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Exploratory local coefficient inference

Source: R/local_inference.R
gwr_local_inference.Rd

Computes local standard errors, test statistics, raw p-values, adjusted p-values, and significance flags from a fit created with `gwrs_control(diagnostics = "full")`. Sparse fits default to an unpenalized refit on each selected local active set; all reported p-values remain exploratory because selection and overlapping neighborhoods induce dependence.

Usage

gwr_local_inference(
  object,
  alpha = 0.05,
  df = c("edf", "residual", "normal"),
  adjust = c("BH", "none", "holm", "bonferroni", "BY", "fdr"),
  adjust_scope = c("coefficient", "global"),
  estimator = c("auto", "post_selection", "penalized"),
  ...
)

Arguments

object

A Gaussian least-squares `gwrs_fit` with full diagnostics, or a `gwrs_selection` whose selected GWR retains full diagnostics.

alpha

Significance level.

df

Reference degrees-of-freedom rule.

adjust

Multiplicity adjustment passed to [stats::p.adjust()].

adjust_scope

Adjust separately by coefficient or over all local tests.

estimator

Use the penalized active-set derivative, the local post-selection refit, or choose automatically.

...

Unused.

Value

A `gwrs_local_inference` object with local estimates, standard errors, statistics, raw `p_value`, adjusted `p_adjusted`, `significant`, coefficient summaries, settings, notes and a calculation status.

Details

The two-sided reference calculation concerns whether each local coefficient is zero. It is distinct from the F3 spatial-constancy diagnostic. By default, BH adjustment is applied separately to the locations of each design-matrix coefficient, including the intercept. Factor contrasts are separate coefficients. `adjust_scope = "global"` instead adjusts over all local coefficient tests in the fitted model. Neither scope includes tests from other candidate models.

The default `df = "edf"` uses effective residual degrees of freedom; `"residual"` uses n minus the smoother trace. If the requested degrees of freedom are unavailable or nonpositive, p-values are NA with a warning. There is no automatic normal fallback; `df = "normal"` requests it explicitly. Unavailable tests also have NA significance flags and NA summary values, rather than apparent nonsignificance or infinite minima.

All results are exploratory. BH does not establish calibration of the underlying reference p-values or account for response-based predictor, kernel, bandwidth or penalty selection, smoothing bias, or dependence between overlapping neighborhoods. Selection context is retained when available; no calibrated post-selection or FDR guarantee is claimed.

Examples

quake <- datasets::quakes[1:36, ]
coords <- as.matrix(quake[, c("long", "lat")])
x <- as.matrix(quake[, c("depth", "stations")])
fit <- gwr_lasso_fit(
  x, quake$mag, coords = coords, k = 24, lambda = 0.05,
  control = gwrs_control(n_threads = 1, diagnostics = "full")
)
inference <- gwr_local_inference(fit, adjust = "BH")
inference$summary
head(inference$local)