lm.RStests.RdThe function reports the estimates of tests chosen among five statistics for
testing for spatial dependence in linear models. The statistics are
the simple RS test for error dependence (“RSerr”), the simple RS test
for a missing spatially lagged dependent variable (“RSlag”), variants
of these adjusted for the presence of the other (“adjRSerr”
tests for error dependence in the possible presence of a missing lagged
dependent variable, “adjRSlag” the other way round), and a portmanteau test
(“SARMA”, in fact “RSerr” + “adjRSlag”). Note: from spdep 1.3-2, the tests are re-named “RS” - Rao's score tests, rather than “LM” - Lagrange multiplier tests to match the naming of tests from the same family in SDM.RStests.
lm.RStests(model, listw, zero.policy=attr(listw, "zero.policy"), test="RSerr",
spChk=NULL, naSubset=TRUE)
lm.LMtests(model, listw, zero.policy=attr(listw, "zero.policy"), test="LMerr",
spChk=NULL, naSubset=TRUE)
# S3 method for RStestlist
print(x, ...)
# S3 method for RStestlist
summary(object, p.adjust.method="none", ...)
# S3 method for RStestlist.summary
print(x, digits=max(3, getOption("digits") - 2), ...)
<!-- %tracew(listw) -->an object of class lm returned by lm, or optionally a vector of externally calculated residuals (run though na.omit if any NAs present) for use when only "RSerr" is chosen; weights and offsets should not be used in the lm object
a listw object created for example by nb2listw,
expected to be row-standardised (W-style)
default attr(listw, "zero.policy") as set when listw was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without
neighbours, if FALSE assign NA
a character vector of tests requested chosen from RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test="all" computes all the tests.
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
default TRUE to subset listw object for omitted observations in model object (this is a change from earlier behaviour, when the model$na.action component was ignored, and the listw object had to be subsetted by hand)
object to be printed
a character string specifying the probability value adjustment (see p.adjust) for multiple tests, default "none"
minimum number of significant digits to be used for most numbers
printing arguments to be passed through
The two types of dependence are for spatial lag \(\rho\) and spatial error \(\lambda\):
$$ \mathbf{y} = \mathbf{X \beta} + \rho \mathbf{W_{(1)} y} + \mathbf{u}, $$ $$ \mathbf{u} = \lambda \mathbf{W_{(2)} u} + \mathbf{e} $$
where \(\mathbf{e}\) is a well-behaved, uncorrelated error term. Tests for a missing spatially lagged dependent variable test that \(\rho = 0\), tests for spatial autocorrelation of the error \(\mathbf{u}\) test whether \(\lambda = 0\). \(\mathbf{W}\) is a spatial weights matrix; for the tests used here they are identical.
A list of class RStestlist of htest objects, each with:
the value of the Rao's score (a.k.a Lagrange multiplier) test.
number of degrees of freedom
the p-value of the test.
a character string giving the method used.
a character string giving the name(s) of the data.
Anselin, L. 1988 Spatial econometrics: methods and models. (Dordrecht: Kluwer); 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 doi:10.1016/0166-0462(95)02111-6 ; Malabika Koley (2024) Specification Testing under General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.
data(oldcol)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
#>
#> Call:
#> lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.418 -6.388 -1.580 9.052 28.649
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 68.6190 4.7355 14.490 < 2e-16 ***
#> HOVAL -0.2739 0.1032 -2.654 0.0109 *
#> INC -1.5973 0.3341 -4.780 1.83e-05 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 11.43 on 46 degrees of freedom
#> Multiple R-squared: 0.5524, Adjusted R-squared: 0.5329
#> F-statistic: 28.39 on 2 and 46 DF, p-value: 9.341e-09
#>
lw <- nb2listw(COL.nb)
res <- lm.RStests(oldcrime.lm, listw=lw, test="all")
summary(res)
#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
#> dependence
#> data:
#> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
#> test weights: lw
#>
#> statistic parameter p.value
#> RSerr 5.723131 1 0.016743 *
#> RSlag 9.363684 1 0.002213 **
#> adjRSerr 0.079495 1 0.777983
#> adjRSlag 3.720048 1 0.053763 .
#> SARMA 9.443178 2 0.008901 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
if (require("spatialreg", quietly=TRUE)) {
oldcrime.slx <- lm(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)
summary(lm.RStests(oldcrime.slx, listw=lw, test=c("adjRSerr", "adjRSlag")))
}
#> Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
#> extra argument ‘listw’ will be disregarded
#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
#> dependence
#> data:
#> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, listw = lw)
#> test weights: lw
#>
#> statistic parameter p.value
#> adjRSerr 0.079495 1 0.77798
#> adjRSlag 3.720048 1 0.05376 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1