72 lines
3.6 KiB
Markdown
72 lines
3.6 KiB
Markdown
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### Moran's I
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#### What is Moran's I and why is it significant for CartoDB?
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Moran's I is a geostatistical calculation which gives a measure of the global
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clustering and presence of outliers within the geographies in a map. Here global
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means over all of the geographies in a dataset. Imagine mapping the incidence
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rates of cancer in neighborhoods of a city. If there were areas covering several
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neighborhoods with abnormally low rates of cancer, those areas are positively
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spatially correlated with one another and would be considered a cluster. If
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there was a single neighborhood with a high rate but with all neighbors on
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average having a low rate, it would be considered a spatial outlier.
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While Moran's I gives a global snapshot, there are local indicators for
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clustering called Local Indicators of Spatial Autocorrelation. Clustering is a
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process related to autocorrelation -- i.e., a process that compares a
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geography's attribute to the attribute in neighbor geographies.
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For the example of cancer rates in neighborhoods, since these neighborhoods have
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a high value for rate of cancer, and all of their neighbors do as well, they are
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designated as "High High" or simply **HH**. For areas with multiple neighborhoods
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with low rates of cancer, they are designated as "Low Low" or **LL**. HH and LL
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naturally fit into the concept of clustering and are in the correlated
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variables.
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"Anticorrelated" geogs are in **LH** and **HL** regions -- that is, regions
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where a geog has a high value and it's neighbors, on average, have a low value
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(or vice versa). An example of this is a "gated community" or placement of a
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city housing project in a rich region. These deliberate developments have
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opposite median income as compared to the neighbors around them. They have a
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high (or low) value while their neighbors have a low (or high) value. They exist
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typically as islands, and in rare circumstances can extend as chains dividing
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**LL** or **HH**.
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Strong policies such as rent stabilization (probably) tend to prevent the
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clustering of high rent areas as they integrate middle class incomes. Luxury
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apartment buildings, which are a kind of gated community, probably tend to skew
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an area's median income upwards while housing projects have the opposite effect.
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What are the nuggets in the analysis?
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Two functions are available to compute Moran I statistics:
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* `cdb_moran_local` computes Moran I measures, quad classification and
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significance values from numerial values associated to geometry entities
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in an input table. The geometries should be contiguous polygons When
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then `queen` `w_type` is used.
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* `cdb_moran_local_rate` computes the same statistics using a ratio between
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numerator and denominator columns of a table.
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The parameters for `cdb_moran_local` are:
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* `table` name of the table that contains the data values
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* `attr` name of the column
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* `signficance` significance threshold for the quads values
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* `num_ngbrs` number of neighbors to consider (default: 5)
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* `permutations` number of random permutations for calculation of
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pseudo-p values (default: 99)
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* `geom_column` number of the geometry column (default: "the_geom")
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* `id_col` PK column of the table (default: "cartodb_id")
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* `w_type` Weight types: can be "knn" for k-nearest neighbor weights
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or "queen" for contiguity based weights.
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The function returns a table with the following columns:
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* `moran` Moran's value
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* `quads` quad classification ('HH', 'LL', 'HL', 'LH' or 'Not significant')
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* `significance` significance value
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* `ids` id of the corresponding record in the input table
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Function `cdb_moran_local_rate` only differs in that the `attr` input
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parameter is substituted by `numerator` and `denominator`.
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