Emerging Hot Spot Analysis

Emerging Hot Spot Analysis identifies trends in spatial clustering over a period of time. Emerging hot spot analysis combines the Getis-Ord Gi* statistic with the Mann-Kendall trend test to determine if there is a temporal trend associated with local clustering of hot and cold spots.

Usage

emerging_hotspot_analysis(
  x,
  .var,
  k = 1,
  include_gi = FALSE,
  nb_col = NULL,
  wt_col = NULL,
  nsim = 199,
  threshold = 0.01,
  ...
)

Arguments

x

a spacetime object and must be a spacetime cube see details for more.

.var

a numeric vector in the spacetime cube with no missing values.

k

default 1. The number of time lags to include in the neighborhood for calculating the local Gi*. See details for more.

include_gi

default FALSE. If TRUE, includes the local Gi* calculations in the attribute gi_star.

nb_col

Optional. Default NULL. The name of the column in the geometry context of x containing spatial neighbors. If NULL, Queen's contiguity neighbors are identified.

wt_col

Optional. Default NULL. The name of the column in the geometry context of x containing spatial weights. If NULL, row standardized weights are used.

nsim

default 199. The number of simulations to run in calculating the simulated p-value for the local Gi*.

threshold

default 0.01. The significance threshold to use.

...

unused.

Value

Returns a data.frame.

Details

How Emerging Hot Spot Analysis Works

Emerging Hot Spot Analysis is a somewhat simple process. It works by first calculating the Gi* statistic for each location in each time period (time-slice). Next, for each location across all time-periods, the Mann-Kendall trend test is done to identify any temporal trend in Gi* values over all time periods. Additionally, each location is classified into one of seventeen categories based on ESRI's emerging hot spot classification criteria.

The Mann-Kendall trend test is done using Kendall::MannKendall(). Kendall is not installed with sfdep and should be installed prior to use.

Using your own neighbors and weights

If you would like to use your own neighbors and weights, they must be created in the geometry context of a spacetime object. The arguments nb_col and wt_col must both be populated in order to use your own neighbor and weights definitions.

Time lagged neighbors

In addition to identifying neighbors in space, emerging hotspot analysis also incorporates the same observations from k periods ago-called a time lag. If the time lag k is 1 and the unit of time is month, the neighbors for the calculation of Gi* would include the spatial neighbors' values at time t and the same spatial neighbors' values at time t-1. If k = 2, it would include t, t-1, and t-2.

Missing values

Presently, there is no method of missing value handling. If there are missing values, the emerging hot spot analysis will fail. Be sure to fill or omit time-slices with missing values prior to using emerging hot spot analysis.

See also

How Emerging Hot Spot Analysis works, Emerging Hot Spot Analysis (Space Time Pattern Mining), and the video Spatial Data Mining II: A Deep Dive into Space-Time Analysis by ESRI.

Examples

if (requireNamespace("Kendall")) {
df_fp <- system.file("extdata", "bos-ecometric.csv", package = "sfdep")
geo_fp <- system.file("extdata", "bos-ecometric.geojson", package = "sfdep")

# read in data
df <- read.csv(df_fp, colClasses = c("character", "character", "integer", "double", "Date"))
geo <- sf::st_read(geo_fp)

# Create spacetime object called `bos`
bos <- spacetime(df, geo,
                 .loc_col = ".region_id",
                 .time_col = "time_period")


