Package 'fastLISA' reference manual

Title:	Fast Local Indicators of Spatial Association (LISA)
Description:	Computes various Local Indicators of Spatial Association (LISA) statistics, including univariate and bivariate local Moran's I, Empirical Bayes local Moran's I, univariate and multivariate local Geary's C, and Getis-Ord G and G* statistics. The methods follow Anselin (1995), Getis and Ord (1992), and Anselin (2019). Leverages a high-performance, plain-C backend with optional 'OpenMP' multi-core support for fast permutation-based pseudo-p-value calculation. Accepts any 'spdep' listw spatial weight matrix, including custom and non-contiguity weights. Uses sample standardisation (n-1) and 'rgeoda'-style permutation p-values. Output cluster codes match 'rgeoda' conventions, including the Isolated category for observations without neighbours.
Authors:	Lizhong Chen [aut, cre]
Maintainer:	Lizhong Chen <[email protected]>
License:	GPL-3
Version:	1.0.1
Built:	2026-07-07 08:30:11 UTC
Source:	https://github.com/lizhongc/fastlisa

Local Getis-Ord G

Description

local_g computes the Getis-Ord local $G_i$ statistic, a Local Indicator of Spatial Association that detects local clustering of high values (“hot spots”) and low values (“cold spots”). For observation $i$ , with row-standardised spatial weights $w^*_{ij}$ and the focal value excluded from both the lag and the denominator,

$G_i = \frac{\sum_{j \ne i} w^*_{ij} x_j}{\sum_k x_k - x_i}.$

A large $G_i$ indicates that $i$ is surrounded by high values; a small $G_i$ indicates a low-value neighbourhood. $G_i$ contains no self term; see local_gstar for the self-inclusive $G^*_i$ .

Usage

local_g(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_g(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

x

Numeric vector of length n.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append permutation-distribution moments E.Gi, Var.Gi, Skew.Gi, and Kurt.Gi. Default FALSE.

p.method

Character; how the observed statistic is located within its permutation distribution. "count" (default) is the standard rule: it counts the permutations at least as extreme as the observed value, matching the folded pseudo p-value reported by rgeoda and spdep. "rank" is the ties-averaged alternative, using spdep's averaged rank of the observed value. The two differ only when a permuted value exactly ties the observed one (discrete or tie-prone data); both return a folded (smaller-tail) value.

Details

Inference uses a conditional permutation test: the focal value $x_i$ is held fixed while the neighbouring values are randomly permuted nsim times. The pseudo p-value is folded (two-tailed),

$p_i = \frac{\min(g,\ \mathrm{nsim} - g) + 1}{\mathrm{nsim} + 1},$

where $g$ is the number of permutations with $G_i^{\mathrm{perm}} \ge G_i^{\mathrm{obs}}$ . The standardised score is $Z.G_i = (G_i - E_{\mathrm{perm}}) / \sqrt{\mathrm{Var}_{\mathrm{perm}}}$ , computed from the permutation mean and variance; Skew.Gi and Kurt.Gi (when moments = TRUE) follow the e1071 type-3 convention.

Observations with a missing x value are labelled Undefined and observations with no neighbours are labelled Isolated; both receive NA for the p-value, Z-score and moments. The C backend re-seeds its random number generator per observation, so results are identical for any n.cores; n.cores is ignored when the package is built without OpenMP.

Value

A numeric matrix of class c("localG", "matrix", "array") with columns Gi, Z.Gi, and Pr(folded) Sim. When moments = TRUE, the permutation-moment columns are appended. It has the following attributes:

cluster: A significance-filtered factor with levels Not significant, High-High, Low-Low, Undefined and Isolated.
gstari: Logical flag set to FALSE indicating local G (not G*).
call: The matched call.

