localmoran.sad: Saddlepoint approximation of local Moran's Ii tests
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
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.
Usage
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localmoran.sad(model, select, nb, glist=NULL, style="W",
zero.policy=NULL, alternative="greater", spChk=NULL,
resfun=weighted.residuals, save.Vi=FALSE,
tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,
save.M=FALSE, Omega = NULL)
## S3 method for class 'localmoransad'
print(x, ...)
## S3 method for class 'localmoransad'
summary(object, ...)
## S3 method for class 'summary.localmoransad'
print(x, ...)
listw2star(listw, ireg, style, n, D, a, zero.policy=NULL)
Arguments
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; if missing, all zones
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
default NULL, use global option value; 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
save.M
if TRUE, save a list of left and right M products in a list for the conditional tests, or a list of the regression model matrix components
Omega
A SAR process matrix may be passed in to test an alternative hypothesis, for example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() is taken internally
x
object to be printed
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
Details
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.
Value
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
Author(s)
Roger Bivand Roger.Bivand@nhh.no
References
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
localmoran, lm.morantest,
lm.morantest.sad, errorsarlm
Examples
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require(maptools)
eire <- readShapePoly(system.file("etc/shapes/eire.shp", package="spdep")[1],
ID="names", proj4string=CRS("+proj=utm +zone=30 +ellps=airy +units=km"))
eire.nb <- poly2nb(eire)
lw <- nb2listw(eire.nb)
#data(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb))
e.locmor
mean(e.locmor[,1])
sum(e.locmor[,1])/Szero(lw)
lm.morantest(e.lm, lw)
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
hist(e.locmor[,"Pr. (Sad)"])
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals))
e.locmorw1
e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent))
e.locmorw2
e.errorsar <- errorsarlm(OWNCONS ~ ROADACC, data=eire,
listw=lw)
e.errorsar
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
Omega <- tcrossprod(invIrW(lw, rho=e.errorsar$lambda))
e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega))
e.clocmor
hist(e.clocmor[,"Pr. (Sad)"])
Example output
Loading required package: sp
Loading required package: Matrix
Loading required package: maptools
Checking rgeos availability: TRUE
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
Warning message:
use rgdal::readOGR or sf::st_read
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.21699668 0.74177148 2.291129e-01 0.95074844
2 Cavan -0.37257361 -0.81297374 7.918834e-01 -1.00603119
3 Clare 0.23197510 0.49502499 3.102912e-01 0.67166518
4 Cork 0.78193548 1.75999915 3.920398e-02 1.74761575
5 Donegal -1.69064059 -1.98244914 9.762855e-01 -1.72031078
6 Dublin -0.16069692 -0.15041940 5.597831e-01 -0.35212627
7 Galway 1.31371473 3.34305297 4.143104e-04 2.66849536
8 Kerry 0.36534866 0.58147812 2.804591e-01 0.78073279
9 Kildare -0.02557544 0.15146558 4.398042e-01 0.04167665
10 Kilkenny 0.57684331 1.62868431 5.168993e-02 1.70897697
11 Laoghis -0.05951798 0.01724651 4.931200e-01 -0.12155465
12 Leitrim 0.38484587 1.27548777 1.010683e-01 1.47227033
13 Limerick 0.11817987 0.34038037 3.667850e-01 0.45727712
14 Longford 1.41643200 3.10732224 9.439524e-04 2.51113769
15 Louth 0.56242920 0.87665682 1.903365e-01 1.07441571
16 Mayo 0.87572704 2.02375701 2.149758e-02 2.05251226
17 Meath 0.00367856 0.16081712 4.361187e-01 0.12813539
18 Monaghan 0.55098311 1.06684464 1.430210e-01 1.23999193
19 Offaly 0.15155556 0.61933942 2.678464e-01 0.80786519
20 Roscommon 2.04368839 6.66107106 1.359196e-11 4.53187292
21 Sligo -0.47579871 -0.73430274 7.686179e-01 -0.94578114
22 Tipperary -0.03454106 0.04843351 4.806854e-01 -0.06919691
23 Waterford 0.85723423 1.98516133 2.356326e-02 1.91385108
24 Westmeath 0.45138572 1.20305006 1.144785e-01 1.36017204
25 Wexford 0.64371834 1.55468550 6.001049e-02 1.63188492
26 Wicklow 0.02441950 0.21823347 4.136236e-01 0.21197000
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 1.708660e-01 -0.06471134 0.14423085 -0.7895263 7.059116 -5.461326
2 Cavan 8.427997e-01 -0.04030838 0.16703857 -0.4622793 6.813004 -5.567356
3 Clare 2.508984e-01 -0.04219377 0.30674823 -0.3579185 6.761932 -7.406885
4 Cork 4.026529e-02 -0.04363826 0.22003250 -0.4363325 6.799081 -6.360927
5 Donegal 9.573120e-01 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382
6 Dublin 6.376282e-01 -0.08240217 0.27093033 -0.7352902 7.009201 -7.420687
7 Galway 3.809592e-03 -0.04389010 0.16491503 -0.5059997 6.838308 -5.573707
8 Kerry 2.174798e-01 -0.03212369 0.46724761 -0.2212594 6.714810 -8.915104
9 Kildare 4.833782e-01 -0.07623733 0.11187546 -1.0416026 7.339962 -4.999621
10 Kilkenny 4.372761e-02 -0.05911601 0.15247016 -0.7040737 6.982131 -5.538889
11 Laoghis 5.483741e-01 -0.06620117 0.15016408 -0.7915137 7.061015 -5.574277
12 Leitrim 7.047395e-02 -0.06828680 0.12621127 -0.8864130 7.157471 -5.186756
13 Limerick 3.237359e-01 -0.04172917 0.22070746 -0.4167943 6.789132 -6.348870
14 Longford 6.017137e-03 -0.04055162 0.21985521 -0.4059156 6.783792 -6.324457
15 Louth 1.413182e-01 -0.04386717 0.47831137 -0.2983105 6.738631 -9.149779
16 Mayo 2.005995e-02 -0.10340651 0.23408152 -0.9804377 7.264328 -7.165847
17 Meath 4.490209e-01 -0.04799533 0.10324707 -0.6949022 6.974408 -4.551176
18 Monaghan 1.074892e-01 -0.04136950 0.30828917 -0.3501006 6.758633 -7.415047
19 Offaly 2.095841e-01 -0.04662212 0.10238870 -0.6782821 6.960676 -4.519986
20 Roscommon 2.923151e-06 -0.04435301 0.09826301 -0.6591526 6.945294 -4.414164
21 Sligo 8.278699e-01 -0.11041170 0.24760301 -1.0156782 7.307311 -7.409091