# conduct EHSA
ehsa <- emerging_hotspot_analysis(
  x = bos,
  .var = "value",
  k = 1,
  nsim = 9
)

ehsa
}
#> Loading required namespace: Kendall
#> Reading layer `bos-ecometric' from data source 
#>   `/private/var/folders/zc/tg2xwck53dg9sls8x4ndzdc00000gn/T/Rtmp2RGXTr/temp_libpath2b6f5ea0db20/sfdep/extdata/bos-ecometric.geojson' 
#>   using driver `GeoJSON'
#> Simple feature collection with 168 features and 1 field
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: -71.19115 ymin: 42.22788 xmax: -70.99445 ymax: 42.3974
#> Geodetic CRS:  NAD83
#>        location         tau     p_value      classification
#> 1   25025010405  0.11111111 0.720514774 no pattern detected
#> 2   25025010404 -0.33333334 0.210497662 no pattern detected
#> 3   25025010801 -0.20000000 0.474274337 no pattern detected
#> 4   25025010702 -0.60000002 0.020044670 no pattern detected
#> 5   25025010204 -0.46666667 0.073638275 no pattern detected
#> 6   25025010802 -0.33333334 0.210497662 no pattern detected
#> 7   25025010104 -0.33333334 0.210497662 no pattern detected
#> 8   25025000703 -0.60000002 0.020044670 no pattern detected
#> 9   25025000504 -0.33333334 0.210497662 no pattern detected
#> 10  25025000704 -0.42222223 0.107404657 no pattern detected
#> 11  25025010103  0.02222222 1.000000000 no pattern detected
#> 12  25025000803 -0.37777779 0.152406260 no pattern detected
#> 13  25025120201 -0.33333334 0.210497662 no pattern detected
#> 14  25025120104  0.46666667 0.073638320 no pattern detected
#> 15  25025110607  0.28888890 0.283130884 no pattern detected
#> 16  25025000302  0.37777779 0.152406216 no pattern detected
#> 17  25025000301  0.37777779 0.152406216 no pattern detected
#> 18  25025140400  0.06666667 0.858027697 no pattern detected
#> 19  25025140300  0.37777779 0.152406216 no pattern detected
#> 20  25025140201  0.46666667 0.073638320 no pattern detected
#> 21  25025140202  0.15555556 0.591505051 no pattern detected
#> 22  25025140102 -0.24444444 0.371093363 no pattern detected
#> 23  25025130402  0.46666667 0.073638320 no pattern detected
#> 24  25025130300  0.33333334 0.210497618 no pattern detected
#> 25  25025130200  0.33333334 0.210497618 no pattern detected
#> 26  25025130100 -0.20000000 0.474274337 no pattern detected
#> 27  25025120700  0.37777779 0.152406216 no pattern detected
#> 28  25025120600  0.60000002 0.020044684 no pattern detected
#> 29  25025120500  0.55555558 0.031823158 no pattern detected
#> 30  25025120400  0.55555558 0.031823158 no pattern detected
#> 31  25025110601  0.55555558 0.031823158 no pattern detected
#> 32  25025110502  0.42222223 0.107404709 no pattern detected
#> 33  25025110501 -0.02222222 1.000000000 no pattern detected
#> 34  25025110401 -0.20000000 0.474274337 no pattern detected
#> 35  25025101102  0.02222222 1.000000000 no pattern detected
#> 36  25025101101  0.37777779 0.152406216 no pattern detected
#> 37  25025101002  0.24444444 0.371093392 no pattern detected
#> 38  25025101001  0.46666667 0.073638320 no pattern detected
#> 39  25025100900  0.51111114 0.049098015 no pattern detected
#> 40  25025100800  0.46666667 0.073638320 no pattern detected
#> 41  25025100601  0.46666667 0.073638320 no pattern detected
#> 42  25025100500  0.37777779 0.152406216 no pattern detected
#> 43  25025100400 -0.24444444 0.371093363 no pattern detected
#> 44  25025100300 -0.28888890 0.283130825 no pattern detected
#> 45  25025100200 -0.15555556 0.591504991 no pattern detected
#> 46  25025100100 -0.06666667 0.858027637 no pattern detected
#> 47  25025092400 -0.15555556 0.591504991 no pattern detected
#> 48  25025092300  0.15555556 0.591505051 no pattern detected
#> 49  25025092200  0.06666667 0.858027697 no pattern detected