References

Getis, A. and Ord, J. K. (1992) The Analysis of Spatial Association by Use of Distance Statistics. Geographical Analysis 24(3), 189–206. doi:10.1111/j.1538-4632.1992.tb00261.x

Ord, J. K. and Getis, A. (1995) Local Spatial Autocorrelation Statistics: Distributional Issues and an Application. Geographical Analysis 27(4), 286–306. doi:10.1111/j.1538-4632.1995.tb00912.x

Examples


lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_g(x, lw, nsim = 99L, n.cores = 1L)
head(res)

lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_g(x, lw, nsim = 99L, n.cores = 1L)
head(res)

Univariate Local Geary's C

Description

local_geary computes the univariate local Geary's $C_i$ , a squared-difference Local Indicator of Spatial Association that measures how much a unit differs from its neighbours. On the sample ( $n-1$ ) standardised variable $z$ (when scale = TRUE) with row-standardised weights $w^*_{ij}$ ,

$C_i = \sum_j w^*_{ij} (z_i - z_j)^2 = z_i^2 - 2 z_i\, \mathrm{lag}(z)_i + \mathrm{lag}(z^2)_i.$

A small $C_i$ means $i$ resembles its neighbours (positive spatial association); a large $C_i$ means it differs from them (negative association, a spatial outlier).

Usage

local_geary(
  x,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_geary(
  x,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

x

Numeric vector of length n.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

scale

Logical; if TRUE (default), standardise data in R.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append permutation-distribution moments E.Ci, Var.Ci, Skew.Ci, and Kurt.Ci. Default FALSE.

p.method

Details

Inference uses a one-tailed conditional permutation test (nsim reps): the observed $C_i$ is compared with the permutation mean to select the tail, and

$p_i = \frac{t + 1}{\mathrm{nsim} + 1},$

where $t$ counts permuted statistics in that tail. The standardised score is $Z.C_i = (C_i - E_{\mathrm{perm}}) / \sqrt{\mathrm{Var}_{\mathrm{perm}}}$ ; Skew.Ci/Kurt.Ci (when moments = TRUE) follow the e1071 type-3 convention. The cluster factor splits significant positive association into High-High/Low-Low/Other Positive and labels significant dissimilarity Negative.

Value

A numeric matrix of class c("localC", "matrix", "array") with columns Ci, Z.Ci, and Pr Sim. When moments = TRUE, the permutation-moment columns are appended. It has the following attributes:

cluster: A significance-filtered factor with levels Not significant, High-High, Low-Low, Other Positive, Negative, Undefined, and Isolated.
call: The matched call.

References

Anselin, L. (1995) Local Indicators of Spatial Association—LISA. Geographical Analysis 27(2), 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x

Examples


lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_geary(x, lw, nsim = 99L, n.cores = 1L)
head(res)

lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_geary(x, lw, nsim = 99L, n.cores = 1L)
head(res)

Local Getis-Ord G*

Description

local_gstar computes the Getis-Ord local $G^*_i$ statistic, the self-inclusive companion of local_g: observation $i$ is treated as its own neighbour (weight 1). With $m_i$ valid neighbours, row-standardised neighbour weights $w_{ij}$ , and global total $S = \sum_k x_k$ ,

$G^*_i = \frac{\left(\frac{\sum_{j \in N_i} w_{ij} x_j}{\sum_j w_{ij}}\right) m_i + x_i}{(m_i + 1)\, S},$

i.e. the average value over the focal unit and its neighbours divided by the global sum. Large $G^*_i$ flags a hot spot and small $G^*_i$ a cold spot, with the focal unit included.

Usage

local_gstar(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_gstar(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

x

Numeric vector of length n.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append permutation-distribution moments E.G*i, Var.G*i, Skew.G*i, and Kurt.G*i. Default FALSE.

p.method

Details

Inference uses a conditional permutation test (nsim reps), with the focal $x_i$ held fixed while neighbour values are permuted. The pseudo p-value is folded (two-tailed),

$p_i = \frac{\min(g,\ \mathrm{nsim} - g) + 1}{\mathrm{nsim} + 1},$

where $g$ counts permutations with $G_i^{*\,\mathrm{perm}} \ge G_i^{*\,\mathrm{obs}}$ . The standardised score $Z.G^*_i = (G^*_i - E_{\mathrm{perm}}) / \sqrt{\mathrm{Var}_{\mathrm{perm}}}$ uses the permutation moments; Skew.G*i/Kurt.G*i (when moments = TRUE) follow the e1071 type-3 convention.