22 Tipperary 5.275836e-01 -0.04872132 0.08571886 -0.7716947 7.042300 -4.198353
23 Waterford 2.781959e-02 -0.05435079 0.21086415 -0.5533724 6.868342 -6.353514
24 Westmeath 8.688774e-02 -0.04181671 0.16806722 -0.4779156 6.821788 -5.599610
25 Wexford 5.135187e-02 -0.05432673 0.20159596 -0.5654870 6.876461 -6.225016
26 Wicklow 4.160652e-01 -0.07022471 0.18808122 -0.7515626 7.023792 -6.198974
Maximum omega sad.r sad.u
1 Carlow 3.908254 0.071122863 0.71853146 0.84900467
2 Cavan 4.599954 -0.051532330 -0.69003582 -0.85816092
3 Clare 6.394234 0.031939551 0.46982957 0.51656357
4 Cork 5.313609 0.083281515 1.43928884 2.24323856
5 Donegal 8.371808 -0.039371561 -1.39288713 -2.19776923
6 Dublin 5.443035 -0.010354512 -0.14127218 -0.14554367
7 Galway 4.520344 0.134873939 2.39189491 4.63522665
8 Kerry 8.144135 0.028431952 0.54051534 0.61545648
9 Kildare 3.169925 0.018723213 0.14926096 0.14688325
10 Kilkenny 4.120105 0.105365819 1.40668493 2.15214600
11 Laoghis 3.985449 0.001724096 0.01660985 0.01657177
12 Leitrim 3.547872 0.109608339 1.18229964 1.66578026
13 Limerick 5.347370 0.027585567 0.32820959 0.34241163
14 Longford 5.351218 0.108368224 2.22687206 4.19385821
15 Louth 8.096967 0.037745731 0.78968254 0.98878788
16 Mayo 4.684091 0.105317102 1.75922892 2.94711915
17 Meath 3.399289 0.020074178 0.15693992 0.15623206
18 Monaghan 6.422179 0.053418031 0.94193428 1.24723730
19 Offaly 3.401055 0.071432961 0.59871278 0.67858124
20 Roscommon 3.349691 0.357114199 4.33885200 10.02517077
21 Sligo 4.759210 -0.036185300 -0.60775394 -0.74635955
22 Tipperary 3.029041 0.006482570 0.04683010 0.04657633
23 Waterford 5.049095 0.093409563 1.61022194 2.62552879
24 Westmeath 4.596009 0.080097979 1.05978192 1.45704611
25 Wexford 4.921174 0.085478829 1.32647942 1.98902088
26 Wicklow 4.513581 0.020437514 0.21417067 0.21406975
[1] 0.3366057
[1] 0.3366057
Global Moran I for regression residuals
data:
model: lm(formula = OWNCONS ~ ROADACC, data = eire)
weights: lw
Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.33660565 -0.05877741 0.01473183
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.160490657 0.41009538 3.408680e-01 0.57729730
2 Cavan -0.144663771 -0.27825575 6.095920e-01 -0.45305168
3 Clare 0.301676582 0.59021701 2.775226e-01 0.78987327
4 Cork 1.520488153 3.49016956 2.413571e-04 2.83665634
5 Donegal -0.435899664 -0.44665946 6.724395e-01 -0.67136090
6 Dublin -0.340222996 -0.60886675 7.286936e-01 -0.85658016
7 Galway 1.469009037 3.64546192 1.334560e-04 2.82274510
8 Kerry 0.268957279 0.49517211 3.102393e-01 0.66861012
9 Kildare 0.002996577 0.12659200 4.496317e-01 0.09978249
10 Kilkenny 0.497968801 1.20610829 1.138879e-01 1.34091379
11 Laoghis -0.026328708 -0.01713904 5.068372e-01 -0.06511750
12 Leitrim 0.277306386 0.80644537 2.099930e-01 1.01176491
13 Limerick 0.263122939 0.67591893 2.495461e-01 0.87759628
14 Longford 0.605211711 1.23874274 1.077204e-01 1.35375850
15 Louth 0.359469683 0.53572990 2.960726e-01 0.73280188
16 Mayo 1.742480472 3.68118786 1.160749e-04 3.01500163
17 Meath -0.112171618 -0.26680698 6.051911e-01 -0.45470531
18 Monaghan 0.241044892 0.46013751 3.227088e-01 0.64094159
19 Offaly 0.129191178 0.40988983 3.409434e-01 0.57205532
20 Roscommon 1.469671750 4.39927211 5.430728e-06 3.13215267
21 Sligo 0.095559559 0.31036587 3.781414e-01 0.38503064
22 Tipperary 0.088352646 0.39958273 3.447319e-01 0.52592105
23 Waterford 1.212658861 2.69846035 3.483052e-03 2.29292584
24 Westmeath 0.256165310 0.61222265 2.701952e-01 0.81620859
25 Wexford 0.619197906 1.31967483 9.347180e-02 1.42553832
26 Wicklow 0.006531073 0.13142161 4.477209e-01 0.10986725
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 0.2818693197 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
2 Cavan 0.6747442370 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
3 Clare 0.2148008928 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
4 Cork 0.0022794326 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
5 Donegal 0.7490046749 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin 0.8041615226 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
7 Galway 0.0023807205 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
8 Kerry 0.2518721070 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
9 Kildare 0.4602585046 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
10 Kilkenny 0.0899742229 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
11 Laoghis 0.5259597777 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
12 Leitrim 0.1558252365 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
13 Limerick 0.1900814236 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
14 Longford 0.0879067180 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
15 Louth 0.2318396371 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
16 Mayo 0.0012848894 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
17 Meath 0.6753393701 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
18 Monaghan 0.2607803159 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
19 Offaly 0.2836422486 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
20 Roscommon 0.0008676481 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
21 Sligo 0.3501073587 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
22 Tipperary 0.2994715317 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
23 Waterford 0.0109261375 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
24 Westmeath 0.2071904211 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
25 Wexford 0.0770008257 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
26 Wicklow 0.4562573299 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
Maximum omega sad.r sad.u
1 Carlow 5.223549 0.033637462 0.38794383 0.41751442
2 Cavan 5.245099 -0.022294725 -0.26091513 -0.27432856
3 Clare 6.631589 0.035302524 0.54866959 0.62630505
4 Cork 4.779848 0.134384022 2.56890121 5.11058941
5 Donegal 9.098033 -0.017507303 -0.40402088 -0.45010348