#> 50  25025092000  0.06666667 0.858027697 no pattern detected
#> 51  25025091900 -0.02222222 1.000000000 no pattern detected
#> 52  25025091800 -0.02222222 1.000000000 no pattern detected
#> 53  25025091700 -0.33333334 0.210497662 no pattern detected
#> 54  25025091600 -0.15555556 0.591504991 no pattern detected
#> 55  25025981100 -0.15555556 0.591504991 no pattern detected
#> 56  25025140105  0.02222222 1.000000000 no pattern detected
#> 57  25025120105  0.02222222 1.000000000 no pattern detected
#> 58  25025120301 -0.11111111 0.720514774 no pattern detected
#> 59  25025071201  0.02222222 1.000000000 no pattern detected
#> 60  25025091001 -0.06666667 0.858027637 no pattern detected
#> 61  25025091500 -0.24444444 0.371093363 no pattern detected
#> 62  25025091400  0.15555556 0.591505051 no pattern detected
#> 63  25025091300  0.46666667 0.073638320 no pattern detected
#> 64  25025091200  0.33333334 0.210497618 no pattern detected
#> 65  25025091100  0.77777779 0.002357483 no pattern detected
#> 66  25025090700  0.64444447 0.012266040 no pattern detected
#> 67  25025090600  0.60000002 0.020044684 no pattern detected
#> 68  25025090400  0.60000002 0.020044684 no pattern detected
#> 69  25025090300  0.73333335 0.004207492 no pattern detected
#> 70  25025090200  0.73333335 0.004207492 no pattern detected
#> 71  25025040801  0.46666667 0.073638320 no pattern detected
#> 72  25025010203  0.60000002 0.020044684 no pattern detected
#> 73  25025110403  0.60000002 0.020044684 no pattern detected
#> 74  25025110201  0.60000002 0.020044684 no pattern detected
#> 75  25025090100  0.51111114 0.049098015 no pattern detected
#> 76  25025082100  0.06666667 0.858027697 no pattern detected
#> 77  25025082000  0.37777779 0.152406216 no pattern detected
#> 78  25025081900  0.24444444 0.371093392 no pattern detected
#> 79  25025081800  0.42222223 0.107404709 no pattern detected
#> 80  25025081700  0.64444447 0.012266040 no pattern detected
#> 81  25025081500  0.68888891 0.007290363 no pattern detected
#> 82  25025081400  0.64444447 0.012266040 no pattern detected
#> 83  25025081300  0.64444447 0.012266040 no pattern detected
#> 84  25025110103  0.51111114 0.049098015 no pattern detected
#> 85  25025110301  0.60000002 0.020044684 no pattern detected
#> 86  25025140106  0.24444444 0.371093392 no pattern detected
#> 87  25025010701  0.42222223 0.107404709 no pattern detected
#> 88  25025010408  0.33333334 0.210497618 no pattern detected
#> 89  25025000503  0.64444447 0.012266040 no pattern detected
#> 90  25025081200  0.82222223 0.001282215 no pattern detected
#> 91  25025081100  0.82222223 0.001282215 no pattern detected
#> 92  25025080900  0.73333335 0.004207492 no pattern detected
#> 93  25025080801  0.82222223 0.001282215 no pattern detected
#> 94  25025080601  0.46666667 0.073638320 no pattern detected
#> 95  25025080500  0.51111114 0.049098015 no pattern detected
#> 96  25025080401  0.20000000 0.474274397 no pattern detected
#> 97  25025080300  0.20000000 0.474274397 no pattern detected
#> 98  25025071101 -0.20000000 0.474274337 no pattern detected
#> 99  25025070900 -0.06666667 0.858027637 no pattern detected
#> 100 25025140107  0.46666667 0.073638320 no pattern detected
#> 101 25025130404  0.15555556 0.591505051 no pattern detected
#> 102 25025130406  0.20000000 0.474274397 no pattern detected
#> 103 25025120103  0.11111111 0.720514774 no pattern detected
#> 104 25025100700  0.64444447 0.012266040 no pattern detected
#> 105 25025100603  0.82222223 0.001282215 no pattern detected
#> 106 25025092101  0.11111111 0.720514774 no pattern detected
#> 107 25025061101  0.64444447 0.012266040 no pattern detected
#> 108 25025070800  0.60000002 0.020044684 no pattern detected
#> 109 25025070700  0.55555558 0.031823158 no pattern detected
