R function for calculating the Hodder-Okell's A index of spatial association

The function allows to calculate the Hodder-Okell's A index of spatial association between the features of two point patterns.

Aindex(x, y, studyplot = NULL, B = 199, addmap = FALSE)

Point pattern (SpatialPointDataframe class).


Point pattern (SpatialPointDataframe class).


Feature (of polygon type; SpatialPolygonsDataFrame class) representing the study area; if not provided, the study area is internally worked out as the bounding polygon based on the union the convex hulls of the x and y patterns. This is only used for visualization purpose, should the user want to plot the two point patterns within the actual study area.


Number of permutations (199 by default).


FALSE (default) or TRUE if the user does not want or wants a map of the study area and of the two patterns to be displayed.


The functions takes as input two point patterns (SpatialPointDataframe class) and calculate the A index. Details about the latter are provided by: Orton C. 1980, "Mathematics in Archeology", Glasgow: William Collins Sons & Co Ltd, pp. 154-155 Blankholm P. 1990, "Intrasite spatial Analysis in Theory and Practice", Aarhus: Aarhus University Press, pp. 130-135.

The A index is about equal to 1 when the two patterns are randomly mingled; it is smaller than 1 when the two patterns are segregated; it is larger than 1 when the features of the two point patterns tend to occur together. The computational details are provided by Blankholm's book cited above (page 132).

The significance of the A index is calculated via the randomized approach devised by: Kintigh K W. 1990, <U+201C>Intrasite Spatial Analysis: A Commentary of Major Methids<U+201D>. In Voorrips A, <U+201C>Mathematics and Information Science in Archaeology: A Flexible Framework<U+201D>, Studies in Modern Archaeology 3: 165-200

Given two patterns A and B being analysed, the procedure keeps the points location unchanged and randomly assigns the points to either pattern. The random re-assignment is performed B times (199 by default) and each time the A index is calculated. One-tailed and two-tailed p values are calculated following the procedure described by Baddeley et al., "Spatial Point Patterns. Methodology and Applications with R", CRC Press 2016, p. 387.


The function produces: -an histogram showing the frequency distribution of the randomized A index, with vertical reference lines representing the 0.025th and 0.975th quantile of the distribution. A black dot represents the observed A index. At the bottom of the chart the randomized p values are reported; -optionally (setting the 'addmap' parameter to TRUE), a map showing the point patterns (and the study area, if supplied).

See Also

distRandSign , distCovarModel , pointsCovarModel

  • Aindex
# calculate the Hodder-Okell's A index for the two patterns, and plot the map
Aindex(springs, points, addmap=TRUE)

# }
Documentation reproduced from package GmAMisc, version 1.0.0, License: GPL (>= 2)

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