6 Dublin 3.161931 -0.040828131 -0.50710580 -0.60543071
7 Galway 4.630361 0.138454493 2.55314856 5.08170760
8 Kerry 7.504775 0.027195108 0.47167584 0.51758880
9 Kildare 3.862240 0.014230854 0.12280697 0.12246022
10 Kilkenny 5.112007 0.071351828 1.03314661 1.41988761
11 Laoghis 5.237883 -0.001502568 -0.01645549 -0.01646868
12 Leitrim 4.395343 0.066207108 0.74158109 0.90609823
13 Limerick 5.146640 0.050265468 0.63703133 0.74253221
14 Longford 6.075040 0.060534639 1.04112815 1.44165700
15 Louth 8.633971 0.025231866 0.49793592 0.55971045
16 Mayo 5.002594 0.135902733 2.75603129 5.62669411
17 Meath 3.741368 -0.028724497 -0.24912602 -0.26221742
18 Monaghan 6.891283 0.028042744 0.43280552 0.47360371
19 Offaly 4.287365 0.040883462 0.38909358 0.41780262
20 Roscommon 3.945151 0.180270100 2.87643937 6.00202551
21 Sligo 5.754236 0.023145822 0.30299868 0.31062426
22 Tipperary 3.454595 0.048932861 0.38768333 0.40902706
23 Waterford 5.297500 0.101874758 1.99944904 3.59542986
24 Westmeath 5.351214 0.044919886 0.56403221 0.65024353
25 Wexford 5.781330 0.066083430 1.11524637 1.57637406
26 Wicklow 4.537075 0.012609906 0.12748740 0.12720134
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.121997164 0.32185426 3.737816e-01 0.45871930
2 Cavan -0.110588620 -0.20105599 5.796726e-01 -0.34808741
3 Clare 0.308759283 0.60290381 2.732863e-01 0.80379674
4 Cork 1.404203115 3.23522979 6.077244e-04 2.69598105
5 Donegal -0.421182109 -0.42837428 6.658107e-01 -0.65187732
6 Dublin -0.443534307 -0.88433550 8.117424e-01 -1.05167518
7 Galway 1.376190254 3.42183495 3.110003e-04 2.70663064
8 Kerry 0.241623387 0.45357724 3.250666e-01 0.61515126
9 Kildare 0.008842913 0.14324202 4.430495e-01 0.12690939
10 Kilkenny 0.382893124 0.93980330 1.736592e-01 1.12810394
11 Laoghis -0.019904450 -0.00246494 5.009834e-01 -0.04176107
12 Leitrim 0.200483743 0.60688769 2.719627e-01 0.80241456
13 Limerick 0.238810092 0.62310059 2.666092e-01 0.81824678
14 Longford 0.466942853 0.96178354 1.680792e-01 1.14088225
15 Louth 0.271710988 0.41271732 3.399069e-01 0.58520655
16 Mayo 1.705850161 3.60778634 1.544103e-04 2.97346461
17 Meath -0.160603054 -0.41587901 6.612507e-01 -0.63254531
18 Monaghan 0.181378604 0.35629110 3.608113e-01 0.50697175
19 Offaly 0.107919508 0.35116431 3.627325e-01 0.49312417
20 Roscommon 1.249826037 3.75170355 8.781854e-05 2.81402777
21 Sligo 0.079431883 0.27999953 3.897389e-01 0.33741411
22 Tipperary 0.085153638 0.38940098 3.484898e-01 0.51126046
23 Waterford 1.022922345 2.28982205 1.101582e-02 2.06385578
24 Westmeath 0.201539331 0.48899468 3.124227e-01 0.67791734
25 Wexford 0.481114325 1.03805702 1.496218e-01 1.21094348
26 Wicklow -0.011694661 0.08710223 4.652951e-01 0.03786608
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 0.323217876 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
2 Cavan 0.636112729 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
3 Clare 0.210757187 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
4 Cork 0.003509083 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
5 Donegal 0.742759841 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin 0.853525699 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
7 Galway 0.003398492 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
8 Kerry 0.269227417 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
9 Kildare 0.449506058 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
10 Kilkenny 0.129638014 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
11 Laoghis 0.516655417 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
12 Leitrim 0.211156597 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
13 Limerick 0.206608144 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
14 Longford 0.126959464 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
15 Louth 0.279204420 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
16 Mayo 0.001472292 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
17 Meath 0.736484694 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
18 Monaghan 0.306087322 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
19 Offaly 0.310962427 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
20 Roscommon 0.002446250 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
21 Sligo 0.367902373 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
22 Tipperary 0.304584343 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
23 Waterford 0.019515696 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
24 Westmeath 0.248912051 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
25 Wexford 0.112958534 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
26 Wicklow 0.484897230 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
Maximum omega sad.r sad.u
1 Carlow 5.223549 0.0272472954 0.306852385 0.321490350
2 Cavan 5.245099 -0.0166242430 -0.190223798 -0.196022741
3 Clare 6.631589 0.0358559846 0.559584155 0.641527095
4 Cork 4.779848 0.1283688794 2.421993662 4.702934834
5 Donegal 9.098033 -0.0169574018 -0.388662370 -0.430528174
6 Dublin 3.161931 -0.0507848831 -0.696824139 -0.892299501
7 Galway 4.630361 0.1333224875 2.431707338 4.745166958
8 Kerry 7.504775 0.0252982005 0.433626352 0.469138111
9 Kildare 3.862240 0.0161278548 0.139072871 0.138837812
10 Kilkenny 5.112007 0.0622219791 0.835166590 1.066654825
11 Laoghis 5.237883 -0.0002164925 -0.002368023 -0.002368244
12 Leitrim 4.395343 0.0543844388 0.571625643 0.652237768
13 Limerick 5.146640 0.0473787285 0.590605630 0.675595582
14 Longford 6.075040 0.0528365356 0.840671447 1.082014178
15 Louth 8.633971 0.0204960239 0.389078238 0.419930705
16 Mayo 5.002594 0.1340509166 2.712635049 5.503894365
17 Meath 3.741368 -0.0415411327 -0.379736494 -0.417998694
18 Monaghan 6.891283 0.0226076552 0.338579266 0.358443998
19 Offaly 4.287365 0.0357600182 0.335019324 0.353243066
20 Roscommon 3.945151 0.1623235556 2.543240406 5.063795948
21 Sligo 5.754236 0.0209568244 0.273376649 0.278204612