#> 110 25025070600  0.60000002 0.020044684 no pattern detected
#> 111 25025070500  0.37777779 0.152406216 no pattern detected
#> 112 25025070300  0.55555558 0.031823158 no pattern detected
#> 113 25025070200  0.46666667 0.073638320 no pattern detected
#> 114 25025070101  0.51111114 0.049098015 no pattern detected
#> 115 25025061200  0.37777779 0.152406216 no pattern detected
#> 116 25025061000  0.33333334 0.210497618 no pattern detected
#> 117 25025060800  0.64444447 0.012266040 no pattern detected
#> 118 25025060700  0.37777779 0.152406216 no pattern detected
#> 119 25025080100  0.55555558 0.031823158 no pattern detected
#> 120 25025060301  0.55555558 0.031823158 no pattern detected
#> 121 25025090901  0.37777779 0.152406216 no pattern detected
#> 122 25025060101  0.20000000 0.474274397 no pattern detected
#> 123 25025060600  0.15555556 0.591505051 no pattern detected
#> 124 25025060400  0.20000000 0.474274397 no pattern detected
#> 125 25025060200  0.20000000 0.474274397 no pattern detected
#> 126 25025050700  0.37777779 0.152406216 no pattern detected
#> 127 25025050600 -0.51111114 0.049097981 no pattern detected
#> 128 25025050500 -0.42222223 0.107404657 no pattern detected
#> 129 25025050400 -0.51111114 0.049097981 no pattern detected
#> 130 25025050300 -0.37777779 0.152406260 no pattern detected
#> 131 25025050200  0.24444444 0.371093392 no pattern detected
#> 132 25025040300  0.02222222 1.000000000 no pattern detected
#> 133 25025040200  0.24444444 0.371093392 no pattern detected
#> 134 25025030500  0.06666667 0.858027697 no pattern detected
#> 135 25025051101  0.20000000 0.474274397 no pattern detected
#> 136 25025051000 -0.37777779 0.152406260 no pattern detected
#> 137 25025030400  0.11111111 0.720514774 no pattern detected
#> 138 25025030300 -0.02222222 1.000000000 no pattern detected
#> 139 25025030200  0.06666667 0.858027697 no pattern detected
#> 140 25025030100  0.33333334 0.210497618 no pattern detected
#> 141 25025020200 -0.02222222 1.000000000 no pattern detected
#> 142 25025010600  0.11111111 0.720514774 no pattern detected
#> 143 25025010500 -0.33333334 0.210497662 no pattern detected
#> 144 25025010300 -0.06666667 0.858027637 no pattern detected
#> 145 25025000802  0.20000000 0.474274397 no pattern detected
#> 146 25025000701 -0.20000000 0.474274337 no pattern detected
#> 147 25025050101 -0.02222222 1.000000000 no pattern detected
#> 148 25025050901 -0.51111114 0.049097981 no pattern detected
#> 149 25025060501 -0.02222222 1.000000000 no pattern detected
#> 150 25025040100 -0.11111111 0.720514774 no pattern detected
#> 151 25025040600  0.60000002 0.020044684 no pattern detected
#> 152 25025000602  0.73333335 0.004207492 no pattern detected
#> 153 25025000601  0.77777779 0.002357483 no pattern detected
#> 154 25025000502 -0.24444444 0.371093363 no pattern detected
#> 155 25025000402 -0.33333334 0.210497662 no pattern detected
#> 156 25025000401 -0.28888890 0.283130825 no pattern detected
#> 157 25025000202 -0.20000000 0.474274337 no pattern detected
#> 158 25025000201 -0.28888890 0.283130825 no pattern detected
#> 159 25025040401 -0.02222222 1.000000000 no pattern detected
#> 160 25025020303  0.42222223 0.107404709 no pattern detected
#> 161 25025070402  0.46666667 0.073638320 no pattern detected
#> 162 25025020302  0.15555556 0.591505051 no pattern detected
#> 163 25025020301  0.37777779 0.152406216 no pattern detected
#> 164 25025020101  0.42222223 0.107404709 no pattern detected
#> 165 25025081001  0.42222223 0.107404709 no pattern detected
#> 166 25025010403  0.33333334 0.210497618 no pattern detected
#> 167 25025000100  0.33333334 0.210497618 no pattern detected
#> 168 25025051200  0.28888890 0.283130884 no pattern detected