spdep (version 1.3-13)

lm.LMtests: Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models

Description

The 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.

Usage

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), ...)

Value

A list of class RStestlist of htest objects, each with:

statistic

the value of the Rao's score (a.k.a Lagrange multiplier) test.

parameter

number of degrees of freedom

p.value

the p-value of the test.

method

a character string giving the method used.

data.name

a character string giving the name(s) of the data.

Arguments

model

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

listw

a listw object created for example by nb2listw, expected to be row-standardised (W-style)

zero.policy

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

test

a character vector of tests requested chosen from RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test="all" computes all the tests.

spChk

should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()

naSubset

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)

x, object

object to be printed

p.adjust.method

a character string specifying the probability value adjustment (see p.adjust) for multiple tests, default "none"

digits

minimum number of significant digits to be used for most numbers

...

printing arguments to be passed through

Author

Roger Bivand and Andrew Bernat

Details

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.

If factors or ordered factors are among explanatory variables in the regression, the coding of the contrasts affects the outcomes of significance tests.

References

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 tools:::Rd_expr_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.

See Also

lm, SD.RStests

Examples

data(oldcol)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
lw <- nb2listw(COL.nb)
res <- lm.RStests(oldcrime.lm, listw=lw, test="all")
summary(res)
if (require("spatialreg", quietly=TRUE)) {
  oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)
  summary(lm.RStests(oldcrime.slx, listw=lw, test=c("adjRSerr", "adjRSlag")))
}
run <- require("codingMatrices", quietly=TRUE)
if (run) {
COL.OLD$fEW <- factor(COL.OLD$EW)
COL.OLD$fDISCBD <- ordered(cut(COL.OLD$DISCBD, c(0, 1.5, 3, 4.5, 6)))
f <- formula(CRIME ~ INC + HOVAL + fDISCBD*fEW)
lw <- nb2listw(COL.nb, style="W")
# default codings
summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="contr.poly", fEW="contr.treatment")),
 lw, test=c("adjRSerr", "adjRSlag")))
}
if (run) {
# use codingMatrices::code_diff for ordered factor
summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="code_diff", fEW="contr.treatment")),
 lw, test=c("adjRSerr", "adjRSlag")))
}
if (run) {
# use codingMatrices::code_control for both
summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="code_control", fEW="code_control")),
 lw, test=c("adjRSerr", "adjRSlag")))
}