22 Tipperary 3.454595 0.0478130890 0.377982061 0.397511387
23 Waterford 5.297500 0.0941811771 1.762051071 2.998984773
24 Westmeath 5.351214 0.0379323563 0.457473561 0.506014991
25 Wexford 5.781330 0.0582538352 0.911459483 1.197527949
26 Wicklow 4.537075 0.0083101099 0.084281843 0.083952776
Call:
errorsarlm(formula = OWNCONS ~ ROADACC, data = eire, listw = lw)
Type: error
Coefficients:
lambda (Intercept) ROADACC
0.783970972 2.892719243 0.002800913
Log likelihood: -64.12465
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint Pr. (Sad)
1 Carlow 0.17958463 -0.5947094 0.7239811 -0.01890330 0.50754088
2 Cavan -0.24752629 -0.9775196 0.8358440 -1.30903980 0.90473956
3 Clare -0.27901332 -0.9987481 0.8410416 -1.41535127 0.92151724
4 Cork 0.37808657 -0.5304596 0.7021033 0.06399752 0.47448610
5 Donegal -1.01894690 -1.4634181 0.9283235 -1.88871176 0.97053477
6 Dublin -0.18171297 -0.9790853 0.8362311 -1.11436909 0.86743956
7 Galway 1.02193392 0.9527104 0.1703684 1.44844018 0.07374699
8 Kerry -0.94967910 -1.1410951 0.8730848 -2.37909984 0.99132251
9 Kildare 0.07005053 -0.6531380 0.7431663 -0.10338268 0.54117037
10 Kilkenny 0.43022233 -0.3097714 0.6216326 0.46873476 0.31962962
11 Laoghis -0.12239132 -0.9818401 0.8369107 -0.97718180 0.83576042
12 Leitrim -0.24203967 -0.9591963 0.8312701 -1.53246522 0.93729616
13 Limerick -0.03214545 -0.7729433 0.7802220 -0.80301563 0.78901715
14 Longford 0.38307457 -0.4899146 0.6879028 0.16621961 0.43399206
15 Louth 0.21301553 -0.6509309 0.7424545 -0.21224286 0.58404122
16 Mayo 0.93971204 0.3895190 0.3484461 1.15011414 0.12504843
17 Meath 0.12484415 -0.6182203 0.7317849 -0.09720924 0.53871988
18 Monaghan -0.16109917 -0.8608004 0.8053260 -1.20575822 0.88604463
19 Offaly -0.00632492 -0.7740865 0.7805602 -0.33915071 0.63275190
20 Roscommon 1.02089434 0.6454803 0.2593080 1.21215484 0.11272656
21 Sligo -2.01629228 -1.8957526 0.9710036 -3.59571724 0.99983825
22 Tipperary -0.10810708 -0.9082666 0.8181313 -1.09721443 0.86372617
23 Waterford 0.44099281 -0.3488980 0.6364171 0.41219208 0.34009932
24 Westmeath -0.06329660 -0.8267635 0.7958144 -0.81444152 0.79230397
25 Wexford 0.30764885 -0.5219835 0.6991591 0.12395159 0.45067680
26 Wicklow -0.01696405 -0.7708237 0.7795943 -0.68244657 0.75252169
Expectation Variance Skewness Kurtosis Minimum Maximum
1 Carlow 0.8594106 1.3067301 2.362830 10.416149 3.842818e-15 20.625854
2 Cavan 1.1247111 1.9706413 2.347202 10.347468 1.645654e+00 25.347412
3 Clare 1.2679075 2.3989667 2.334022 10.287656 2.485514e+00 27.944266
4 Cork 1.2841619 2.9175885 2.362830 10.416149 -1.311825e-16 30.819886
5 Donegal 1.7253176 3.5165361 2.172101 9.492322 8.227735e+00 33.179887
6 Dublin 0.9462666 1.3272767 2.331563 10.276364 1.928660e+00 20.781739
7 Galway 0.4507425 0.3594525 2.362830 10.416149 1.141669e-15 10.817820
8 Kerry 2.6933181 10.1923430 2.307813 10.165571 7.170613e+00 57.469021
9 Kildare 0.5337375 0.5040109 2.362830 10.416149 1.614907e-15 12.809701
10 Kilkenny 0.7317135 0.9472544 2.362830 10.416149 1.319558e-16 17.561124
11 Laoghis 0.6035313 0.5466371 2.336004 10.296727 1.143655e+00 13.341096
12 Leitrim 1.2258673 2.3419742 2.347302 10.347916 1.788145e+00 27.632671
13 Limerick 1.5147253 4.0050949 2.362668 10.415466 2.341575e-01 36.119250
14 Longford 1.0996746 2.1395028 2.362830 10.416149 -2.230539e-17 26.392190
15 Louth 1.5875247 4.4588765 2.362830 10.416149 5.889558e-16 38.100592
16 Mayo 0.6190018 0.6779043 2.362830 10.416149 2.935421e-16 14.856044
17 Meath 0.7025947 0.8733619 2.362830 10.416149 2.285203e-16 16.862273
18 Monaghan 1.5519575 3.9603952 2.357838 10.394611 1.306155e+00 35.940826
19 Offaly 0.3048481 0.1615938 2.362560 10.415009 6.073802e-02 7.255616
20 Roscommon 0.5492905 0.5338124 2.362830 10.416149 2.151233e-15 13.182972
21 Sligo 2.3130309 5.2152684 1.886102 7.938452 1.739456e+01 38.118181
22 Tipperary 0.7147978 0.8208667 2.354040 10.377921 7.922253e-01 16.362923
23 Waterford 0.8228671 1.1979643 2.362830 10.416149 4.497917e-16 19.748810
24 Westmeath 0.8426747 1.2007878 2.360962 10.408167 4.379239e-01 19.786268
25 Wexford 1.0063847 1.7918951 2.362830 10.416149 3.741552e-15 24.153234
26 Wicklow 0.9927146 1.7157587 2.362598 10.415171 1.833509e-01 23.641799
omega sad.r sad.u
1 Carlow -0.017838445 -0.38297864 -0.33313444
2 Cavan -0.066132686 -1.21593174 -1.36168607
3 Clare -0.066612495 -1.30513950 -1.50704634
4 Cork -0.010368849 -0.33915224 -0.29581077
5 Donegal -0.045800560 -1.66568211 -2.41507712
6 Dublin -0.056683666 -1.03296352 -1.12358095
7 Galway 0.031762999 1.14153965 1.62047131
8 Kerry -0.079689478 -2.19374447 -3.29442684
9 Kildare -0.025051490 -0.36678690 -0.33300843
10 Kilkenny 0.003214930 0.09217313 0.09542852
11 Laoghis -0.065438984 -0.89335502 -0.96282448
12 Leitrim -0.092395569 -1.43474087 -1.65068998
13 Limerick -0.047140361 -0.97737318 -0.82423539
14 Longford -0.007176480 -0.22762622 -0.20810761
15 Louth -0.018552545 -0.58005971 -0.46861208
16 Mayo 0.019992306 0.84088286 1.09059603
17 Meath -0.026958325 -0.44558658 -0.38151849
18 Monaghan -0.062388993 -1.21509186 -1.20138907
19 Offaly -0.044380046 -0.41568117 -0.40266553
20 Roscommon 0.023338188 0.88169765 1.17993252
21 Sligo -0.131646725 -3.40243091 -6.56750182
22 Tipperary -0.089378126 -1.06748200 -1.10190604
23 Waterford 0.001151043 0.03534525 0.03581919
24 Westmeath -0.058470591 -0.88397322 -0.83127661
25 Wexford -0.009550494 -0.26689924 -0.24045992
26 Wicklow -0.050401551 -0.84395065 -0.73641406
spdep documentation built on Aug. 19, 2017, 3:01 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
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.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 | localmoran.sad(model, select, nb, glist=NULL, style="W",
zero.policy=NULL, alternative="greater", spChk=NULL,
resfun=weighted.residuals, save.Vi=FALSE,
tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,
save.M=FALSE, Omega = NULL)
## S3 method for class 'localmoransad'
print(x, ...)
