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@article{Duque2012,
	Author = {Duque, Juan C and Anselin, Luc and Rey, Sergio J},
	Date-Added = {2019-02-28 14:14:32 -0800},
	Date-Modified = {2019-02-28 14:14:42 -0800},
	Journal = {Journal of Regional Science},
	Keywords = {regionalization},
	Number = {3},
	Pages = {397--419},
	Publisher = {Wiley Online Library},
	Title = {THE MAX-P-REGIONS PROBLEM*},
	Volume = {52},
	Year = {2012},
	Bdsk-File-1 = { }}

@article{Rey_2011,
	Author = {Rey, Sergio J. and Anselin, Luc and Folch, David C. and Arribas-Bel, Daniel and Sastr{\'e} Guti{\'e}rrez, Myrna L. and Interlante, Lindsey},
	Date-Added = {2019-02-28 13:51:18 -0800},
	Date-Modified = {2019-02-28 13:51:18 -0800},
	Doi = {10.1177/0891242410383414},
	Issn = {1552-3543},
	Journal = {Economic Development Quarterly},
	Month = {Nov},
	Number = 1,
	Pages = {54--64},
	Publisher = {SAGE Publications},
	Title = {Measuring Spatial Dynamics in Metropolitan Areas},
	Url = {http://dx.doi.org/10.1177/0891242410383414},
	Volume = 25,
	Year = 2011,
	Bdsk-Url-1 = {http://dx.doi.org/10.1177/0891242410383414}}

@article{Biemann:2011,
	Abstract = { Optimal matching (OM) is a method that assesses sequence similarity. It was originally developed to study protein and DNA sequences and was later transferred to the social sciences where it was applied accordingly. However, there is an ongoing debate on the adequacy of its use in the social sciences, as a superficial transfer might not respond to the significant differences between typical sequences in biological and social settings. In this paper, I elaborate on these differences and introduce a distinction between two sequence types{\^a}namely, common ancestors and unfolding processes. While the first sequence type is typically found in biological settings (e.g., DNA sequences), the latter applies to most sequences studied in the social sciences (e.g., careers). Based on this distinction, I present a new way of coding sequences as an extension to conventional OM analyses and demonstrate its usefulness in simulated and empirical examples. The paper concludes with a discussion of this new approach and its integration into previous extensions of OM. },
	Author = {Torsten Biemann},
	Date-Added = {2019-02-28 12:42:06 -0800},
	Date-Modified = {2019-02-28 12:42:06 -0800},
	Doi = {10.1111/j.1467-9531.2011.01235.x},
	Eprint = {https://doi.org/10.1111/j.1467-9531.2011.01235.x},
	Journal = {Sociological Methodology},
	Number = {1},
	Pages = {195-221},
	Title = {A Transition-Oriented Approach to Optimal Matching},
	Url = {https://doi.org/10.1111/j.1467-9531.2011.01235.x},
	Volume = {41},
	Year = {2011},
	Bdsk-File-1 = { },
	Bdsk-Url-1 = {https://doi.org/10.1111/j.1467-9531.2011.01235.x}}

@article{Formby:2004fk,
	Author = {John P. Formby and W. James Smith and Buhong Zheng},
	Date-Added = {2018-07-06 22:21:00 +0000},
	Date-Modified = {2018-07-06 22:21:00 +0000},
	Doi = {https://doi.org/10.1016/S0304-4076(03)00211-2},
	Journal = {Journal of Econometrics},
	Keywords = {mobility, distributional dynamics},
	Number = {1},
	Pages = {181--205},
	Publisher = {Elsevier},
	Title = {Mobility measurement, transition matrices and statistical inference},
	Url = {http://www.sciencedirect.com/science/article/pii/S0304407603002112},
	Volume = {120},
	Year = {2004},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0304407603002112},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0304-4076(03)00211-2}}

@article{Rey2011,
	Author = {Rey, Sergio J. and Murray, Alan T. and Anselin, Luc},
	Date-Added = {2018-07-03 17:53:40 +0000},
	Date-Modified = {2018-07-03 17:53:45 +0000},
	Doi = {10.1007/s12076-010-0048-2},
	Journal = {Letters in Spatial and Resource Sciences},
	Keywords = {directional.py},
	Number = {1},
	Pages = {81--90},
	Publisher = {Springer},
	Title = {Visualizing regional income distribution dynamics},
	Url = {https://doi.org/10.1007/s12076-010-0048-2},
	Volume = {4},
	Year = {2011},
	Bdsk-Url-1 = {https://doi.org/10.1007/s12076-010-0048-2}}

