regression-tests.sample-tests

geary-c-test

(geary-c-test values neighbour-weights)
Executes a Geary's C test for checking spatial
autocorrelation in the sample of observations.
   values: Sample values.
   neighbour-weights: A hash-map of neighbour indexes
                      and associated weights.
returns: A Geary's C statistic (for sample).

## Usage

   (require '[regression-tests.sample-tests :refer :all])

   ``````````` example from
   ```````````   Goodchild, M. F. (1986). Spatial Autocorrelation, CATMOG 47.
   ```````````                            Geo Books, Norwich, UK, 56 pp.
   ```````````   example in 1.3.1 Geary's index (area objects, interval attributes), p. 14.

   (def values [3 2 2 1])
   (def neighbour-weights {[0 1] 1 [0 2] 1 [0 3] 1 [1 0] 1 [1 3] 1
                            [2 0] 1 [2 3] 1 [3 0] 1 [3 1] 1 [3 2] 1})

   (geary-c-test values neighbour-weights)
   => 6/5

## References
    [1] Geary, R. (1954). The Contiguity Ratio and Statistical Mapping.
        The Incorporated Statistician, 5(3): 115-145. DOI: 10.2307/2986645.

geary-c-test-population

(geary-c-test-population values neighbour-weights)
Executes a Geary's C test for checking spatial
autocorrelation in the population of observations.
   values: Population values.
   neighbour-weights: A hash-map of neighbour indexes
                      and associated weights.
returns: A Geary's C statistic (for population).

## Usage

   (require '[regression-tests.sample-tests :refer :all])

   ``````````` example from
   ```````````   Goodchild, M. F. (1986). Spatial Autocorrelation, CATMOG 47.
   ```````````                            Geo Books, Norwich, UK, 56 pp.
   ```````````   example in 1.3.1 Geary's index (area objects, interval attributes), p. 14,
   ```````````   corrected with n/(n-1) to get population statistics.

   (def values [3 2 2 1])
   (def neighbour-weights {[0 1] 1 [0 2] 1 [0 3] 1 [1 0] 1 [1 3] 1
                            [2 0] 1 [2 3] 1 [3 0] 1 [3 1] 1 [3 2] 1})

   (geary-c-test-population values neighbour-weights)
   => 1.6

## References
    [1] Geary, R. (1954). The Contiguity Ratio and Statistical Mapping.
        The Incorporated Statistician, 5(3): 115-145. DOI: 10.2307/2986645.
    [2] Chen, Y. (2013). New Approaches for Calculating Moran’s Index of Spatial Autocorrelation.
        PLoS ONE, 8(7): e68336. DOI:10.1371/journal.pone.0068336.

moran-i-test

(moran-i-test values neighbour-weights)
Executes a Moran's I test for checking spatial
autocorrelation in the sample of observations.
   values: Sample values.
   neighbour-weights: A hash-map of neighbour indexes
                      and associated weights.
returns: A Moran's I statistic.

## Usage

   (require '[regression-tests.sample-tests :refer :all])

   ``````````` example from
   ```````````    vignettes for R package ape v. 3.4 Moran's I
   ```````````    https://cran.r-project.org/web/packages/ape/vignettes/MoranI.pdf
   ```````````    E. Paradis Moran's Autocorrelation Coefficient in Comparative Methods Nov. 29, 2015
   ```````````    example in 2.1 Phylogenetic Distances, pp. 2-4.

   (def values [4.09434 3.61092 2.37024 2.02815 -1.46968])
   (def neighbour-weights  {[0 1] 0.505744983336052 [0 2] 0.216747850001166
                            [0 3] 0.171300720162211 [0 4] 0.106206446500571
                            [1 0] 0.505744983336052 [1 2] 0.216747850001166
                            [1 3] 0.171300720162211 [1 4] 0.106206446500571
                            [2 1] 0.304848067656604 [2 0] 0.304848067656604
                            [2 3] 0.240928311535057 [2 4] 0.149375553151735
                            [3 1] 0.276243093922652 [3 2] 0.276243093922652
                            [3 0] 0.276243093922652 [3 4] 0.171270718232044
                            [4 1] 0.25 [4 2] 0.25
                            [4 3] 0.25 [4 0] 0.25})

   (moran-i-test values neighbour-weights)
   => -0.07312179438450675

## References
    [1] Moran, P. (1950). Notes on Continuous Stochastic Phenomena.
        Biometrika, 37(1-2): 17-23. DOI: 10.2307/2332142.