## S3 method for class 'localmoransad'
summary(object, ...)
## S3 method for class 'summary.localmoransad'
print(x, ...)
listw2star(listw, ireg, style, n, D, a, zero.policy=NULL)
|
Arguments
model |
an object of class |
select |
an integer vector of the id. numbers of zones to be tested; if missing, all zones |
nb |
a list of neighbours of class |
glist |
a list of general weights corresponding to neighbours |
style |
can take values W, B, C, and S |
zero.policy |
default NULL, use global option value; 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 |
resfun |
default: weighted.residuals; the function to be used to extract residuals from the |
save.Vi |
if TRUE, return the star-shaped weights lists for each zone tested |
tol |
the desired accuracy (convergence tolerance) for |
maxiter |
the maximum number of iterations for |
tol.bounds |
offset from bounds for |
save.M |
if TRUE, save a list of left and right M products in a list for the conditional tests, or a list of the regression model matrix components |
Omega |
A SAR process matrix may be passed in to test an alternative hypothesis, for example |
x |
object to be printed |
object |
object to be summarised |
... |
arguments to be passed through |
listw |
a |
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 |
Details
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.
Value
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 |
Author(s)
Roger Bivand Roger.Bivand@nhh.no
References
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
localmoran, lm.morantest,
lm.morantest.sad, errorsarlm
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | require(maptools)
eire <- readShapePoly(system.file("etc/shapes/eire.shp", package="spdep")[1],
ID="names", proj4string=CRS("+proj=utm +zone=30 +ellps=airy +units=km"))
eire.nb <- poly2nb(eire)
lw <- nb2listw(eire.nb)
#data(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb))
e.locmor
mean(e.locmor[,1])
sum(e.locmor[,1])/Szero(lw)
lm.morantest(e.lm, lw)
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
hist(e.locmor[,"Pr. (Sad)"])
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals))
e.locmorw1
e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent))
e.locmorw2
e.errorsar <- errorsarlm(OWNCONS ~ ROADACC, data=eire,
listw=lw)
e.errorsar
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
Omega <- tcrossprod(invIrW(lw, rho=e.errorsar$lambda))
e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega))
e.clocmor
hist(e.clocmor[,"Pr. (Sad)"])
|
Example output
Loading required package: sp
Loading required package: Matrix
Loading required package: maptools
Checking rgeos availability: TRUE
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
Warning message:
use rgdal::readOGR or sf::st_read
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.21699668 0.74177148 2.291129e-01 0.95074844
2 Cavan -0.37257361 -0.81297374 7.918834e-01 -1.00603119
3 Clare 0.23197510 0.49502499 3.102912e-01 0.67166518
4 Cork 0.78193548 1.75999915 3.920398e-02 1.74761575
5 Donegal -1.69064059 -1.98244914 9.762855e-01 -1.72031078
6 Dublin -0.16069692 -0.15041940 5.597831e-01 -0.35212627
7 Galway 1.31371473 3.34305297 4.143104e-04 2.66849536
8 Kerry 0.36534866 0.58147812 2.804591e-01 0.78073279
9 Kildare -0.02557544 0.15146558 4.398042e-01 0.04167665
10 Kilkenny 0.57684331 1.62868431 5.168993e-02 1.70897697
11 Laoghis -0.05951798 0.01724651 4.931200e-01 -0.12155465
12 Leitrim 0.38484587 1.27548777 1.010683e-01 1.47227033
13 Limerick 0.11817987 0.34038037 3.667850e-01 0.45727712
14 Longford 1.41643200 3.10732224 9.439524e-04 2.51113769
15 Louth 0.56242920 0.87665682 1.903365e-01 1.07441571
16 Mayo 0.87572704 2.02375701 2.149758e-02 2.05251226
17 Meath 0.00367856 0.16081712 4.361187e-01 0.12813539
18 Monaghan 0.55098311 1.06684464 1.430210e-01 1.23999193
19 Offaly 0.15155556 0.61933942 2.678464e-01 0.80786519
20 Roscommon 2.04368839 6.66107106 1.359196e-11 4.53187292
21 Sligo -0.47579871 -0.73430274 7.686179e-01 -0.94578114
22 Tipperary -0.03454106 0.04843351 4.806854e-01 -0.06919691
23 Waterford 0.85723423 1.98516133 2.356326e-02 1.91385108
24 Westmeath 0.45138572 1.20305006 1.144785e-01 1.36017204
25 Wexford 0.64371834 1.55468550 6.001049e-02 1.63188492
26 Wicklow 0.02441950 0.21823347 4.136236e-01 0.21197000
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 1.708660e-01 -0.06471134 0.14423085 -0.7895263 7.059116 -5.461326
2 Cavan 8.427997e-01 -0.04030838 0.16703857 -0.4622793 6.813004 -5.567356
3 Clare 2.508984e-01 -0.04219377 0.30674823 -0.3579185 6.761932 -7.406885
4 Cork 4.026529e-02 -0.04363826 0.22003250 -0.4363325 6.799081 -6.360927
5 Donegal 9.573120e-01 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382
6 Dublin 6.376282e-01 -0.08240217 0.27093033 -0.7352902 7.009201 -7.420687
7 Galway 3.809592e-03 -0.04389010 0.16491503 -0.5059997 6.838308 -5.573707
8 Kerry 2.174798e-01 -0.03212369 0.46724761 -0.2212594 6.714810 -8.915104
9 Kildare 4.833782e-01 -0.07623733 0.11187546 -1.0416026 7.339962 -4.999621
10 Kilkenny 4.372761e-02 -0.05911601 0.15247016 -0.7040737 6.982131 -5.538889
11 Laoghis 5.483741e-01 -0.06620117 0.15016408 -0.7915137 7.061015 -5.574277
12 Leitrim 7.047395e-02 -0.06828680 0.12621127 -0.8864130 7.157471 -5.186756
13 Limerick 3.237359e-01 -0.04172917 0.22070746 -0.4167943 6.789132 -6.348870
14 Longford 6.017137e-03 -0.04055162 0.21985521 -0.4059156 6.783792 -6.324457
15 Louth 1.413182e-01 -0.04386717 0.47831137 -0.2983105 6.738631 -9.149779
16 Mayo 2.005995e-02 -0.10340651 0.23408152 -0.9804377 7.264328 -7.165847
17 Meath 4.490209e-01 -0.04799533 0.10324707 -0.6949022 6.974408 -4.551176
18 Monaghan 1.074892e-01 -0.04136950 0.30828917 -0.3501006 6.758633 -7.415047
19 Offaly 2.095841e-01 -0.04662212 0.10238870 -0.6782821 6.960676 -4.519986
20 Roscommon 2.923151e-06 -0.04435301 0.09826301 -0.6591526 6.945294 -4.414164
