Lagrange multiplier (Rao score) tests for spatial dependence after OLS
Source:R/SpatialLmTests.R
lmdiag.RdFrom the OLS fit of y on X (an intercept is prepended when X has no
constant column), with residuals u, sigma2 = u'u/n,
T = tr((W' + W) W), nJ = ((WXb)'M(WXb) + T sigma2) / sigma2,
d_err = u'Wu / sigma2 and d_lag = u'Wy / sigma2: lmerr is
RSerr = d_err^2 / T, lmlag is RSlag = d_lag^2 / nJ, lmrerr and
lmrlag the robust adjRSerr and adjRSlag of Anselin, Bera, Florax and
Yoon (1996), lmsarma and lmjoint the joint SARMA = adjRSlag + RSerr
(2 df), and lmdiag all five (as spdep::lm.RStests). lmrerr2 is the
one-sided standard normal form of the Bera-Yoon robust error score.
lmslx is the Koley-Bera score test for the lagged regressors WX
(k_x df) and lmsdm the joint spatial Durbin test of rho = 0 and
gamma = 0 (1 + k_x df), as spdep::SD.RStests. lmkp is the
Kelejian-Prucha (2001) Moran-type test for spatial error in the spatial
lag model estimated by spatial 2SLS, in the Anselin-Kelejian form of
miiv. sphet is the studentised Breusch-Pagan (Koenker) n R^2 of
the squared residuals on (1, Z), Z defaulting to W e^2.
Usage
lmdiag(y, X, W)
lmerr(y, X, W)
lmlag(y, X, W)
lmrerr(y, X, W)
lmrlag(y, X, W)
lmsarma(y, X, W)
lmjoint(y, X, W)
lmrerr2(y, X, W)
lmslx(y, X, W)
lmsdm(y, X, W)
lmkp(y, X, W)
sphet(residuals, W, Z = NULL)Value
A list with statistic, p_value, df and test-specific parts;
lmdiag returns all five statistics and p-values.
References
Anselin, L. (1988). Lagrange multiplier test diagnostics for spatial dependence and spatial heterogeneity. Geographical Analysis 20, 1-17. Anselin, L., Bera, A. K., Florax, R. and Yoon, M. J. (1996). Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics 26, 77-104. Bera, A. K. and Yoon, M. J. (1993). Specification testing with locally misspecified alternatives. Econometric Theory 9, 649-658. Koley, M. and Bera, A. K. (2024). To use, or not to use the spatial Durbin model? Spatial Economic Analysis 19, 30-56. Kelejian, H. H. and Prucha, I. R. (2001). On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219-257. Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics 17, 107-112.