@article{Rey2016a,
	Abstract = {Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series.},
	Author = {Rey, Sergio J. and Kang, Wei and Wolf, Levi},
	Date-Added = {2018-06-20 17:13:29 +0000},
	Date-Modified = {2018-06-20 17:13:38 +0000},
	Doi = {10.1007/s10109-016-0234-x},
	Issn = {1435-5949},
	Journal = {Journal of Geographical Systems},
	Number = {4},
	Pages = {377--398},
	Title = {The properties of tests for spatial effects in discrete {Markov} chain models of regional income distribution dynamics},
	Url = {http://dx.doi.org/10.1007/s10109-016-0234-x},
	Volume = {18},
	Year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10109-016-0234-x}}

@article{Kang2018,
	Abstract = {Spatial effects have been recognized to play an important role in transitional dynamics of regional incomes. Detection and evaluation of both spatial heterogeneity and spatial dependence in discrete Markov chain models, which have been widely applied to the study of regional income distribution dynamics and convergence, are vital, but under-explored issues. Indeed, in this spatiotemporal setting, spatial effects can take much more complex forms than that in a pure cross-sectional setting. In this paper, we address two test frameworks. The first is a conditional spatial Markov chains test framework, which can be used to detect spatial heterogeneity and temporally lagged spatial dependence; the second is a joint spatial Markov chains test framework, which tests for contemporaneous spatial dependence. A series of Monte Carlo experiments are designed to examine size, power and robustness properties of these tests for a range of sample sizes (spatial                                                                   {\$}{\$}{\backslash}times {\$}{\$}                                                      {\texttimes}                                                 temporal dimensions), for different levels of discretization granularity and for different number of regimes. Results indicate that all tests display good size property except when sample size is fairly small. All tests for spatial dependence are similar in almost all aspects---size, power and robustness. Conditional spatial Markov tests for spatial heterogeneity have highest power for detecting spatial heterogeneity. Granularity of discretization has a major impact on the size properties of the tests when sample size is fairly small.},
	Author = {Kang, Wei and Rey, Sergio J.},
	Date-Added = {2018-06-20 17:09:37 +0000},
	Date-Modified = {2018-06-20 17:09:37 +0000},
	Day = {06},
	Doi = {10.1007/s00168-017-0859-9},
	Issn = {1432-0592},
	Journal = {The Annals of Regional Science},
	Month = {Jan},
	Title = {Conditional and joint tests for spatial effects in discrete {Markov} chain models of regional income distribution dynamics},
	Url = {https://doi.org/10.1007/s00168-017-0859-9},
	Year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00168-017-0859-9}}

@article{Rey2016,
	Abstract = { In the study of income inequality dynamics, the concept of exchange mobility plays a central role. Applications of classical rank correlation statistics have been used to assess the degree to which individual economies swap positions in the income distribution over time. These classic measures ignore the underlying geographical pattern of rank changes. Rey (2004) introduced a spatial concordance statistic as an extension of Kendall's rank correlation statistic, a commonly employed measure of exchange mobility. This article suggests local forms of the global spatial concordance statistic: local indicators of mobility association (LIMA). The LIMA statistics allow for the decomposition of the global measure into the contributions associated with individual locations. They do so by considering the degree of concordance (stability) or discordance (exchange mobility) reflected within an economy's local spatial context. Different forms of the LIMAs derive from alternative expressions of the neighborhood and neighbor set. Additionally, the additive decomposition of the LIMAs permits the development of a mesolevel analytic to examine whether the overall space--time concordance is driven by either interregional or intraregional concordance. The measures are illustrated in a case study that examines regional income dynamics in Mexico. },
	Author = {Sergio J. Rey},
	Date-Added = {2018-06-12 22:59:18 +0000},
	Date-Modified = {2018-06-12 22:59:33 +0000},
	Doi = {10.1080/24694452.2016.1151336},
	Journal = {Annals of the American Association of Geographers},
	Keywords = {LIMA},
	Number = {4},
	Pages = {788-803},
	Title = {Space--Time Patterns of Rank Concordance: Local Indicators of Mobility Association with Application to Spatial Income Inequality Dynamics},
	Url = {https://doi.org/10.1080/24694452.2016.1151336},
	Volume = {106},
	Year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1080/24694452.2016.1151336}}

@incollection{Rey2004a,
	Abstract = {This chapter discusses the importance of distributional dynamics in
	the evolution of regional incomes. Serge starts with spatial Markov
	stuff, but then extends it to include the spatial tau decomposition
	and the measures of inter-intra regional cohesion.},
	Address = {Hampshire},
	Author = {Rey, Sergio J.},
	Booktitle = {Spatial econometrics and spatial statistics},
	Date-Added = {2018-06-12 22:57:36 +0000},
	Date-Modified = {2018-06-12 22:57:51 +0000},
	Editor = {Getis, A. and M{\'{u}}r, J. and Zoeller, H.},
	Keywords = {convergence, rank.py},
	Pages = {193-213},
	Publisher = {Palgrave},
	Title = {Spatial dependence in the evolution of regional income distributions},
	Year = {2004}}