Value

A numeric matrix of class c("localG", "matrix", "array") with columns G*i, Z.G*i, and Pr(folded) Sim. When moments = TRUE, the permutation-moment columns are appended. It has the following attributes:

cluster: A significance-filtered factor with levels Not significant, High-High, Low-Low, Undefined and Isolated.
gstari: Logical flag set to TRUE indicating local G*.
call: The matched call.

References

Getis, A. and Ord, J. K. (1992) The Analysis of Spatial Association by Use of Distance Statistics. Geographical Analysis 24(3), 189–206. doi:10.1111/j.1538-4632.1992.tb00261.x

Ord, J. K. and Getis, A. (1995) Local Spatial Autocorrelation Statistics: Distributional Issues and an Application. Geographical Analysis 27(4), 286–306. doi:10.1111/j.1538-4632.1995.tb00912.x

Examples


lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_gstar(x, lw, nsim = 99L, n.cores = 1L)
head(res)

lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_gstar(x, lw, nsim = 99L, n.cores = 1L)
head(res)

Univariate Local Moran's I

Description

local_moran computes the univariate local Moran's $I_i$ , the classic Local Indicator of Spatial Association measuring whether a value coincides with its neighbours' average. On the sample ( $n-1$ ) standardised variable $z$ with row-standardised weights $w^*_{ij}$ ,

$I_i = z_i \sum_j w^*_{ij} z_j = z_i\, \mathrm{lag}(z)_i.$

A positive $I_i$ indicates similarity to neighbours (a High-High or Low-Low cluster); a negative $I_i$ indicates a spatial outlier (High-Low or Low-High). Standardisation uses the sample standard deviation ( $n-1$ denominator).

Usage

local_moran(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_moran(
  x,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

x

Numeric vector of length n.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append the permutation-distribution moments E.Ii, Var.Ii, Skew.Ii, and Kurt.Ii to the result matrix. Default FALSE.

p.method

Details

This is the $x = y$ special case of bivariate local Moran's I, so the computation delegates to local_moran_bv (with scale = TRUE) and relabels the columns. Inference uses a conditional permutation test (nsim reps) with the folded two-tailed pseudo p-value $p_i = (\min(g, \mathrm{nsim}-g)+1)/(\mathrm{nsim}+1)$ , where $g$ is the number of permutations with $I^{\mathrm{perm}} \ge I^{\mathrm{obs}}$ . The standardised score is $Z.I_i = (I_i - E_{\mathrm{perm}})/\sqrt{\mathrm{Var}_{\mathrm{perm}}}$ and Skew.Ii/Kurt.Ii (when moments = TRUE) use the e1071 type-3 convention. NA observations are Undefined and neighbourless observations are Isolated (both NA in p-value, Z-score and moments). The C backend re-seeds its random number generator per observation, so results are identical for any n.cores.

Value

A numeric matrix of class c("localmoran", "matrix", "array") with n rows and 3 columns by default:

Ii: Observed univariate Moran statistic.
Z.Ii: Standardised Z-score computed from permutation moments.
Pr(folded) Sim: rgeoda-style folded empirical permutation p-value.

When moments = TRUE, the permutation-distribution columns E.Ii, Var.Ii, Skew.Ii, and Kurt.Ii are appended. The matrix has the following attributes:

quadr: Moran scatter-plot quadrant classification.
cluster: A significance-filtered factor with levels Not significant, High-High, Low-Low, Low-High, High-Low, Undefined and Isolated.

