of economic convergence. International Regional Science Review, 26(3):363–392, 2003. URL: https://doi.org/10.1177/0160017603253789, doi:10.1177/0160017603253789.
Chr05: David Christensen. Fast algorithms for the calculation of kendall’s τ. Computational Statistics, 20(1):51–62, Mar 2005. URL: https://doi.org/10.1007/BF02736122”, doi:10.1007/BF02736122.
FSZ04: John P. Formby, W. James Smith, and Buhong Zheng. Mobility measurement, transition matrices and statistical inference. Journal of Econometrics, 120(1):181–205, 2004. URL: http://www.sciencedirect.com/science/article/pii/S0304407603002112, doi:https://doi.org/10.1016/S0304-4076(03)00211-2.
Ibe09: Oliver Ibe. Markov processes for stochastic modeling. Elsevier Academic Press, Amsterdam, 2009.
KR18: Wei Kang and Sergio J. Rey. Conditional and joint tests for spatial effects in discrete markov chain models of regional income distribution dynamics. The Annals of Regional Science, 61(1):73–93, Jul 2018. URL: https://doi.org/10.1007/s00168-017-0859-9, doi:10.1007/s00168-017-0859-9.
KS67: John G. Kemeny and James Laurie Snell. Finite markov chains. Van Nostrand, 1967.
KKK62: S. Kullback, M. Kupperman, and H. H. Ku. Tests for contingency tables and Markov chains. Technometrics, 4(4):573–608, 1962. URL: http://www.jstor.org/stable/1266291, doi:10.2307/1266291.
PTVF07: William H Press, Saul A Teukolsky, William T Vetterling, and Brian P Flannery. Numerical recipes: the art of scientific computing. Cambridge Univ Pr, Cambridge, 3rd edition, 2007.
Rey01: Sergio J. Rey. Spatial empirics for economic growth and convergence. Geographical Analysis, 33(3):195–214, 2001. URL: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.2001.tb00444.x, doi:10.1111/j.1538-4632.2001.tb00444.x.
Rey04: Sergio J. Rey. Spatial dependence in the evolution of regional income distributions. In A. Getis, J. Múr, and H. Zoeller, editors, Spatial econometrics and spatial statistics, pages 193–213. Palgrave, Hampshire, 2004.
Rey14a: Sergio J. Rey. Fast algorithms for a space-time concordance measure. Computational Statistics, 29(3-4):799–811, 2014. URL: https://doi.org/10.1007/s00180-013-0461-2, doi:10.1007/s00180-013-0461-2.
Rey14b: Sergio J. Rey. Rank-based Markov chains for regional income distribution dynamics. Journal of Geographical Systems, 16(2):115–137, 2014.
Rey16: Sergio J. Rey. Space–time patterns of rank concordance: local indicators of mobility association with application to spatial income inequality dynamics. Annals of the American Association of Geographers, 106(4):788–803, 2016. URL: https://doi.org/10.1080/24694452.2016.1151336, doi:10.1080/24694452.2016.1151336.
RKW16: Sergio J. Rey, Wei Kang, and Levi Wolf. The properties of tests for spatial effects in discrete Markov chain models of regional income distribution dynamics. Journal of Geographical Systems, 18(4):377–398, 2016. URL: http://dx.doi.org/10.1007/s10109-016-0234-x, doi:10.1007/s10109-016-0234-x.
RMA11: Sergio J. Rey, Alan T. Murray, and Luc Anselin. Visualizing regional income distribution dynamics. Letters in Spatial and Resource Sciences, 4(1):81–90, 2011. URL: https://doi.org/10.1007/s12076-010-0048-2, doi:10.1007/s12076-010-0048-2.