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CONTIG: Monte Carlo Contiguity Assessment

Developed by Christopher Papalas and Keith Kintigh


            In unconstrained clustering, spatial contiguity (or proximity) of units assigned to the same composition-based cluster provides the foundation for interpretation. Because only the type compositions for the grid squares are used in the cluster analysis there is no mechanical tendency inherent in the procedure that would cause spatially coherent patterning in the cluster assignments. Thus, large contiguous areas of the same cluster must indicate either spatial structure inherent in the data (Whallon 1984: 276, Blankholm 1991: 77, 81) or a chance occurrence. The program is available as freeware in contig.zip.


            With unconstrained clustering, interpretation usually proceeds from maps of cluster assignments, and tables summarizing the type composition represented by each cluster. To our knowledge, the possibility of an apparent spatial pattern being a result of a chance occurrence has never been systematically evaluated. The method we propose provides a statistical remedy to this problem.


            Quantifying Contiguity. Fundamentally, we want to assess the likelihood that a grid map, shows more contiguity than we would expect by chance. In order to do this, we need some way to measure contiguity. For each grid square, we might simply count the number of adjacent squares that are assigned to the same compositional cluster and add half the number of same-cluster squares that are immediately diagonal. Thus, a square completely surrounded by units assigned to the same cluster has a contiguity (C) of exactly six. These measurements can be simply summed to produce both cluster-specific and global measures of contiguity for a particular map. (Squares not included in the analysis are simply ignored—they present no additional problems.)


            Assessing the Significance of Observed Contiguity. The likelihood that a global contiguity as large as the observed could be due to chance can then be evaluated using a Monte Carlo analysis. To do this, the specific cluster assignments of the occupied squares are randomized, holding constant the occupied grid locations and the number of squares assigned to each compositional cluster. For each randomized map, the global (and cluster-specific) contiguity measure is calculated. By comparing the aggregate contiguity measure obtained from a large number of randomized maps with the observed measure, one can assess the likelihood of obtaining by chance a contiguity measure that is as high as the observed measure. These calculations can be performed using CONTIG.


SEQUENCE OF PROGRAM PROMPTS


Kmeans [P]lot File or Grid [M]ap {P} ?


            The program will read either a plt file produced by KMEANS or a grid with a fixed number of rows and columns. Each grid unit is assigned a number (the cluster aassignment), where 0 is used to indicate gruid units that do not participate in the analysis.

 

Output Listing File {.lst} ?


View Map {Y} ?


            On-screen view of the map.


Random Generator Seed {0} ?


Number of Random Trials {1000} ?


1000     Indicates Program Progress

End

Sample Program Input

4, 4

1221

1221

0121

0121

 

Sample Program Output


1221

1221

0121

0121


Grid Contiguity Computation 1000 Trials, 4 Rows, 4 Cols
  Measure counts adjacency +1, diagonal +0.5
            Obs            Mean     Std    Min    Max 
Clu Count Contig   Prob   Random  Random Random Random
___ _____ ______ ______ _________ ______ ______ ______
All    14     41 0.5040     41.03   0.13     32     59
  1     8     11 0.9980     16.99   0.11     10     27
  2     6     15 0.0330      9.04   0.09      3     18

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Page Last Updated - 22-Jul-2007