References

Anselin, L. (1995) Local Indicators of Spatial Association—LISA. Geographical Analysis 27(2), 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x

Examples


lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_moran(x, lw, nsim = 99L, n.cores = 1L, moments = TRUE)
head(res)

lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
res <- local_moran(x, lw, nsim = 99L, n.cores = 1L, moments = TRUE)
head(res)

Bivariate Local Moran's I

Description

local_moran_bv computes the bivariate local Moran's $I_{bv,i}$ , which correlates a variable $x$ at $i$ with the spatial lag of a second variable $y$ over $i$ 's neighbours. On the sample ( $n-1$ ) standardised variables $z_x, z_y$ (when scale = TRUE) with row-standardised weights $w^*_{ij}$ ,

$I_{bv,i} = z_{x,i} \sum_j w^*_{ij} z_{y,j} = z_{x,i}\, \mathrm{lag}(z_y)_i.$

A positive $I_{bv,i}$ means $i$ 's $x$ value coincides with high lagged $y$ nearby; a negative value indicates spatial mismatch. The univariate local Moran's I is the special case $x = y$ (see local_moran). The backend is plain C with optional OpenMP parallelism.

Usage

local_moran_bv(
  x,
  y,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_moran_bv(
  x,
  y,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

x

Numeric vector of length n; the first variable.

y

Numeric vector of length n; the second variable (lagged).

listw

A listw object from spdep (any style: "W", "B", "C", etc., including custom distance-decay weights). Observations with no neighbours receive cluster code 6 (Isolated).

nsim

Integer; number of permutations for the pseudo p-value. Default 999L.

scale

Logical; if TRUE (default), x and y are standardised in R (sample std dev). Set to FALSE only if you have pre-standardised the data.

iseed

Integer seed for the RNG, or NULL (default) to use the package default (123456789). Passed as the seed argument to the C backend.

p.value

Numeric; observations with $p > \text{p.value}$ are recoded to cluster 0 (Not significant). Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append the permutation-distribution moments E.Ibvi, Var.Ibvi, Skew.Ibvi, and Kurt.Ibvi to the result matrix. Default FALSE.

p.method

Details

Inference uses a conditional permutation test (nsim reps): the neighbour $y$ -values are permuted with the focal observation held fixed. See the P-values and Cluster codes sections below for the folded p-value and the cluster coding. The standardised score is $Z.I_{bv,i} = (I_{bv,i} - E_{\mathrm{perm}})/\sqrt{\mathrm{Var}_{\mathrm{perm}}}$ ; Skew.Ibvi/Kurt.Ibvi (when moments = TRUE) follow the e1071 type-3 convention. NA observations are Undefined and neighbourless observations are Isolated (both NA in p-value, Z-score and moments). The C backend re-seeds its random number generator per observation, so results are identical for any n.cores.

Value

A numeric matrix of class c("localmoran", "matrix", "array") with n rows and 3 columns by default:

Ibvi: Observed bivariate Moran statistic.
Z.Ibvi: Standardised Z-score computed from permutation moments.
Pr(folded) Sim: rgeoda-style folded empirical permutation p-value.

When moments = TRUE, the permutation-distribution columns E.Ibvi, Var.Ibvi, Skew.Ibvi, and Kurt.Ibvi are appended. The matrix has the following attributes:

quadr: A data.frame with three factor columns (mean, median, pysal) giving the Moran scatter-plot quadrant for each observation, computed on the original (unscaled) data scale.
cluster: A factor representing cluster classification (Not significant, High-High, Low-Low, Low-High, High-Low, Undefined, Isolated).
call: The matched call.

Standardisation

Both x and y are standardised using the sample standard deviation ( $n-1$ denominator) in R before computing the statistic, consistent with the blisa backend.

P-values

Permutation p-values use the folded two-tailed formula matching rgeoda:

$p = (\min(\#\{perm \ge obs\},\, \#\{perm < obs\}) + 1) \,/\, (nsim + 1)$

No normal approximation is computed.

Cluster codes

The returned cluster factor attribute is based on integer codes 0–6:

0	Not significant
1	High-High
2	Low-Low
3	Low-High
4	High-Low
5	Undefined (NA input)
6	Isolated (no neighbours)

Codes 5 and 6 are preserved regardless of the significance cutoff.