21 Sligo 8.278699e-01 -0.11041170 0.24760301 -1.0156782 7.307311 -7.409091
22 Tipperary 5.275836e-01 -0.04872132 0.08571886 -0.7716947 7.042300 -4.198353
23 Waterford 2.781959e-02 -0.05435079 0.21086415 -0.5533724 6.868342 -6.353514
24 Westmeath 8.688774e-02 -0.04181671 0.16806722 -0.4779156 6.821788 -5.599610
25 Wexford 5.135187e-02 -0.05432673 0.20159596 -0.5654870 6.876461 -6.225016
26 Wicklow 4.160652e-01 -0.07022471 0.18808122 -0.7515626 7.023792 -6.198974
Maximum omega sad.r sad.u
1 Carlow 3.908254 0.071122863 0.71853146 0.84900467
2 Cavan 4.599954 -0.051532330 -0.69003582 -0.85816092
3 Clare 6.394234 0.031939551 0.46982957 0.51656357
4 Cork 5.313609 0.083281515 1.43928884 2.24323856
5 Donegal 8.371808 -0.039371561 -1.39288713 -2.19776923
6 Dublin 5.443035 -0.010354512 -0.14127218 -0.14554367
7 Galway 4.520344 0.134873939 2.39189491 4.63522665
8 Kerry 8.144135 0.028431952 0.54051534 0.61545648
9 Kildare 3.169925 0.018723213 0.14926096 0.14688325
10 Kilkenny 4.120105 0.105365819 1.40668493 2.15214600
11 Laoghis 3.985449 0.001724096 0.01660985 0.01657177
12 Leitrim 3.547872 0.109608339 1.18229964 1.66578026
13 Limerick 5.347370 0.027585567 0.32820959 0.34241163
14 Longford 5.351218 0.108368224 2.22687206 4.19385821
15 Louth 8.096967 0.037745731 0.78968254 0.98878788
16 Mayo 4.684091 0.105317102 1.75922892 2.94711915
17 Meath 3.399289 0.020074178 0.15693992 0.15623206
18 Monaghan 6.422179 0.053418031 0.94193428 1.24723730
19 Offaly 3.401055 0.071432961 0.59871278 0.67858124
20 Roscommon 3.349691 0.357114199 4.33885200 10.02517077
21 Sligo 4.759210 -0.036185300 -0.60775394 -0.74635955
22 Tipperary 3.029041 0.006482570 0.04683010 0.04657633
23 Waterford 5.049095 0.093409563 1.61022194 2.62552879
24 Westmeath 4.596009 0.080097979 1.05978192 1.45704611
25 Wexford 4.921174 0.085478829 1.32647942 1.98902088
26 Wicklow 4.513581 0.020437514 0.21417067 0.21406975
[1] 0.3366057
[1] 0.3366057
Global Moran I for regression residuals
data:
model: lm(formula = OWNCONS ~ ROADACC, data = eire)
weights: lw
Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.33660565 -0.05877741 0.01473183
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.160490657 0.41009538 3.408680e-01 0.57729730
2 Cavan -0.144663771 -0.27825575 6.095920e-01 -0.45305168
3 Clare 0.301676582 0.59021701 2.775226e-01 0.78987327
4 Cork 1.520488153 3.49016956 2.413571e-04 2.83665634
5 Donegal -0.435899664 -0.44665946 6.724395e-01 -0.67136090
6 Dublin -0.340222996 -0.60886675 7.286936e-01 -0.85658016
7 Galway 1.469009037 3.64546192 1.334560e-04 2.82274510
8 Kerry 0.268957279 0.49517211 3.102393e-01 0.66861012
9 Kildare 0.002996577 0.12659200 4.496317e-01 0.09978249
10 Kilkenny 0.497968801 1.20610829 1.138879e-01 1.34091379
11 Laoghis -0.026328708 -0.01713904 5.068372e-01 -0.06511750
12 Leitrim 0.277306386 0.80644537 2.099930e-01 1.01176491
13 Limerick 0.263122939 0.67591893 2.495461e-01 0.87759628
14 Longford 0.605211711 1.23874274 1.077204e-01 1.35375850
15 Louth 0.359469683 0.53572990 2.960726e-01 0.73280188
16 Mayo 1.742480472 3.68118786 1.160749e-04 3.01500163
17 Meath -0.112171618 -0.26680698 6.051911e-01 -0.45470531
18 Monaghan 0.241044892 0.46013751 3.227088e-01 0.64094159
19 Offaly 0.129191178 0.40988983 3.409434e-01 0.57205532
20 Roscommon 1.469671750 4.39927211 5.430728e-06 3.13215267
21 Sligo 0.095559559 0.31036587 3.781414e-01 0.38503064
22 Tipperary 0.088352646 0.39958273 3.447319e-01 0.52592105
23 Waterford 1.212658861 2.69846035 3.483052e-03 2.29292584
24 Westmeath 0.256165310 0.61222265 2.701952e-01 0.81620859
25 Wexford 0.619197906 1.31967483 9.347180e-02 1.42553832
26 Wicklow 0.006531073 0.13142161 4.477209e-01 0.10986725
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 0.2818693197 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
2 Cavan 0.6747442370 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
3 Clare 0.2148008928 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
4 Cork 0.0022794326 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
5 Donegal 0.7490046749 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin 0.8041615226 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
7 Galway 0.0023807205 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
8 Kerry 0.2518721070 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
9 Kildare 0.4602585046 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
10 Kilkenny 0.0899742229 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
11 Laoghis 0.5259597777 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
12 Leitrim 0.1558252365 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
13 Limerick 0.1900814236 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
14 Longford 0.0879067180 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
15 Louth 0.2318396371 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
16 Mayo 0.0012848894 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
17 Meath 0.6753393701 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
18 Monaghan 0.2607803159 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
19 Offaly 0.2836422486 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
20 Roscommon 0.0008676481 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
21 Sligo 0.3501073587 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
22 Tipperary 0.2994715317 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
23 Waterford 0.0109261375 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
24 Westmeath 0.2071904211 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
25 Wexford 0.0770008257 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
26 Wicklow 0.4562573299 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
Maximum omega sad.r sad.u
1 Carlow 5.223549 0.033637462 0.38794383 0.41751442
