slxos

Orthogonal SLX score tests for spatial Durbin models (Herrera-Gómez, 2026).

The SLX score test decomposes exactly, in every sample, as

RS_theta = PS_theta + OS_theta

where PS_theta is the projection onto the common-factor direction — numerically the classical robust lag test RS*_rho of Anselin (1996) — and OS_theta is the orthogonal remainder that isolates covariate-specific spillovers (the part the classical battery cannot see). Everything is computed from one OLS fit and a row-standardized weight matrix W.

Install

# from a local source tarball
install.packages("slxos_0.1.0.tar.gz", repos = NULL, type = "source")

Base R only (Imports: stats). spdep/spData are optional (Suggests): if you pass a listw, spdep is used to coerce it.

Quick start

library(slxos)
data(columbus)                                   # Anselin (1988), 49 neighbourhoods

## guided sequence from a formula (chooses OF_theta vs the closed-form
## rescaled sandwich by regime, exactly as in the paper's guided sequence)
slx_test(CRIME ~ INC + HOVAL, data = columbus, W = columbus_W)

## the full battery and decomposition
X <- cbind(1, columbus$INC, columbus$HOVAL)
slx_scores(columbus$CRIME, X, columbus_W)

slx_test() prints the decomposition, the SARAR regime (rho, lambda) when the rescaled sandwich is used, the decisive test, and a one-line verdict.

Functions

• slx_test(formula, data, W, calibrate = "auto", ...) — the applied sequence.
• slx_scores(y, X, W) — classical battery + RS_theta = PS_theta + OS_theta, exact OF_theta, orientation cosine, identity/decomposition gaps.
• sarar_mle(y, X, W) — SARAR ML under H0: theta = 0.
• os_rescaled(y, X, W, lambda) — closed-form error-robust rescaled sandwich, a single SARAR fit and no resampling (feed it the SARAR lambda; NULL estimates it via sarar_mle).

Bundled datasets

Five ready-to-use cross-sections, each as a data.frame plus its row-standardized weight matrix <name>_W: columbus (Anselin 1988 crime), stlouis (homicide), baltimore (house prices), georgia (GWR data), and ertur (Ertur & Koch 2007 growth, with ertur_W the inverse-squared great-circle W1). The script system.file("examples/reproduce_appendix.R", package = "slxos") reproduces the appendix table across all five:

source(system.file("examples/reproduce_appendix.R", package = "slxos"))

ertur gives OS_theta ~ 0 (aligned, like the paper); stlouis and baltimore reject; columbus and georgia do not.

Weight matrices

Pass a dense matrix, a Matrix, or a spdep listw. The exact identity requires W row-standardized (W %*% 1 = 1); set row_standardize = TRUE to standardize, or pass an already-standardized W. Islands (zero row sums) are rejected.

Notes

• OS_theta is a chi^2_{k-2} score test; OF_theta is its exact-F counterpart under normality; both are undefined at k = 2.
• Under spatial-error contamination OS_theta over-rejects; use calibrate = "sandwich", which the "auto" rule also selects when RS*_lambda is significant. The rescaling must take lambda from the SARAR fit, not an SEM-only fit, which conflates the lag. No resampling is used anywhere in the package, matching the paper's closed-form correction.