Spatial Regression (SAR / SEM / SDM / SAC) for Climate-Health Associations

Fits maximum-likelihood spatial regression models that account for spatial spillovers between geographic units (e.g. municipalities) in climate-health studies. Four model families are supported: the Spatial Autoregressive Model (SAR / spatial lag), the Spatial Error Model (SEM), the Spatial Durbin Model (SDM), and the Spatial Autocorrelation Model (SAC).

Usage

sus_mod_spatial_reg(
  df,
  formula,
  W,
  model = c("lag", "error", "durbin", "sac"),
  method = c("eigen", "LU", "Chebyshev", "MC"),
  zero_policy = TRUE,
  lang = "pt",
  verbose = TRUE
)

Arguments

df: A data.frame or climasus_df containing all variables in formula. If an sf object, geometry is dropped automatically.
formula: A formula specifying the outcome and predictors, e.g. deaths ~ mean_temp + precip + pib_pc.
W: A climasus_weights object produced by sus_mod_spatial_weights(). Must contain a listw element whose length matches nrow(df).
model: Character. Spatial model family. One of "lag" (SAR, default), "error" (SEM), "durbin" (SDM), or "sac" (SAC).
method: Character. Estimation method passed to the underlying spatialreg function. One of "eigen" (default), "LU", "Chebyshev", or "MC". "eigen" is exact; the others are approximations suitable for large datasets.
zero_policy: Logical. If TRUE (default), spatial units with no neighbours (islands) are allowed and receive a zero spatial lag/error. Passed to all spatialreg and spdep calls.
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_reg", "list") with the following named elements:

$model: Character. The model argument value.
$model_label: Character. Human-readable model name.
$coefficients: data.frame with columns term, estimate, std_error, z_value, p_value for all covariates (excluding the spatial parameters rho/lambda).
$rho: Numeric spatial lag parameter (NULL for the error model).
$lambda: Numeric spatial error parameter (NULL for the lag and durbin models).
$impacts: data.frame with columns term, direct, indirect, total (from spatialreg::impacts()), or NULL for the error model or when impact computation fails.
$aic: Numeric. AIC of the spatial model.
$lm_aic: Numeric. AIC of the OLS baseline (same formula, same data).
$moran_residuals: Named list with elements I (Moran statistic), p_value (analytical p-value), and z (z-score).
$fitted: Numeric vector of fitted values.
$residuals: Numeric vector of model residuals.
$call: The matched function call.

Model families

"lag" (SAR): The outcome in unit $i$ depends on a weighted average of outcomes in neighbouring units (spatial lag). Estimated via spatialreg::lagsarlm(). Contains a spatial lag parameter rho.
"error" (SEM): Spatial dependence enters through a spatially autocorrelated error term. Estimated via spatialreg::errorsarlm(). Contains a spatial error parameter lambda.
"durbin" (SDM): Extends the SAR model by including spatially lagged covariates (Durbin terms). Estimated via spatialreg::lagsarlm() with Durbin = TRUE. Contains both rho and lagged-covariate coefficients.
"sac" (SAC): Contains both a spatial lag of the outcome (rho) and a spatial error term (lambda). Estimated via spatialreg::sacsarlm().

Impacts

For models with a spatial lag (lag, durbin, sac), the total effect of a covariate is decomposed into direct (own-unit), indirect (spillover), and total effects using spatialreg::impacts() with R simulations for inference. For the error model impacts equal OLS slopes and no decomposition is meaningful; the $impacts element will be NULL.

Residual diagnostics

After fitting, spdep::moran.test() is applied to the model residuals to verify that spatial autocorrelation has been adequately absorbed. A non-significant Moran p-value indicates a well-specified spatial model.

References

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers.

LeSage, J., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press / Taylor & Francis.

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

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Panels. Springer.

Examples

if (FALSE) { # \dontrun{
library(climasus4r)

# W <- sus_mod_spatial_weights(shp, style = "W")
result <- sus_mod_spatial_reg(
  df      = my_df,
  formula = deaths ~ mean_temp + precip + pib_pc,
  W       = W,
  model   = "lag",
  lang    = "pt"
)
print(result)
summary(result)

# SDM with spillovers
result_sdm <- sus_mod_spatial_reg(
  df      = my_df,
  formula = deaths ~ mean_temp + precip,
  W       = W,
  model   = "durbin"
)
result_sdm$impacts
} # }