chens_moran: Global and local Moran's I

In seanhardison1/dream: functions you shouldn't need to think about

Global and local Moran's I

Description

Estimate global and local Moran's I (also known as LISA) using the methods proposed in Chen 2013.

Usage

chens_moran(df, z, dist, weight_func = "nexp", sample = T)

Arguments

df	Data.frame with a unique observation (or sample) per row.
z	The character name of the column holding the sample vector.
weight_func	Spatial weight function forming the hypothetical spatial dependence structure of observations. Currently limited to inverse distance ("inv") and negative exponential ("nexp").
sample	If TRUE, estimates are calculated for the spatial sample. If FALSE, estimates are calculated for the spatial population. The choice of Moran's I for the spatial sample or population depends on the scope of the study.

Details

chens_moran estimates global and local Moran's I using the methods proposed in Chen 2013. Takes inspiration from the much more complete Irescale package (Fuentes et al. 2019).

Value

A list object containing the global estimate for Moran's I (global_estimate) and the input data.frame with new columns for the following:

f	The matrix-vector product of the Real Spatial Weights Matrix and standardized vector z. Represents the autocorrelation pattern of observations.
f_star	The matrix-vector product of the Ideal Spatial Weights Matrix and the standardized vector z. Represents the global autocorrelation estimate (i.e., the regression line of f ~ z).
f_residuals	The residuals of spatial autocorrelation (f - f_star). Useful for diagnosing fit of spatial weights function.
z	The standardized vector of observations.
lisa	The Local Indicators of Spatial Association (LISA), or local Moran's I. Equivalent to the diagonal of the Ideal Spatial Weights Matrix.

References

Anselin, Luc. "The Moran scatterplot as an ESDA tool to assess local instability in spatial." Spatial Analytical 4 (1996): 111.

Chen, Yanguang. "New approaches for calculating Moran’s index of spatial autocorrelation." PloS one 8.7 (2013).

Ivan Fuentes, Thomas DeWitt, Thomas Ioerger and Michael Bishop (2019). Irescale: Calculate and Rectify Moran's I. R package version 2.3.0. https://CRAN.R-project.org/package=Irescale

Examples

library(dplyr)
library(ggplot2)

# These data are rail distances between captial cities in China. Read them in and convert them
# to a matrix.
city_distances <- read.csv(system.file("extdata/city_distance_matrix.csv", package = "dream"))
dist_mat <- city_distances %>% dplyr::select(-X) %>% as.matrix()

# pop_sizes are population sizes of Chinese capital cities in the year 2000.
pop_sizes <- read.csv(system.file("extdata/city_population_sizes.csv", package = "dream"))

# Find global and local Moran's I for the sample using inverse distance weighting
output <- chens_moran(df = pop_sizes, z = "population", dist = dist_mat,
weight_func = "inv", sample = T)

# Visualize Moran's scatterplot following Chen 2013. The slope of the regression line is global
# Moran's I, and the relationship between f and z represents the autocorrelation pattern among cities.

ggplot(data = output$morans_scatter) +
 geom_point(aes(x = z, y = f)) +
 geom_line(aes(x = z, y = f_star))

seanhardison1/dream documentation built on Feb. 28, 2024, 12:36 p.m.