lm.LMtests
Lagrange Multiplier diagnostics for spatial dependence in linear models
The function reports the estimates of tests chosen among five statistics for testing for spatial dependence in linear models. The statistics are the simple LM test for error dependence (LMerr), the simple LM test for a missing spatially lagged dependent variable (LMlag), variants of these robust to the presence of the other (RLMerr, RLMlag  RLMerr tests for error dependence in the possible presence of a missing lagged dependent variable, RLMlag the other way round), and a portmanteau test (SARMA, in fact LMerr + RLMlag). Note: from spdep 0.332, the value of the weights matrix trace term is returned correctly for both underlying symmetric and asymmetric neighbour lists, before 0.332, the value was wrong for listw objects based on asymmetric neighbour lists, such as knearest neighbours (thanks to Luc Anselin for finding the bug).
 Keywords
 spatial
Usage
lm.LMtests(model, listw, zero.policy=NULL, test="LMerr", spChk=NULL, naSubset=TRUE)
"print"(x, ...)
"summary"(object, p.adjust.method="none", ...)
"print"(x, digits=max(3, getOption("digits")  2), ...)
Arguments
 model
 an object of class
lm
returned bylm
, or optionally a vector of externally calculated residuals (run thoughna.omit
if any NAs present) for use when only "LMerr" is chosen; weights and offsets should not be used in thelm
object  listw
 a
listw
object created for example bynb2listw
, expected to be rowstandardised (Wstyle)  zero.policy
 default NULL, 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 LMerr, LMlag, RLMerr, RLMlag, 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
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 $e$ is a wellbehaved, uncorrelated error term. Tests for a missing spatially lagged dependent variable test that $rho = 0$, tests for spatial autocorrelation of the error $u$ test whether $lambda = 0$. $W$ is a spatial weights matrix; for the tests used here they are identical.
Value

A list of class
LMtestlist
of htest
objects, each with: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, 77104.
See Also
Examples
data(oldcol)
oldcrime.lm < lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
res < lm.LMtests(oldcrime.lm, nb2listw(COL.nb), test=c("LMerr", "LMlag",
"RLMerr", "RLMlag", "SARMA"))
summary(res)
lm.LMtests(oldcrime.lm, nb2listw(COL.nb))
lm.LMtests(residuals(oldcrime.lm), nb2listw(COL.nb))