References

Anselin, L. (1995) Local Indicators of Spatial Association—LISA. Geographical Analysis 27(2), 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x

Examples


lw  <- spdep::nb2listw(spdep::cell2nb(7, 7))
x   <- as.numeric(seq_len(49))
y   <- rev(x)
res <- local_moran_bv(x, y, lw, nsim = 99L, n.cores = 1L, moments = TRUE)
head(res)
attr(res, "quadr")

lw  <- spdep::nb2listw(spdep::cell2nb(7, 7))
x   <- as.numeric(seq_len(49))
y   <- rev(x)
res <- local_moran_bv(x, y, lw, nsim = 99L, n.cores = 1L, moments = TRUE)
head(res)
attr(res, "quadr")

Local Moran's I with Empirical Bayes (EB) Rate

Description

local_moran_eb computes local Moran's I on Empirical Bayes (EB) variance-stabilised rates, for event-count data observed over a population at risk. Raw rates $p_i = \mathrm{event}_i / \mathrm{base}_i$ from small populations are noisy; EB standardisation shrinks them toward the global rate $b = \sum \mathrm{event} / \sum \mathrm{base}$ using a variance component $\hat{a}$ ,

$z_i = \frac{p_i - b}{\sqrt{\hat{a} + b/\mathrm{base}_i}},$

and local Moran's I is then computed on $z$ . This follows the GeoDa/libgeoda EBLocalMoran formulation.

Usage

local_moran_eb(
  event,
  base,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_moran_eb(
  event,
  base,
  listw,
  nsim = 999L,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

event

Numeric vector of events (e.g. case counts).

base

Numeric vector of populations at risk.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append the permutation-distribution moments E.Ii, Var.Ii, Skew.Ii, and Kurt.Ii to the result matrix. Default FALSE.

p.method

Details

Two standardisations are applied and are not redundant: the EB rate standardisation above stabilises the rate variance, and the usual sample ( $n-1$ ) z-score standardisation that local Moran's I requires is then applied to the EB rates internally. Because univariate Moran's I on a standardised variable equals the bivariate statistic with $x = y$ , the permutation engine is reused via local_moran_bv. Inference is a conditional permutation test (nsim reps); the folded two-tailed pseudo p-value and the score $Z.I_i = (I_i - E_{\mathrm{perm}})/\sqrt{\mathrm{Var}_{\mathrm{perm}}}$ are as in local_moran, and Skew.Ii/Kurt.Ii (when moments = TRUE) use the e1071 type-3 convention.

Observations with NA event/base or base $\le 0$ are labelled Undefined; observations with no neighbours are Isolated; both receive NA for the p-value, Z-score and moments. The C backend re-seeds its random number generator per observation, so results are identical for any n.cores.

Value

A numeric matrix of class c("local_moran_eb", "matrix") with n rows and 3 columns by default:

Ii: Observed Local Moran statistic computed on EB-standardised rates.
Z.Ii: Standardised Z-score computed from permutation moments.
Pr(folded) Sim: Folded empirical permutation p-value.

When moments = TRUE, the permutation-distribution columns E.Ii, Var.Ii, Skew.Ii, and Kurt.Ii are appended. The matrix has the following attributes:

quadr: Moran scatter-plot quadrant classification.
cluster: A significance-filtered factor with levels Not significant, High-High, Low-Low, Low-High, High-Low, Undefined and Isolated.
call: The matched call.
nsim: Number of simulations used.

References

Assunção, R. M. and Reis, E. A. (1999) A new proposal to adjust Moran's I for population density. Statistics in Medicine 18(16), 2147–2162. doi:10.1002/(SICI)1097-0258(19990830)18:16<2147::AID-SIM179>3.0.CO;2-I

Anselin, L. (1995) Local Indicators of Spatial Association—LISA. Geographical Analysis 27(2), 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x

Examples


lw    <- spdep::nb2listw(spdep::cell2nb(7, 7))
event <- as.numeric(seq_len(49))
base  <- rep(100, 49)
res <- local_moran_eb(event, base, lw, nsim = 99L, n.cores = 1L)
head(res)

lw    <- spdep::nb2listw(spdep::cell2nb(7, 7))
event <- as.numeric(seq_len(49))
base  <- rep(100, 49)
res <- local_moran_eb(event, base, lw, nsim = 99L, n.cores = 1L)
head(res)

