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Spatial Stats

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SpatialStats

SpatialStats is an ActiveRecord/Rails plugin that utilizes PostGIS to compute weights/statistics of spatial data sets in Rails Apps.

Installation

Add this line to your application's Gemfile:

gem 'spatial_stats'

And then execute:

$ bundle

Or install it yourself as:

$ gem install spatial_stats

Usage

Weights

Weights define the spatial relation between members of a dataset. Contiguous operations are supported for polygons and multipolygons, and distant operations are supported for points.

To compute weights, you need an ActiveRecord::Relation scope and a geometry field. From there, you can pick what type of weight operation to compute (knn, queen neighbors, etc.).

Compute Queen Weights

# County table has the following fields: avg_income: float, geom: multipolygon.
scope = County.all
geom_field = :geom
weights = SpatialStats::Weights::Contiguous.queen(scope, geom_field)
# => #<SpatialStats::Weights::WeightsMatrix>

Compute KNN of Centroids

The field being queried does not have to be defined in the schema, but could be computed during the query for scope.

This example finds the inverse distance weighted, 5 nearest neighbors for the centroid of each county.

scope = County.all.select("*, st_centroid(geom) as geom")
weights = SpatialStats::Weights::Distant.idw_knn(scope, :geom, 5)
# => #<SpatialStats::Weights::WeightsMatrix>

Define WeightsMatrix without Query

Weight matrices can be defined by a hash that describes each key's neighbor and weight.

Example: Define WeightsMatrix and get the matrix in row_standardized format.

weights = {
    1 => [{ id: 2, weight: 1 }, { id: 4, weight: 1 }],
    2 => [{ id: 1, weight: 1 }],
    3 => [{ id: 4, weight: 1 }],
    4 => [{ id: 1, weight: 1 }, { id: 3, weight: 1 }]
}
keys = weights.keys
wm = SpatialStats::Weights::WeightsMatrix.new(weights)
#  => #<SpatialStats::Weights::WeightsMatrix:0x0000561e205677c0 @keys=[1, 2, 3, 4], @weights={1=>[{:id=>2, :weight=>1}, {:id=>4, :weight=>1}], 2=>[{:id=>1, :weight=>1}], 3=>[{:id=>4, :weight=>1}], 4=>[{:id=>1, :weight=>1}, {:id=>3, :weight=>1}]}, @n=4>

wm = wm.standardize
#  => #<SpatialStats::Weights::WeightsMatrix:0x0000561e205677c0 @keys=[1, 2, 3, 4], @weights={1=>[{:id=>2, :weight=>0.5}, {:id=>4, :weight=>0.5}], 2=>[{:id=>1, :weight=>1}], 3=>[{:id=>4, :weight=>1}], 4=>[{:id=>1, :weight=>0.5}, {:id=>3, :weight=>0.5}]}, @n=4>

wm.dense
# => Numo::DFloat[
#    [0, 0.5, 0, 0.5],
#    [1, 0, 0, 0],
#    [0, 0, 0, 1],
#    [0.5, 0, 0.5, 0]
#   ]

wm.sparse
# => #<SpatialStats::Weights::CSRMatrix @m=4, @n=4, @nnz=6>

Lagged Variables

Spatially lagged variables can be computed with weights matrix and 1-D vector (Array).

Compute a Lagged Variable

weights = {
    1 => [{ id: 2, weight: 1 }, { id: 4, weight: 1 }],
    2 => [{ id: 1, weight: 1 }],
    3 => [{ id: 4, weight: 1 }],
    4 => [{ id: 1, weight: 1 }, { id: 3, weight: 1 }]
}
wm = SpatialStats::Weights::WeightsMatrix.new(weights).standardize
vec = [1, 2, 3, 4]
lagged_var = SpatialStats::Utils::Lag.neighbor_sum(wm, vec)
# => [3.0, 1.0, 4.0, 2.0]

Global Stats

Global stats compute a value for the dataset, like how clustered the observations are within the region.

Most stat classes take three parameters: scope, data_field, and weights. All stat classes have the stat method that will compute the target statistic. These are also aliased with the common name of the statistic, such as i for Moran or c for Geary.