2 Cavan 5.245099 -0.022294725 -0.26091513 -0.27432856
3 Clare 6.631589 0.035302524 0.54866959 0.62630505
4 Cork 4.779848 0.134384022 2.56890121 5.11058941
5 Donegal 9.098033 -0.017507303 -0.40402088 -0.45010348
6 Dublin 3.161931 -0.040828131 -0.50710580 -0.60543071
7 Galway 4.630361 0.138454493 2.55314856 5.08170760
8 Kerry 7.504775 0.027195108 0.47167584 0.51758880
9 Kildare 3.862240 0.014230854 0.12280697 0.12246022
10 Kilkenny 5.112007 0.071351828 1.03314661 1.41988761
11 Laoghis 5.237883 -0.001502568 -0.01645549 -0.01646868
12 Leitrim 4.395343 0.066207108 0.74158109 0.90609823
13 Limerick 5.146640 0.050265468 0.63703133 0.74253221
14 Longford 6.075040 0.060534639 1.04112815 1.44165700
15 Louth 8.633971 0.025231866 0.49793592 0.55971045
16 Mayo 5.002594 0.135902733 2.75603129 5.62669411
17 Meath 3.741368 -0.028724497 -0.24912602 -0.26221742
18 Monaghan 6.891283 0.028042744 0.43280552 0.47360371
19 Offaly 4.287365 0.040883462 0.38909358 0.41780262
20 Roscommon 3.945151 0.180270100 2.87643937 6.00202551
21 Sligo 5.754236 0.023145822 0.30299868 0.31062426
22 Tipperary 3.454595 0.048932861 0.38768333 0.40902706
23 Waterford 5.297500 0.101874758 1.99944904 3.59542986
24 Westmeath 5.351214 0.044919886 0.56403221 0.65024353
25 Wexford 5.781330 0.066083430 1.11524637 1.57637406
26 Wicklow 4.537075 0.012609906 0.12748740 0.12720134
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
1 Carlow 0.121997164 0.32185426 3.737816e-01 0.45871930
2 Cavan -0.110588620 -0.20105599 5.796726e-01 -0.34808741
3 Clare 0.308759283 0.60290381 2.732863e-01 0.80379674
4 Cork 1.404203115 3.23522979 6.077244e-04 2.69598105
5 Donegal -0.421182109 -0.42837428 6.658107e-01 -0.65187732
6 Dublin -0.443534307 -0.88433550 8.117424e-01 -1.05167518
7 Galway 1.376190254 3.42183495 3.110003e-04 2.70663064
8 Kerry 0.241623387 0.45357724 3.250666e-01 0.61515126
9 Kildare 0.008842913 0.14324202 4.430495e-01 0.12690939
10 Kilkenny 0.382893124 0.93980330 1.736592e-01 1.12810394
11 Laoghis -0.019904450 -0.00246494 5.009834e-01 -0.04176107
12 Leitrim 0.200483743 0.60688769 2.719627e-01 0.80241456
13 Limerick 0.238810092 0.62310059 2.666092e-01 0.81824678
14 Longford 0.466942853 0.96178354 1.680792e-01 1.14088225
15 Louth 0.271710988 0.41271732 3.399069e-01 0.58520655
16 Mayo 1.705850161 3.60778634 1.544103e-04 2.97346461
17 Meath -0.160603054 -0.41587901 6.612507e-01 -0.63254531
18 Monaghan 0.181378604 0.35629110 3.608113e-01 0.50697175
19 Offaly 0.107919508 0.35116431 3.627325e-01 0.49312417
20 Roscommon 1.249826037 3.75170355 8.781854e-05 2.81402777
21 Sligo 0.079431883 0.27999953 3.897389e-01 0.33741411
22 Tipperary 0.085153638 0.38940098 3.484898e-01 0.51126046
23 Waterford 1.022922345 2.28982205 1.101582e-02 2.06385578
24 Westmeath 0.201539331 0.48899468 3.124227e-01 0.67791734
25 Wexford 0.481114325 1.03805702 1.496218e-01 1.21094348
26 Wicklow -0.011694661 0.08710223 4.652951e-01 0.03786608
Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
1 Carlow 0.323217876 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
2 Cavan 0.636112729 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
3 Clare 0.210757187 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
4 Cork 0.003509083 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
5 Donegal 0.742759841 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin 0.853525699 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
7 Galway 0.003398492 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
8 Kerry 0.269227417 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
9 Kildare 0.449506058 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
10 Kilkenny 0.129638014 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
11 Laoghis 0.516655417 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
12 Leitrim 0.211156597 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
13 Limerick 0.206608144 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
14 Longford 0.126959464 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
15 Louth 0.279204420 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
16 Mayo 0.001472292 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
17 Meath 0.736484694 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
18 Monaghan 0.306087322 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
19 Offaly 0.310962427 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
20 Roscommon 0.002446250 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
21 Sligo 0.367902373 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
22 Tipperary 0.304584343 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
23 Waterford 0.019515696 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
24 Westmeath 0.248912051 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
25 Wexford 0.112958534 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
26 Wicklow 0.484897230 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
Maximum omega sad.r sad.u
1 Carlow 5.223549 0.0272472954 0.306852385 0.321490350
2 Cavan 5.245099 -0.0166242430 -0.190223798 -0.196022741
3 Clare 6.631589 0.0358559846 0.559584155 0.641527095
4 Cork 4.779848 0.1283688794 2.421993662 4.702934834
5 Donegal 9.098033 -0.0169574018 -0.388662370 -0.430528174
6 Dublin 3.161931 -0.0507848831 -0.696824139 -0.892299501
7 Galway 4.630361 0.1333224875 2.431707338 4.745166958
8 Kerry 7.504775 0.0252982005 0.433626352 0.469138111
9 Kildare 3.862240 0.0161278548 0.139072871 0.138837812
10 Kilkenny 5.112007 0.0622219791 0.835166590 1.066654825
11 Laoghis 5.237883 -0.0002164925 -0.002368023 -0.002368244
12 Leitrim 4.395343 0.0543844388 0.571625643 0.652237768
13 Limerick 5.146640 0.0473787285 0.590605630 0.675595582
14 Longford 6.075040 0.0528365356 0.840671447 1.082014178
15 Louth 8.633971 0.0204960239 0.389078238 0.419930705
