Global Moran's I and LISA Local Autocorrelation for Health Outcomes

Computes Moran's I global spatial autocorrelation statistic and Local Indicators of Spatial Association (LISA) for a numeric health outcome measured at municipality level. The global statistic tests whether the outcome is spatially clustered across the study region; the local statistics identify significant High-High (hotspots), Low-Low (coldspots), High-Low, and Low-High spatial outlier clusters.

Usage

sus_mod_spatial_moran(
  df,
  outcome,
  W,
  municipalities = NULL,
  permutations = 999L,
  alpha = 0.05,
  adjust_p = c("fdr", "bonferroni", "none"),
  lang = "pt",
  verbose = TRUE
)

Arguments

df: A data.frame or climasus_df containing at least the columns code_muni (7-digit IBGE municipality code) and the outcome column named by outcome. The row order must correspond to the spatial units encoded in W unless municipalities is supplied to subset and reorder.
outcome: Character. Name of the numeric outcome column in df (e.g. "deaths", "rate_100k", "hospitalization_rate").
W: A climasus_weights object produced by sus_mod_spatial_weights(). Must contain a listw element (a listw-class object from spdep) whose length matches nrow(df) after any filtering by municipalities.
municipalities: Optional character or integer vector of code_muni values to include. When supplied the function subsets and reorders df to match this vector before computation. Default NULL (use all rows).
permutations: Positive integer. Number of Monte Carlo permutations for both global and local inference. Default 999.
alpha: Numeric in (0, 1). Significance threshold applied to p-adjusted local Moran p-values when assigning quadrant labels. Default 0.05.
adjust_p: Character. Method passed to stats::p.adjust() for multiple-testing correction of local Moran p-values. One of "fdr" (default), "bonferroni", or "none".
lang: Character. Output language for messages: "pt" (default), "en", or "es".
verbose: Logical. If TRUE (default), print progress messages via cli.

Value

An object of class c("climasus_spatial_moran", "list") with the following named elements:

$global: One-row data.frame with columns I, E.I, Var.I, Z.I, p_value (analytical), and p_simulated (permutation-based).
$local: data.frame with one row per spatial unit and columns code_muni, Ii (local Moran statistic), Z.Ii (z-score), p_raw (unit-level permutation p), p_adj (adjusted p), and quadrant (factor: "HH", "LL", "HL", "LH", "NS").
$n_HH: Integer. Number of significant HH (hotspot) units.
$n_LL: Integer. Number of significant LL (coldspot) units.
$n_HL: Integer. Number of significant HL spatial outlier units.
$n_LH: Integer. Number of significant LH spatial outlier units.
$outcome_name: Character. The outcome argument value.
$call: The matched function call.

Global statistic

Moran's I is computed via permutation inference using spdep::moran.mc(). The observed statistic is compared against the empirical null distribution obtained by randomly permuting the outcome values across spatial units. The reported p_simulated is the proportion of permuted values as extreme as or more extreme than the observed I.

Local statistic (LISA)

Local Moran statistics are computed via spdep::localmoran_perm(), which uses conditional permutation to generate unit-specific null distributions. Each observation is assigned a LISA quadrant based on its standardised value and the standardised spatial lag:

HH: High value surrounded by high neighbours (hotspot).
LL: Low value surrounded by low neighbours (coldspot).
HL: High value surrounded by low neighbours (spatial outlier).
LH: Low value surrounded by high neighbours (spatial outlier).
NS: Not significant at the specified alpha level.

References

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1-2), 17-23.

Anselin, L. (1995). Local indicators of spatial association—LISA. Geographical Analysis, 27(2), 93-115.

Bivand, R. S., Pebesma, E., & Gomez-Rubio, V. (2013). Applied Spatial Data Analysis with R (2nd ed.). Springer.

Examples

if (FALSE) { # \dontrun{
# Requires spdep and a climasus_weights object W
library(climasus4r)

# W <- sus_mod_spatial_weights(shp, style = "W")
result <- sus_mod_spatial_moran(
  df           = my_df,
  outcome      = "deaths",
  W            = W,
  permutations = 999,
  alpha        = 0.05,
  adjust_p     = "fdr",
  lang         = "pt"
)
print(result)

# Access local clusters
result$local[result$local$quadrant == "HH", ]
} # }