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Pre-Modeling Spatial Diagnostic and Autocorrelation Tests

Source: R/spatial_test.R
spatial_test.Rd

Evaluates whether spatial autocorrelation is present in direct domain estimates and regression residuals, conducts Lagrange Multiplier (LM) tests (Anselin, 1988), and performs comparative model fit tests between the standard Fay-Herriot (eblup_fh) and Spatial Fay-Herriot (eblup_sfh) models. Provides an explicit, automated recommendation on whether a spatial model is statistically necessary.

Usage

spatial_test(
  formula,
  vardir = NULL,
  data,
  W = NULL,
  alpha = 0.05,
  alternative = c("greater", "two.sided", "less")
)

Arguments

formula

Regression formula describing the model (e.g. y ~ x1 + x2).

vardir

Optional vector, column name, or formula referencing sampling variances of the direct estimator. Required for full model comparison (Standard FH vs Spatial FH).

data

A data.frame or sf polygon object containing the variables in formula.

W

Proximity or spatial adjacency matrix. If NULL and data is an sf polygon object, it is automatically constructed via create_weights.

alpha

Significance level for hypothesis tests (default is 0.05).

alternative

Alternative hypothesis for Moran's I ("greater", "two.sided", "less").

Value

An object of class c("fastsae_spatial_test", "list") containing:

response_test

Global Moran's I test results on direct response variable \(y\).

residual_test

Moran's I, Anselin LM-Error, and Anselin LM-Lag test results on regression residuals.

model_comparison

ML log-likelihoods, AIC, BIC, and the likelihood ratio test (LRT) of \(\rho = 0\) comparing standard vs spatial FH, both fitted by ML (if vardir provided).

spatial_recommended

Logical recommendation, from a single test at level alpha (see Details).

decision_test

The test behind spatial_recommended: "lrt" or "lm_error".

reason

Character string explaining the recommendation.

Details

Moran's \(I\) uses the randomisation variance of Cliff and Ord (1981); the LM-error and LM-lag statistics follow Anselin (1988). These tests assume homoscedastic OLS errors, whereas direct estimates have domain-specific sampling variances, so they are descriptive. The recommendation therefore rests on one test, so that its false positive rate is alpha: with vardir, the likelihood ratio test of \(\rho = 0\) between eblup_fh and eblup_sfh fitted by ML (which accounts for the sampling variances); without it, the LM-error test.

References

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

  2. Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models & Applications. Pion London.

  3. Petrucci, A., & Salvati, N. (2006). Small area estimation for spatial correlation in watershed erosion assessment. Journal of Agricultural, Biological, and Environmental Statistics, 11(2), 169-182.

  4. Pratesi, M., & Salvati, N. (2008). Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Statistical Methods & Applications, 17(1), 113-141.

Examples

library(fastsae)
data(mys)
data(mys_proxmat)

# Run spatial diagnostics on simulated survey data
st <- spatial_test(
  formula = y ~ x1 + x2,
  vardir = "vardir",
  data = mys,
  W = mys_proxmat
)
print(st)
#> 
#> ── Pre-Modeling Spatial Diagnostic Tests (fastsae) ─────────────────────────────
#> 
#> ── 1. Direct Response Variable (ESDA) ──
#> 
#> • Global Moran's I: -0.2773 (Expected: -0.0323, z-stat: -2.049)
#> • p-value: "0.9798" [ns]
#> ℹ Direct estimates show no significant spatial clustering.
#> 
#> ── 2. Regression Residuals (Controlling for Auxiliary Variables) ──
#> 
#> • Residual Moran's I: -0.2577 (z-stat: -1.875, p-value: "0.9696") [ns]
#> • Anselin LM-Error Test: 3.967 (df = 1, p-value: "0.0464") [*]
#> • Anselin LM-Lag Test: 2.055 (df = 1, p-value: "0.1517")
#> 
#> ── 3. Model Comparison (Standard FH vs Spatial FH) ──
#> 
#> • Standard FH: sigma2_u = 2.2353, ML LogLik = -65.22, AIC = 138.44
#> • Spatial FH (SAR): sigma2_u = 0.8462, rho = -1, ML LogLik = -63.12, AIC =
#>   136.23
#> • Likelihood Ratio: Chisq = 4.2 (df = 1, p-value = "0.04042") [*]
#> • Information Delta: Delta AIC = -2.2, Delta BIC = -0.73
#> 
#> ── 4. Final Recommendation ──
#> 
#> Decision test: likelihood ratio test (FH vs Spatial FH) at alpha = 0.05.
#> ✔ SPATIAL MODEL RECOMMENDED: Significant spatial spillover detected.
#> ✔ The likelihood ratio test of rho = 0 rejects the standard Fay-Herriot model
#>   in favour of the Spatial Fay-Herriot model.
#> ℹ Recommended functions: `eblup_sfh()` (Frequentist) or `hb_area(..., spatial =
#>   'bym2')` (Bayesian).