Multivariate Local Geary's C

Description

local_multigeary computes the multivariate local Geary's $C_i$ (Anselin 2019), the average across $K$ variables of the univariate squared-difference statistic. On the sample ( $n-1$ ) standardised variables $z^1,\dots,z^K$ (when scale = TRUE) with row-standardised weights $w^*_{ij}$ ,

$C_i = \frac{1}{K} \sum_{v=1}^{K} \sum_j w^*_{ij} (z^v_i - z^v_j)^2.$

A small $C_i$ indicates that $i$ is similar to its neighbours across all variables (positive association); a large $C_i$ indicates multivariate dissimilarity (a spatial outlier).

Usage

local_multigeary(
  df,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)
local_multigeary(
  df,
  listw,
  nsim = 999L,
  scale = TRUE,
  iseed = NULL,
  p.value = 0.05,
  n.cores = 1L,
  moments = FALSE,
  p.method = c("count", "rank")
)

Arguments

df

A data.frame or matrix with selected variables.

listw

A listw object from spdep.

nsim

Integer; number of permutations. Default 999L. Must be at least 1.

scale

Logical; if TRUE (default), standardise each variable in R.

iseed

Integer seed for RNG, or NULL.

p.value

Numeric significance cutoff. Default 0.05.

n.cores

Integer; number of OpenMP threads. Default 1L; set higher to use multiple cores. Ignored on platforms without OpenMP.

moments

Logical; if TRUE, append permutation-distribution moments E.Ci, Var.Ci, Skew.Ci, and Kurt.Ci. Default FALSE.

p.method

Details

Inference uses a one-tailed conditional permutation test (nsim reps); each replicate applies the same permuted neighbour configuration to every variable. The observed $C_i$ is compared with the permutation mean to choose the tail, and $p_i = (t + 1)/(\mathrm{nsim} + 1)$ , where $t$ counts permuted statistics in that tail. The standardised score is $Z.C_i = (C_i - E_{\mathrm{perm}})/\sqrt{\mathrm{Var}_{\mathrm{perm}}}$ ; Skew.Ci/Kurt.Ci (when moments = TRUE) follow the e1071 type-3 convention. Significant units are labelled Positive (similar) or Negative (dissimilar).

Rows with any missing value are labelled Undefined and observations with no neighbours are labelled Isolated; both receive NA for the p-value, Z-score and moments. The C backend re-seeds its random number generator per observation, so results are identical for any n.cores; n.cores is ignored when the package is built without OpenMP.

Value

cluster: A significance-filtered factor with levels Not significant, Positive, Negative, Undefined, and Isolated.
call: The matched call.

References

Anselin, L. (2019) A Local Indicator of Multivariate Spatial Association: Extending Geary's c. Geographical Analysis 51(2), 133–150. doi:10.1111/gean.12164

Examples


lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
df <- cbind(x, rev(x))
res <- local_multigeary(df, lw, nsim = 99L, n.cores = 1L)
head(res)

lw <- spdep::nb2listw(spdep::cell2nb(7, 7))
x  <- as.numeric(seq_len(49))
df <- cbind(x, rev(x))
res <- local_multigeary(df, lw, nsim = 99L, n.cores = 1L)
head(res)

Package 'fastLISA'

Help Index

Local Getis-Ord G

Description

Usage

Arguments

Details

Value

References

Examples

Univariate Local Geary's C

Description

Usage

Arguments

Details

Value

References

Examples

Local Getis-Ord G*

Description

Usage

Arguments

Details

Value

References

Examples

Univariate Local Moran's I

Description

Usage

Arguments

Details

Value

References

Examples

Bivariate Local Moran's I

Description

Usage

Arguments

Details

Value

Standardisation

P-values

Cluster codes

References

Examples

Local Moran's I with Empirical Bayes (EB) Rate

Description

Usage

Arguments

Details

Value

References

Examples

Multivariate Local Geary's C

Description

Usage

Arguments

Details

Value

References

Examples