@article{Rey2014,
	Author = {Rey, Sergio J.},
	Date-Added = {2018-06-12 22:54:57 +0000},
	Date-Modified = {2018-06-12 22:55:04 +0000},
	Doi = {10.1007/s00180-013-0461-2},
	Journal = {Computational Statistics},
	Keywords = {concordance, rank.py, LIMA},
	Number = {3-4},
	Pages = {799-811},
	Publisher = {Springer},
	Title = {Fast algorithms for a space-time concordance measure},
	Url = {https://doi.org/10.1007/s00180-013-0461-2},
	Volume = {29},
	Year = {2014},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00180-013-0461-2}}

@book{Press2007,
	Address = {Cambridge},
	Author = {Press, William H and Teukolsky, Saul A and Vetterling, William T and Flannery, Brian P},
	Date-Added = {2018-06-12 22:53:57 +0000},
	Date-Modified = {2018-06-12 22:54:05 +0000},
	Edition = {3rd},
	Keywords = {rank.py},
	Publisher = {Cambridge Univ Pr},
	Title = {Numerical recipes: the art of scientific computing},
	Year = {2007}}

@article{Christensen2005,
	Abstract = {Traditional algorithms for the calculation of Kendall's $\tau$ between two datasets of n samples have a calculation time of O(n2). This paper presents a suite of algorithms with expected calculation time of O(n log n) or better using a combination of sorting and balanced tree data structures. The literature, e.g. Dwork et al. (2001), has alluded to the existence of O(n log n) algorithms without any analysis: this paper gives an explicit descriptions of such algorithms for general use both for the case with and without duplicate values in the data. Execution times for sample data are reduced from 3.8 hours to around 1--2 seconds for one million data pairs.},
	Author = {Christensen, David},
	Date-Added = {2018-06-12 22:50:55 +0000},
	Date-Modified = {2018-06-12 22:51:11 +0000},
	Doi = {10.1007/BF02736122},
	Journal = {Computational Statistics},
	Month = {Mar},
	Number = {1},
	Pages = {51--62},
	Title = {Fast algorithms for the calculation of Kendall's $\tau$},
	Url = {https://doi.org/10.1007/BF02736122"},
	Volume = {20},
	Year = {2005},
	Bdsk-Url-1 = {https://doi.org/10.1007/BF02736122%22},
	Bdsk-Url-2 = {https://doi.org/10.1007/BF02736122}}

@article{Kullback1962,
	Author = {Kullback, S. and Kupperman, M. and Ku, H. H.},
	Date-Added = {2018-06-12 22:49:01 +0000},
	Date-Modified = {2018-06-12 22:49:07 +0000},
	Doi = {10.2307/1266291},
	Journal = {Technometrics},
	Keywords = {markov, markov.py},
	Number = {4},
	Pages = {573--608},
	Publisher = {JSTOR},
	Title = {Tests for contingency tables and {Markov} chains},
	Url = {http://www.jstor.org/stable/1266291},
	Volume = {4},
	Year = {1962},
	Bdsk-Url-1 = {http://www.jstor.org/stable/1266291},
	Bdsk-Url-2 = {https://doi.org/10.2307/1266291}}

@article{Bickenbach2003,
	Author = {Frank Bickenbach and Eckhardt Bode},
	Date-Added = {2018-06-12 22:47:20 +0000},
	Date-Modified = {2018-06-12 22:47:31 +0000},
	Doi = {10.1177/0160017603253789},
	Journal = {International Regional Science Review},
	Number = {3},
	Pages = {363-392},
	Title = {Evaluating the {Markov} property in studies of economic convergence},
	Url = {https://doi.org/10.1177/0160017603253789},
	Volume = {26},
	Year = {2003},
	Bdsk-Url-1 = {https://doi.org/10.1177/0160017603253789}}

@book{Kemeny1967,
	Author = {John G. Kemeny and Snell, James Laurie},
	Date-Added = {2018-06-12 22:44:29 +0000},
	Date-Modified = {2018-06-12 22:44:40 +0000},
	Keywords = {markov chain, ergodic.py, mobility},
	Publisher = {Van Nostrand},
	Title = {Finite markov chains},
	Year = {1967},
	Bdsk-File-1 = { }}

@article{Rey2001,
	Author = {Rey, Sergio J.},
	Date-Added = {2018-06-12 21:11:59 +0000},
	Date-Modified = {2018-06-12 21:13:29 +0000},
	Doi = {10.1111/j.1538-4632.2001.tb00444.x},
	Journal = {Geographical Analysis},
	Number = {3},
	Pages = {195--214},
	Publisher = {Wiley Online Library},
	Title = {Spatial empirics for economic growth and convergence},
	Url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.2001.tb00444.x},
	Volume = {33},
	Year = {2001},
	Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.2001.tb00444.x},
	Bdsk-Url-2 = {https://doi.org/10.1111/j.1538-4632.2001.tb00444.x}}