Compute Moran's I

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Global::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Global::Moran>

moran.stat
# => 0.834

moran.i
# => 0.834

Compute Moran's I without Querying Data

To calculate the statistic by using an array of data and not querying a database field. The order of the data must correspond to the order of weights.keys.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)

field = nil
moran = SpatialStats::Global::Moran.new(scope, field, weights)
# => <SpatialStats::Global::Moran>

# data is automatically standardized on input
data = [1,2,3,4,5,6]
moran.x = data

moran.stat
# => 0.521

Compute Moran's I Z-Score

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Global::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Global::Moran>

moran.z_score
# => 3.2

Run a Permutation Test on Moran's I

All stat classes have the mc method which takes permutations and seed as its parameters. mc runs a permutation test on the class and returns the psuedo p-value.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Global::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Global::Moran>

moran.mc(999, 123_456)
# => 0.003

Get Summary of Permutation Test

All stat classes have the summary method which takes permutations and seed as its parameters. summary runs stat and mc then combines the results into a hash.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Global::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Global::Moran>

moran.summary(999, 123_456)
# => {stat: 0.834, p: 0.003}

Local Stats

Local stats compute a value each observation in the dataset, like how similar its neighbors are to itself. Local stats operate similarly to global stats, except that almost every operation will return an array of length n where n is the number of observations in the dataset.

Most stat classes take three parameters: scope, data_field, and weights. All stat classes have the stat method that will compute the target statistic. These are also aliased with the common name of the statistic, such as i for Moran or c for Geary.

Compute Moran's I

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Local::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Local::Moran>

moran.stat
# => [0.888, 0.675, 0.2345, -0.987, -0.42, ...]

moran.i
# => [0.888, 0.675, 0.2345, -0.987, -0.42, ...]

Compute Moran's I without Querying Data

To calculate the statistic by using an array of data and not querying a database field. The order of the data must correspond to the order of weights.keys.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)

field = nil
moran = SpatialStats::Local::Moran.new(scope, field, weights)
# => <SpatialStats::Local::Moran>

# data is automatically standardized on input
data = [1,2,3,4,5,6]
moran.x = data

moran.stat
# => [0.521, 0.123, -0.432, -0.56,. ...]

Compute Moran's I Z-Scores

Note: Many classes do not have a variance or expectation method implemented and this will raise a NotImplementedError.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Local::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Local::Moran>

moran.z_score
# => # => [0.65, 1.23, 0.42, 3.45, -0.34, ...]

Run a Permutation Test on Moran's I

All stat classes have the mc method which takes permutations and seed as its parameters. mc runs a permutation test on the class and returns the psuedo p-values.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Local::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Local::Moran>

moran.mc(999, 123_456)
# => [0.24, 0.13, 0.53, 0.023, 0.65, ...]

Get Summary of Permutation Test

All stat classes have the summary method which takes permutations and seed as its parameters. summary runs stat, mc, and groups then combines the results into a hash array indexed by weight.keys.

scope = County.all
weights = SpatialStats::Weights::Contiguous.rook(scope, :geom)
moran = SpatialStats::Local::Moran.new(scope, :avg_income, weights)
# => <SpatialStats::Local::Moran>

moran.summary(999, 123_456)
# => [{key: 1, stat: 0.521, p: 0.24, group: 'HH'}, ...]

Contributing

Once cloned, run the following commands to setup the test database.

cd ./spatial_stats
bundle install
cd test/dummy
rake db:create
rake db:migrate

If you are getting an error, you may need to set the following environment variables.

$PGUSER # default "postgres"
$PGPASSWORD # default ""
$PGHOST # default "127.0.0.1"
$PGPORT # default "5432"
$PGDATABASE # default "spatial_stats_test"

If the dummy app is setup correctly, run the following:

cd ../..
rake

This will run the tests. If they all pass, then your environment is setup correctly.

Note: It is recommended to have GEOS installed and linked to RGeo. You can test this by running the following:

cd test/dummy
rails c

RGeo::Geos.supported?
# => true

Path Forward

Summaries of milestones for v1.x and v2.0. These lists are subject to change. If you have an additional feature you want to see for either milestone, open up an issue or PR.

v1.x

  1. Global Measurements
    • Geary's C
    • GetisOrd
  2. Local Measurements
    • Join Count
  3. Utilities
    • Add support for .gal/.swm file imports
    • Add support for Rate variables
    • Add support for Bayes smoothing
    • Add support for Bonferroni Bounds and FDR
  4. General
    • Add new stat constructors that only rely on a weights matrix and data vector
    • Point Pattern Analysis Module
    • Regression Module

v2.0

  • Break gem into core spatial_stats that will not include queries module and spatial_stats-activerecord. This will remove the dependency on rails for the core gem.
  • Create spatial_stats-import/geojson/shp gem that will allow importing files and generating a WeightsMatrix. Will likely rely on RGeo or another spatial lib.

Other TODOs

  • Update Docs to show from_observation when version is bumped
  • Refactor MultivariateGeary so that it can be used without activerecord by adding from_observations and supporting methods.

License

The gem is available as open source under the terms of the BSD-3-Clause.