16 Mayo 5.002594 0.1340509166 2.712635049 5.503894365
17 Meath 3.741368 -0.0415411327 -0.379736494 -0.417998694
18 Monaghan 6.891283 0.0226076552 0.338579266 0.358443998
19 Offaly 4.287365 0.0357600182 0.335019324 0.353243066
20 Roscommon 3.945151 0.1623235556 2.543240406 5.063795948
21 Sligo 5.754236 0.0209568244 0.273376649 0.278204612
22 Tipperary 3.454595 0.0478130890 0.377982061 0.397511387
23 Waterford 5.297500 0.0941811771 1.762051071 2.998984773
24 Westmeath 5.351214 0.0379323563 0.457473561 0.506014991
25 Wexford 5.781330 0.0582538352 0.911459483 1.197527949
26 Wicklow 4.537075 0.0083101099 0.084281843 0.083952776
Call:
errorsarlm(formula = OWNCONS ~ ROADACC, data = eire, listw = lw)
Type: error
Coefficients:
lambda (Intercept) ROADACC
0.783970972 2.892719243 0.002800913
Log likelihood: -64.12465
Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint Pr. (Sad)
1 Carlow 0.17958463 -0.5947094 0.7239811 -0.01890330 0.50754088
2 Cavan -0.24752629 -0.9775196 0.8358440 -1.30903980 0.90473956
3 Clare -0.27901332 -0.9987481 0.8410416 -1.41535127 0.92151724
4 Cork 0.37808657 -0.5304596 0.7021033 0.06399752 0.47448610
5 Donegal -1.01894690 -1.4634181 0.9283235 -1.88871176 0.97053477
6 Dublin -0.18171297 -0.9790853 0.8362311 -1.11436909 0.86743956
7 Galway 1.02193392 0.9527104 0.1703684 1.44844018 0.07374699
8 Kerry -0.94967910 -1.1410951 0.8730848 -2.37909984 0.99132251
9 Kildare 0.07005053 -0.6531380 0.7431663 -0.10338268 0.54117037
10 Kilkenny 0.43022233 -0.3097714 0.6216326 0.46873476 0.31962962
11 Laoghis -0.12239132 -0.9818401 0.8369107 -0.97718180 0.83576042
12 Leitrim -0.24203967 -0.9591963 0.8312701 -1.53246522 0.93729616
13 Limerick -0.03214545 -0.7729433 0.7802220 -0.80301563 0.78901715
14 Longford 0.38307457 -0.4899146 0.6879028 0.16621961 0.43399206
15 Louth 0.21301553 -0.6509309 0.7424545 -0.21224286 0.58404122
16 Mayo 0.93971204 0.3895190 0.3484461 1.15011414 0.12504843
17 Meath 0.12484415 -0.6182203 0.7317849 -0.09720924 0.53871988
18 Monaghan -0.16109917 -0.8608004 0.8053260 -1.20575822 0.88604463
19 Offaly -0.00632492 -0.7740865 0.7805602 -0.33915071 0.63275190
20 Roscommon 1.02089434 0.6454803 0.2593080 1.21215484 0.11272656
21 Sligo -2.01629228 -1.8957526 0.9710036 -3.59571724 0.99983825
22 Tipperary -0.10810708 -0.9082666 0.8181313 -1.09721443 0.86372617
23 Waterford 0.44099281 -0.3488980 0.6364171 0.41219208 0.34009932
24 Westmeath -0.06329660 -0.8267635 0.7958144 -0.81444152 0.79230397
25 Wexford 0.30764885 -0.5219835 0.6991591 0.12395159 0.45067680
26 Wicklow -0.01696405 -0.7708237 0.7795943 -0.68244657 0.75252169
Expectation Variance Skewness Kurtosis Minimum Maximum
1 Carlow 0.8594106 1.3067301 2.362830 10.416149 3.842818e-15 20.625854
2 Cavan 1.1247111 1.9706413 2.347202 10.347468 1.645654e+00 25.347412
3 Clare 1.2679075 2.3989667 2.334022 10.287656 2.485514e+00 27.944266
4 Cork 1.2841619 2.9175885 2.362830 10.416149 -1.311825e-16 30.819886
5 Donegal 1.7253176 3.5165361 2.172101 9.492322 8.227735e+00 33.179887
6 Dublin 0.9462666 1.3272767 2.331563 10.276364 1.928660e+00 20.781739
7 Galway 0.4507425 0.3594525 2.362830 10.416149 1.141669e-15 10.817820
8 Kerry 2.6933181 10.1923430 2.307813 10.165571 7.170613e+00 57.469021
9 Kildare 0.5337375 0.5040109 2.362830 10.416149 1.614907e-15 12.809701
10 Kilkenny 0.7317135 0.9472544 2.362830 10.416149 1.319558e-16 17.561124
11 Laoghis 0.6035313 0.5466371 2.336004 10.296727 1.143655e+00 13.341096
12 Leitrim 1.2258673 2.3419742 2.347302 10.347916 1.788145e+00 27.632671
13 Limerick 1.5147253 4.0050949 2.362668 10.415466 2.341575e-01 36.119250
14 Longford 1.0996746 2.1395028 2.362830 10.416149 -2.230539e-17 26.392190
15 Louth 1.5875247 4.4588765 2.362830 10.416149 5.889558e-16 38.100592
16 Mayo 0.6190018 0.6779043 2.362830 10.416149 2.935421e-16 14.856044
17 Meath 0.7025947 0.8733619 2.362830 10.416149 2.285203e-16 16.862273
18 Monaghan 1.5519575 3.9603952 2.357838 10.394611 1.306155e+00 35.940826
19 Offaly 0.3048481 0.1615938 2.362560 10.415009 6.073802e-02 7.255616
20 Roscommon 0.5492905 0.5338124 2.362830 10.416149 2.151233e-15 13.182972
21 Sligo 2.3130309 5.2152684 1.886102 7.938452 1.739456e+01 38.118181
22 Tipperary 0.7147978 0.8208667 2.354040 10.377921 7.922253e-01 16.362923
23 Waterford 0.8228671 1.1979643 2.362830 10.416149 4.497917e-16 19.748810
24 Westmeath 0.8426747 1.2007878 2.360962 10.408167 4.379239e-01 19.786268
25 Wexford 1.0063847 1.7918951 2.362830 10.416149 3.741552e-15 24.153234
26 Wicklow 0.9927146 1.7157587 2.362598 10.415171 1.833509e-01 23.641799
omega sad.r sad.u
1 Carlow -0.017838445 -0.38297864 -0.33313444
2 Cavan -0.066132686 -1.21593174 -1.36168607
3 Clare -0.066612495 -1.30513950 -1.50704634
4 Cork -0.010368849 -0.33915224 -0.29581077
5 Donegal -0.045800560 -1.66568211 -2.41507712
6 Dublin -0.056683666 -1.03296352 -1.12358095
7 Galway 0.031762999 1.14153965 1.62047131
8 Kerry -0.079689478 -2.19374447 -3.29442684
9 Kildare -0.025051490 -0.36678690 -0.33300843
10 Kilkenny 0.003214930 0.09217313 0.09542852
11 Laoghis -0.065438984 -0.89335502 -0.96282448
12 Leitrim -0.092395569 -1.43474087 -1.65068998
13 Limerick -0.047140361 -0.97737318 -0.82423539
14 Longford -0.007176480 -0.22762622 -0.20810761
15 Louth -0.018552545 -0.58005971 -0.46861208
16 Mayo 0.019992306 0.84088286 1.09059603
17 Meath -0.026958325 -0.44558658 -0.38151849
18 Monaghan -0.062388993 -1.21509186 -1.20138907
19 Offaly -0.044380046 -0.41568117 -0.40266553
20 Roscommon 0.023338188 0.88169765 1.17993252
21 Sligo -0.131646725 -3.40243091 -6.56750182
22 Tipperary -0.089378126 -1.06748200 -1.10190604
23 Waterford 0.001151043 0.03534525 0.03581919
24 Westmeath -0.058470591 -0.88397322 -0.83127661
25 Wexford -0.009550494 -0.26689924 -0.24045992
26 Wicklow -0.050401551 -0.84395065 -0.73641406
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