localmoran.sad {spdep} | R Documentation |
The function implements Tiefelsdorf's application of the Saddlepoint
approximation to local Moran's Ii's reference distribution. If the model
object is of class "lm", global independence is assumed; if of class
"sarlm", global dependence is assumed to be represented by the spatial
parameter of that model. Tests are reported separately for each zone
selected, and may be summarised using summary.localmoransad
.
Values of local Moran's Ii agree with those from localmoran()
,
but in that function, the standard deviate - here the Saddlepoint
approximation - is based on the randomisation assumption.
localmoran.sad(model, select, nb, glist=NULL, style="W", zero.policy=FALSE, alternative="greater", spChk=NULL, resfun=weighted.residuals, save.Vi=FALSE, tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001) as.data.frame.localmoransad(x, row.names=NULL, optional=FALSE) print.localmoransad(x, ...) summary.localmoransad(object, ...) print.summary.localmoransad(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=FALSE)
model |
an object of class lm returned by lm (assuming no global spatial autocorrelation), or an object of class sarlm returned by a spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented by the model spatial coefficient); weights may be specified in the lm fit, but offsets should not be used |
select |
an integer vector of the id. numbers of zones to be tested |
nb |
a list of neighbours of class nb |
glist |
a list of general weights corresponding to neighbours |
style |
can take values W, B, C, and S |
zero.policy |
if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA |
alternative |
a character string specifying the alternative hypothesis, must be one of greater (default), less or two.sided. |
spChk |
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption() |
resfun |
default: weighted.residuals; the function to be used to extract residuals from the lm object, may be residuals , weighted.residuals , rstandard , or rstudent |
save.Vi |
if TRUE, return the star-shaped weights lists for each zone tested |
tol |
the desired accuracy (convergence tolerance) for uniroot |
maxiter |
the maximum number of iterations for uniroot |
tol.bounds |
offset from bounds for uniroot |
x |
object to be printed |
row.names |
ignored argument to as.data.frame.localmoransad ;
row names assigned from localmoransad object |
optional |
ignored argument to as.data.frame.localmoransad ;
row names assigned from localmoransad object |
object |
object to be summarised |
... |
arguments to be passed through |
listw |
a listw object created for example by nb2listw |
ireg |
a zone number |
n |
internal value depending on listw and style |
D |
internal value depending on listw and style |
a |
internal value depending on listw and style |
The function implements the analytical eigenvalue calculation together with trace shortcuts given or suggested in Tiefelsdorf (2002), partly following remarks by J. Keith Ord, and uses the Saddlepoint analytical solution from Tiefelsdorf's SPSS code.
If a histogram of the probability values of the saddlepoint estimate for the assumption of global independence is not approximately flat, the assumption is probably unjustified, and re-estimation with global dependence is recommended.
No n by n matrices are needed at any point for the test assuming no global dependence, the star-shaped weights matrices being handled as listw lists. When the test is made on residuals from a spatial regression, taking a global process into account. n by n matrices are necessary, and memory constraints may be reached for large lattices.
A list with class localmoransad
containing "select" lists, each with
class moransad
with the following components:
statistic |
the value of the saddlepoint approximation of the standard deviate of local Moran's Ii. |
p.value |
the p-value of the test. |
estimate |
the value of the observed local Moran's Ii. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string giving the method used. |
data.name |
a character string giving the name(s) of the data. |
internal1 |
Saddlepoint omega, r and u |
df |
degrees of freedom |
tau |
maximum and minimum analytical eigenvalues |
i |
zone tested |
Roger Bivand Roger.Bivand@nhh.no
Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206; see also Tiefelsdorf's SPSS code: http://geog-www.sbs.ohio-state.edu/faculty/tiefelsdorf/GeoStat.htm.
localmoran
, lm.morantest
,
lm.morantest.sad
, errorsarlm
data(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire.df) e.locmor <- summary(localmoran.sad(e.lm, eire.nb, select=1:nrow(eire.df))) e.locmor mean(e.locmor[,1]) lm.morantest(e.lm, nb2listw(eire.nb)) hist(e.locmor[,"Pr. (Sad)"]) e.wlm <- lm(OWNCONS ~ ROADACC, data=eire.df, weights=RETSALE) e.locmorw1 <- summary(localmoran.sad(e.wlm, eire.nb, select=1:nrow(eire.df), resfun=weighted.residuals)) e.locmorw1 e.locmorw2 <- summary(localmoran.sad(e.wlm, eire.nb, select=1:nrow(eire.df), resfun=rstudent)) e.locmorw2 e.errorsar <- errorsarlm(OWNCONS ~ ROADACC, data=eire.df, listw=nb2listw(eire.nb)) e.errorsar e.clocmor <- summary(localmoran.sad(e.errorsar, eire.nb, select=1:nrow(eire.df))) e.clocmor hist(e.clocmor[,"Pr. (Sad)"])